HP 12C PLANTINUM User Manual

HP 12C Platinum

Solutions Handbook

HP would like to thank the following for their contribution:

Tony Hutchins, Wellington, NZ

Luiz Vieira, UNIPAC, Brazil

Gene Wright, Lipscomb University, USA

NOTICE

Hewlett-Packard Company makes no express or implied warranty with regard to the keystroke procedures and program material offered or their merchantability or their fitness for any particular purpose. The keystroke procedures and program material are made available solely on an "as is" basis, and the entire risk as to their quality and performance is with the user. Should the keystroke procedures or program material prove defective, the user (and not Hewlett-Packard Company nor any other party) shall bear the entire cost of all necessary correction and all incidental and consequential damages. Hewlett-Packard Company shall not be liable for any incidental or consequential damages in connection with or arising out of the furnishing, use, or performance of the keystroke procedures or program material.

Introduction

About This Handbook

This HP 12C Platinum Solutions Handbook has been designed to supplement the HP 12C Platinum Owner's Handbook by providing a variety of applications in the financial area.

Programs and/or step-by-step keystroke procedures with corresponding examples in each specific topic are explained. We hope that this book will serve as a reference guide to many of your problems and will show you how to redesign our examples to fit your specific needs.

This book expands the original HP-12C Solutions handbook with additional solutions in algebraic mode. It contains the same RPN program keystrokes and RPN step-by-step procedure keystrokes, in columns headed “12c platinum / 12C RPN Keystrokes”. The alternative algebraic keystrokes are tablulated under “12c platinum ALG Keystrokes”. In program listings the “Display” columns show the keycodes as seen on the HP 12C Platinum.

Appendix A also contains algebraic listings for all the RPN programs given in Part III of the HP 12C Platinum Owner’s Handbook.

Presentation of Algebraic and RPN

The conventions used to differentiate between RPN and ALG mode are:

1.

Program Listings

Complete and separate listings are given for all programs. They appear side by side

in two columns with RPN on the left and Algebraic on the right.

2.

Step-by-Step Keystroke Procedures

As for programs separate columns are used, with the RPN keystrokes on the left

and the Algebraic keystrokes on the right.

3.

Program Instructions

Program instruction steps are generally the same for both modes. Any differences

are shown by clearly framing alternative steps and annotating the step or steps in the first frame as RPN, and those in the second as ALG.

4.

Text

Occasionally there are small differences which need to be indicated in the text

2

Introduction 3

itself and the ALG alternative is then indicated parenthetically.

5.

Usage of \(³) To activate the ³ key it is sufficient just to press \, with the HP 12C

Platinum in ALG mode. In step-by-step and program instructions where the only difference between the modes is that \ is used in RPN mode and ³ is used in ALG mode, \(³) has been used to indicate both alternatives.

Using the RPN Programs on the HP-12C

Apart from GTO instructions, the keystrokes given in this book are exactly the same for the HP 12C Platinum and the HP-12C. There are two notational differences to bear in mind when typing the RPN programs into the HP-12C:

1.

One keycode, for F, is different.

2. Line numbers tabulated as 000 to 099 refer to lines displayed as 00 to 99 on the HP-12C. The relevant two digit line numbers should be used when typing GTO instructions on the HP-12C.

Notes:

1. All display columns in the examples this book show 2 decimals. This is set by

pressing f2.

All programs that do rounding, amortization or depreciation will give slightly

different answers if other than 2 decimals are showing.

2. Three of the original programs have been updated: a. The last program in the Real Estate section (ATNCPR) now takes the capital

gains tax rate as a separate input, and an extra example has been added showing a different type of tax basis.

b. In the Personal Finance section the IRA program now handles explicit

inflation input and withdrawal tax rate input and the Stock Portfolio program handles stock prices with decimal fractions rather than fractions expressed in terms of eighths.

3. Market data (i.e.: interest rates; real estate values, growth rates and rents; taxes; expenses; etc.) used in the examples in this book do not necessarily represent typical current actual data, or reflect recent market trends.

Real Estate

Refinancing

It can be mutually advantageous to both borrower and lender to refinance an existing mortgage which has an interest rate substantially below the current market rate, with a loan at a below-market rate. The borrower has the immediate use of tax-free cash, while the lender has substantially increased debt service on a relatively small cash outlay.

To find the benefits to both borrower and lender:

1. Calculate the monthly payment on the existing mortgage.

2. Calculate the monthly payment on the new mortgage.

3. Calculate the net monthly payment received by the lender (and paid by the borrower) by adding the figure found in Step 1 to the figure found in Step 2.

4. Calculate the Net Present Value (NPV) to the lender of the net cash advanced.

5. Calculate the yield to the lender as an IRR.

6. Calculate the NPV to the borrower of the net cash received.

Example: An investment property has an existing mortgage which originated 8 years ago with an original term of 25 years, fully amortized in level monthly payments at 6.5% interest. The current balance is $133,190.

Although the going current market interest rate is 11.5%, the lender has agreed to refinance the property with a $200,000, 17 year, level-monthly-payment loan at 9.5% interest.

What are the NPV and effective yield to the lender on the net amount of cash actually advanced?

What is the NPV to the borrower on this amount if he can earn a 15.25% equity yield rate on the net proceeds of the loan?

12c platinum / 12C

RPN Keystrokes

gÂ fCLEARG

17gA

6.5gC

133190$ P?0

12c platinum

ALG Keystrokes

gÂ fCLEARG

17gA

6.5gC 133190$ P?0

Display Comments

-1,080.33

Monthly payment on existing mortgage received by lender.

7

8 Real Estate

12c platinum / 12C

RPN Keystrokes

9.5gC 200000Þ$

P

:0+P +:0P

:$ :$

133190+?0 +133190³?0

11.5gC$ 11.5gC$$

:0- -:0³

:0$¼ :0$¼

12§ §12³

15.25gC$ 15.25gC$$

:0- -:0³

12c platinum

ALG Keystrokes

9.5gC 200000Þ$ P

Display Comments

1,979.56

899.23

-66,810.00

-80,425.02

-13,615.02

14.83

-65,376.72

1,433.28

Monthly payment on new mortgage. Net monthly payment (to lender).

Net amount of cash advanced (by lender). Present value of net monthly payment. NPV to lender of net cash advanced.

% nominal yield (IRR). Present value of net monthly payment at

15.25%. NPV to borrower.

Wrap-Around Mortgage

A wrap-around mortgage is essentially the same as a refinancing mortgage, except that the new mortgage is granted by a different lender, who assumes the payments on the existing mortgage, which remains in full force. The new (second) mortgage is thus "wrapped around" the existing mortgage. The "wrap-around" lender advances the net difference between the new (second) mortgage and the existing mortgage in cash to the borrower, and receives as net cash flow, the difference between debt service on the new (second) mortgage and debt service on the existing mortgage.

When the terms of the original mortgage and the wrap-around are the same, the procedures in calculating NPV and IRR to the lender and NPV to the borrower are exactly the same as those presented in the preceding section on refinancing.

Example 1: A mortgage loan on an income property has a remaining balance of $200,132.06. When the load originated 8 years ago, it had a 20 year term with full amortization in level monthly payments at 6.75% interest.

A lender has agreed to "wrap" a $300,000 second mortgage at 10%, with full amortization in level monthly payments over 12 years. What is the effective yield (IRR) to the lender on the net cash advanced?

Real Estate 9

PV

PMT

B

PV

PMT

12c platinum / 12C

RPN Keystrokes

gÂ fCLEARG

20\ 8-gA

12c platinum

ALG Keystrokes

gÂ fCLEARG

208³gA

Display Comments

144.00

Total number of months remaining in original loan (into n).

6.75gC 6.75gC

200132.06$ 200132.06$

P?0 P?0

0.56 200,132.06

-2,031.55

Monthly interest rate (into i). Loan amount (into PV). Monthly payment on existing mortgage (calculated).

10gC 10gC

0.83

Monthly interest on wraparound.

300000Þ$ 300000Þ$

-300,000.00

Amount of wrap-around (into PV).

P P

3,585.23

Monthly payment on wraparound (calculated).

:0+P +:0P

1,553.69

Net monthly payment received (into PMT).

:$ :$

200132.06+$ +200132.06$

¼12§ ¼§12³

-99,867.94

15.85

Net cash advanced (into PV). Nominal yield (IRR) to lender (calculated).

Sometimes the wrap around mortgage will have a longer payback period than the original mortgage, or a balloon payment may exist.

1

AL

for n2 Years

(+)

2

(–)

... ...

for n1 Years

1

2

10 Real Estate

Where:

= number of years remaining in original mortgage

n

1

PMT

= yearly payment of original mortgage

1

= remaining balance of original mortgage

PV

1

n

= number of years in wrap-around mortgage

2

= yearly payment of wrap-around mortgage

PMT

2

PV

= total amount of wrap-around mortgage

2

BAL = balloon payment

Example 2: A customer has an existing mortgage with a balance of $125,010, a remaining term of 200 months, and a $1051.61 monthly payment. He wishes to obtain a $200,000, 9 ½% wrap-around with 240 monthly payments of $1681.71 and a balloon payment at the end of the 240th month of $129,963.35. If you, as a lender, accept the proposal, what is your rate of return?

$125010

$1681.71 $1681.71 $1681.71

240 mos.

$ 129963.35

... ...

$ -1051.61

200 mos.

$ -200000

12c platinum / 12C

RPN Keystrokes

gÂ gÂ fCLEARG fCLEARG

200000Þ\ 200000Þ 125010+gJ +125010gJ

1051.61Þ\ 1051.61Þ

1681.71+ +1681.71gK

$ -1051.61

12c platinum

ALG Keystrokes

Display Comments

-74,990.00

630.10

Net investment.

Net cash flow received by lender.

Real Estate 11

12c platinum / 12C

RPN Keystrokes

gK99ga ~gK ~ga ~gK 2ga

gFgK

39ga 39ga

~129963.35+ ~+129963.35 gK gK fL12§ fL§12³

If you, as a lender, know the yield on the entire transaction, and you wish to obtain the payment amount on the wrap-around mortgage to achieve this yield, use the following procedure. Once the monthly payment is known, the borrower's periodic interest rate may also be determined.

1.

Press the gÂ and press fCLEARG.

2.

Key in the remaining periods of the original mortgage and press n.

3.

Key in the desired annual yield and press gC.

4. Key in the monthly payment to be made by the lender on the original mortgage and

press ÞP.

5.

Press $.

6.

RPN: Key in the net amount of cash advanced and press +Þ$.

6.

ALG: Press +, key in the net amount of cash advanced and press ³Þ$.

7.

Key in the total term of the wrap-around mortgage and press n.

8.

If a balloon payment exists, key it in and press M.

9.

Press P to obtain the payment amount necessary to achieve the desired yield.

10.

Key in the amount of the wrap-around mortgage and press Þ$¼ to obtain the borrower's periodic interest rate.

Example 3: Your firm has determined that the yield on a wrap-around mortgage should be 12% annually. In the previous example, what monthly payment must be received to achieve this yield on a $200,000 wrap-around? What interest rate is the borrower paying?

12c platinum

ALG Keystrokes

99ga ~gK ~ga ~gK

2ga

1681.71gK

Display Comments

1,681.71

39.00

131,645.06

11.84

The above cash flow occurs 200 times. Next cash flow received by lender. Cash flow occurs 39 times.

Final cash flow. Rate of return to lender.

12 Real Estate

12c platinum / 12C

RPN Keystrokes

gÂ gÂ fCLEARG fCLEARG

200n12gC 200n12gC

1051.61ÞP 1051.61ÞP

$74990+ $+74990³ Þ$ Þ$

240n 240n

129963.35MP 129963.35MP

200000Þ$¼ 200000Þ$¼ 12§ §12³

12c platinum

ALG Keystrokes

Display Comments

-165,776.92

1,693.97

9.58

Number of periods and monthly interest rate. Monthly payment.

Present value of payments plus cash advanced.

Monthly payment received by lender.

Annual interest rate paid by borrower.

Income Property Cash Flow Analysis

Before-Tax Cash Flows

The before-tax cash flows applicable to real estate analysis and problems are:

• Potential Gross Income

• Effective Gross Income

• Net Operating Income (also called Net Income Before Recapture)

• Cash Throw-off to Equity (also called Gross Spendable Cash)

The derivation of these cash flows follows a set sequence:

1. Calculate Potential Gross Income by multiplying the rent per unit times the number of units, times the number of rental payment periods per year. This gives the rental income the property would generate if it were fully occupied.

2. Deduct Allowance for Vacancy and Rental Loss. This is usually expressed as a percentage. The result is Rent Collections (which is also Effective Gross Income if there is no "Other Income").

3. Add "Other Income" such as receipts from concessions (laundry equipment, etc.), produced from sources other than the rental office space. This is Effective Gross Income.

4. Deduct Operating Expenses. These are expenditures the landlord-investor must make, by contract or custom, to preserve the property and keep in capable of producing the gross income. The result is the Net Operating Income.

5. Deduct Annual Debt Service on the mortgage. This produces Cash Throw-Off to Equity.

Real Estate 13

Thus: Effective Gross Income =Potential Gross Income - Vacancy Loss + Other Income. Net Operating Income =Effective Gross Income - Operating Expenses. Cash Throw-Off =Net Operating Income - Annual Dept Service.

Example: A 60 unit apartment building has rentals of $250 per unit per month. With a 5% vacancy rate, the annual operating cost is $76,855.

The property has just been financed with a $700,000 mortgage, fully amortized in a level monthly payments at 11.5% over 20 years.

a. What is the Effective Gross Income?

b. What is the Net Operating Income?

12c platinum / 12C

RPN Keystrokes

gÂ fCLEARG

60\ 250§12§ 250§125b- 5b76855- 76855³ 20gA 20gAd

11.5gC 11.5gCd 700000$ 700000$

P12§ P§12+ + ~³

c. What is the Cash Throw-Off to Equity?

12c platinum

ALG Keystrokes

gÂ

Display Comments

fCLEARG 60§

180,000.00 171,000.00 94,145.00

-89,580.09 4,564.91

Potential Gross Income. Effective Gross Income. Net Operating Income.

Annual Debt Service. Cash Throw-Off.

Before-Tax Reversions (Resale Proceeds)

The reversion receivable at the end of the income projection period is usually based on forecast or anticipated resale of the property at that time. The before tax reversion amount applicable to real estate analysis and problems are:

• Sale Price.

• Cash Proceeds of Resale.

• Outstanding Mortgage Balance.

• Net Cash Proceeds of Resale to Equity.

The derivation of these reversions is as follows:

1. Forecast or estimate Sales Price. Deduct sales and Transaction Costs. The result is the Proceeds of Resale.

14 Real Estate

2. Calculate the Outstanding Balance of the Mortgage at the end of the Income Projection Period and subtract it from Proceeds of Resale. The result is Net Cash Proceeds of Resale.

Thus: Cash Proceeds of Resale = Sales Price - Transaction Costs. Net Cash Proceeds of Resale = Cash Proceeds of Resale - Outstanding Mortgage Balance.

Example: The apartment property in the preceding example is expected to be resold in 10 years. The anticipated resale price is $800,000. The transaction costs are expected to be 7% of the resale price. The mortgage is the same as that indicated in the preceding example.

• What will the Mortgage Balance be in 10 years?

• What are the Cash Proceeds of Resale and Net Cash Proceeds of Resale?

12c platinum / 12C

RPN Keystrokes

gÂ gÂ fCLEARG fCLEARG

20gA 20gA

11.5gC 11.5gC

700000$ 700000$ P P 10gA 10gA M MM 800000\ 8000007b- 7b+ + ~³

12c platinum

ALG Keystrokes

Display Comments

240.00

0.96

-7,465.01

120.00

-530,956.57

744,000.00 213,043.43

Mortgage term. Mortgage rate. Property value. Monthly payment. Projection period. Mortgage balance in 10 years. Estimated resale. Cash Proceeds of Resale. Net Cash Proceeds of Resale.

After-Tax Cash Flows

The After-Tax Cash Flow (ATCF) is found for the each year by deducting the Income Tax Liability for that year from the Cash Throw Off.

Where Taxable Income = Net Operating Income - interest - depreciation, Tax Liability = Taxable Income x Marginal Tax Rate, and After Tax Cash Flow = Cash Throw Off - Tax Liability.

The After-Tax Cash Flow for the initial and successive years may be calculated by the following HP 12C Platinum program. This program calculates the Net Operating Income using the Potential Gross Income, operational cost and vacancy rate. The Net Operating

Real Estate 15

income is readjusted each year from the growth rates in Potential Gross Income and operational costs.

The user is able to change the method of finding the depreciation from declining balance to straight line. To make the change, key in fV at line 032 (ALG: 026) of the program in place of f#.

12c platinum / 12C

RPN KEYSTROKES

fs fCLEARÎ

0

n ?1 :7 Æ

2

z ?7

1 ?+1 1 2

f! ?0 :5 n :¼ :6 ¼ d ?6 d :$ :4 $ d ?4 d gm g(036 :1 f# ?-0

0 g(017

DISPLAY

000, 001, 0 002, 11 003, 44 1 004, 45 7 005, 26 006, 2 007, 10 008, 44 7 009, 1 010,44 40 1 011, 1 012, 2 013, 42 11 014, 44 0 015, 45 5 016, 11 017, 45 12 018, 45 6 019, 12 020, 33 021, 44 6 022, 33 023, 45 13 024, 45 4 025, 13 026, 33 027, 44 4 028, 33 029, 43 35 030,43,33,036 031, 45 1 032, 42 25 033,44 30 0 034, 0 035,43,33,017

12c platinum

ALG KEYSTROKES

fs fCLEARÎ

0 n 1 2

f! ?0 :5 n :¼ :6 ¼ d ?6 d :$ :4 $ d ?4 d gm g(030

1

?+1 :1 f# ?-0

0

g(009 :2

- :.0 b

- :3

DISPLAY

000, 001, 0 002, 11 003, 1 004, 2 005, 42 11 006, 44 0 007, 45 5 008, 11 009, 45 12 010, 45 6 011, 12 012, 33 013, 44 6 014, 33 015, 45 13 016, 45 4 017, 13 018, 33 019, 44 4 020, 33 021, 43 35 022,43,33,030 023, 1 024,44 40 1 025, 45 1 026, 42 25 027,44 30 0 028, 0 029,43,33,009 030, 45 2 031, 30 032,45 48 0 033, 25 034, 30 035, 45 3

16 Real Estate

12c platinum / 12C

RPN KEYSTROKES

n :2 :8 b ?+2 d :.0 b

-

:3 :9 b ?+3 d

-

1

:7 ?§0

-

§

:P

1 2

§

+ :0

-

:1 gu ~ t g(009 fs

n: Used i: Annual % PV: Used PMT: Monthly FV: 0 R0: Used R1: Counter R2: PGI R3: Oper. cost R4: Dep. value R5: Dep. Life R6: Factor (DB) R7: Tax Rate R8: % gr. (PGI) R9: % gr. (op) R.0: Vacancy rt.

DISPLAY

036, 11 037, 45 2 038, 45 8 039, 25 040,44 40 2 041, 33 042,45 48 0 043, 25 044, 30 045, 45 3 046, 45 9 047, 25 048,44 40 3 049, 33 050, 30 051, 1 052, 45 7 053,44 20 0 054, 30 055, 20 056, 45 14 057, 1 058, 2 059, 20 060, 40 061, 45 0 062, 30 063, 45 1 064, 43 31 065, 34 066, 31

067,43,33,009

REGISTERS

12c platinum

ALG KEYSTROKES

³ ?+0 + :P gA ³ :7 b ?§0 d

- :0 ³ :1 gu ~ t :2 + :8 b ³ ?2 :3 + :9 b ³ ?3 g(001 fs

DISPLAY

036, 36 037,44 40 0 038, 40 039, 45 14 040, 43 11 041, 36 042, 45 7 043, 25 044,44 20 0 045, 33 046, 30 047, 45 0 048, 36 049, 45 1 050, 43 31 051, 34 052, 31 053, 45 2 054, 40 055, 45 8 056, 25 057, 36 058, 44 2 059, 45 3 060, 40 061, 45 9 062, 25 063, 36 064, 44 3 065,43,33,001

Real Estate 17

Program Instructions:

1.

Press gÂ and press fCLEARH.

2. Key in loan values:

● Key in annual interest rate and press gC

● Key in principal to be paid and press $

● Key in monthly payment and press ÞP

(If any of the values are not known, they should be solved for.)

3.

Key in Potential Gross Income (PGI) and press ?2.

4.

Key in Operational cost and press ?3.

5.

Key in depreciable value and press ?4.

6.

Key in depreciable life and press ?5.

7.

Key in factor (for declining balance only) and press ?6.

8.

Key in the Marginal Tax Rate (as a percentage) and press ?7.

9. Key in the growth rate in Potential Gross Income (0 for no growth) and press

?8.

10.

Key in the growth rate in operational cost (0 if no growth) and press ?9.

11.

Key in the vacancy rate (0 for no vacancy rate) and press ?.0.

12. RPN: Key in the desired depreciation function at line 032 in the program.

12. ALG: Key in the desired depreciation function at line 026 in the program.

13.

Press t to compute ATCF. The display will pause showing the year and then will stop with the ATCF for that year. The Y-register contains the year.

14.

Continue pressing t to compute successive After-Tax Cash Flows.

Example 1: A triplex was recently purchased for $100,000 with a 30 year loan at 12.25% and a 20% down payment. Not including a 5% annual vacancy rate, the potential gross income is $9,900 with an annual growth rate of 6%. Operating expenses are $3,291.75 with a 2.5% growth rate. The depreciable value is $75,000 with a projected useful life of $20 years. Assuming a 125% declining balance depreciation, what are the After-Tax Cash Flows for the first 10 years if the investors Marginal Tax Rate is 35%?

12c platinum / 12C

RPN Keystrokes

gÂ gÂ fCLEARH fCLEARH

100000\ 10000020b-$ 20b$

12.25gC 12.25gC 30gA 30gA P PP 9900?2 9900?2

12c platinum

ALG Keystrokes

Display Comments

80,000.00

1.02 360

-838.32 9,900.00

Mortgage amount. Monthly interest rate. Mortgage term. Monthly payment. Potential Gross Income.

18 Real Estate

ATCF

12c platinum / 12C

RPN Keystrokes

3291.75?3 3291.75?3

75000?4 75000?4 20?5 20?5 125?6 125?6 35?7 35?7 6?8 6?8

12c platinum

ALG Keystrokes

Display Comments

3,291.75 75,000.00

20.00

125.00

35.00

6.00

1st year operating cost. Depreciable value. Useful life. Declining balance factor. Marginal Tax Rate. Potential Gross Income growth rate.

2.5?9 2.5?9

5?.0 5?.0

t t

2.50

5.00

1.00

-1,020.88

2.00

-822.59

3.00

-598.85

4.00

-348.94

5.00

-72.16

6.00

232.35

7.00

565.48

8.00

928.23

9.00 1,321.62

10.00 1,746.81

Operating cost growth. Vacancy rate. Year 1

1

Year 2

2

Year 3

3

Year 4

4

Year 5

5

Year 6

6

Year 7

7

Year 8

8

Year 9

9

Year 10

10

Example 2: An office building was purchased for $1,400,000. The value of depreciable improvements is $1,200,000 with a 35 year economic life. Straight line depreciation will be used. The property is financed with a $1,050,000 loan. The terms of the loan are 9.5% interest and $9,173.81 monthly payments for 25 years. The office building generates a Potential Gross Income of $175,200 which grows at a 3.5% annual rate. The operating cost is $40,296.00 with a 1.6% annual growth rate. Assuming a Marginal Tax Rate of 50% and a vacancy rate of 7%, what are the After-Tax Cash Flows for the first 5 years?

Real Estate 19

12c platinum / 12C

RPN Keystrokes

gÂ fCLEARH

1050000$

9173.81ÞP

9.5gC 25gA 175200?2 175200?2

40296?3 40296?3

1200000?4 1200000?4 35?5 35?5 50?7 50?7

3.5?8 3.5?8

1.6?9 1.6?9

7?.0 7?.0

g(031 g(025 fsfV fsfV

fst fst

t t

12c platinum

ALG Keystrokes

gÂ fCLEARH

1050000$

9173.81ÞP

9.5gC 25gA

Display Comments

175,200.00

40,296.00

1,200,000.00

35.00

50.00

3.50

1.60

7.00

032, 42 23 026, 42 23

1.00 18,021.07

2.00 20,014.26

3.00 22,048.90

4.00 24,123.14

5.00 26,234.69

Potential Gross Income. 1st year operating cost. Depreciable value. Depreciable life. Marginal tax rate. Potential Gross Income growth rate. Operating cost growth rate. Vacancy rate. Go to dep. step.

RPN:Change to SL ALG:depreciation

Year 1 ATCF1 Year 2 ATCF2 Year 3 ATCF3 Year 4 ATCF4 Year 5 ATCF5

After-Tax Net Cash Proceeds of Resale

The After-Tax Net Cash Proceeds of Resale (ATNCPR) is the after-tax reversion to equity; generally, the estimated resale price of the property less commissions, outstanding debt and any tax claim.

The After-Tax Net Cash Proceeds can be found using the HP 12C Platinum program which follows.

20 Real Estate

This program uses declining balance depreciation to find the amount of depreciation from purchase to sale. This amount is used to determine the excess depreciation (which is equal to the amount of actual depreciation minus the amount of the straight line depreciation).

The Marginal Tax Rate (MTR) that the user inputs is applied to this excess depreciation.

The Capital Gains Tax Rate (CGTR) that the user inputs is applied to the capital gain from purchase to sale less the expenses of sale (i.e. the NCPR or Net cash Proceeds of Resale), plus the straight line depreciation.

The user may change to a different depreciation method by keying in the desired function at line 026 (ALG: 029) in place of f#.

In addition the user may nullify the straight line depreciation by keying in a 0 at line 035 (ALG: 039) in place of fV. This means that all of the actual depreciation from purchase to sale is then treated as "excess" or unrecaptured depreciation. This is illustrated below in Example 2.

12c platinum / 12C

RPN KEYSTROKES

fs fCLEARÎ gÂ ?2 gA d b

-

?0 ~

-

:7 b ?1 :P fB P M ?+0 fCLEARG :3 $ :4 n :5 ¼ :2 f# d

DISPLAY

000, 001, 43 8 002, 44 2 003, 43 11 004, 33 005, 25 006, 30 007, 44 0 008, 34 009, 30 010, 45 7 011, 25 012, 44 1 013, 45 14 014, 42 14 015, 14 016, 15 017,44 40 0 018, 42 34 019, 45 3 020, 13 021, 45 4 022, 11 023, 45 5 024, 12 025, 45 2 026, 42 25 027, 33

12c platinum

ALG KEYSTROKES

fs fCLEARÎ gÂ ?2 gA d ~

- ~ b

- ?0 ~

§ :7 ³ ?1 :P fB P M ?+0 fCLEARG :3 $ :4 n :5 ¼

DISPLAY

000, 001, 43 8 002, 44 2 003, 43 11 004, 33 005, 34 006, 30 007, 34 008, 25 009, 30 010, 44 0 011, 34 012, 20 013, 45 7 014, 36 015, 44 1 016, 45 14 017, 42 14 018, 14 019, 15 020,44 40 0 021, 42 34 022, 45 3 023, 13 024, 45 4 025, 11 026, 45 5 027, 12

Real Estate 21

12c platinum / 12C

RPN KEYSTROKES

:3 ~

- :6 b ?+1 :2 fV :2

§ :7 :6

- b ?+1 :0 :1

- g(000 fs

DISPLAY

028, 45 3 029, 34 030, 30 031, 45 6 032, 25 033,44 40 1 034, 45 2 035, 42 23 036, 45 2 037, 20 038, 45 7 039, 45 6 040, 30 041, 25 042,44 40 1 043, 45 0 044, 45 1 045, 30 046,43,33,000

12c platinum

ALG KEYSTROKES

:2 f# ~ :3

- ~

§ :6 ³ ?+1 :2 fV

§ :2 ³ :7

- :6

§ ~ + :1

§

1

b

- ?1 :0 ~ ³ g(000 fs

DISPLAY

028, 45 2 029, 42 25 030, 34 031, 45 3 032, 30 033, 34 034, 20 035, 45 6 036, 36 037,44 40 1 038, 45 2 039, 42 23 040, 20 041, 45 2 042, 36 043, 45 7 044, 30 045, 45 6 046, 20 047, 34 048, 40 049, 45 1 050, 20 051, 1 052, 25 053, 30 054, 44 1 055, 45 0 056, 34 057, 36 058,43,33,000

REGISTERS

n: Used i: Used PV: Used PMT: Used FV: Used R0: NCPR R

: Tax paid R2: Desired yr.

1

R3: Dep. value R4: Dep. life R5: Factor R6: MTR R7: CGTR R8-R.3: Unused

Program Instructions:

1.

Key in the program and press fCLEARH.

22 Real Estate

2. Key in the loan values:

(If any of the values are unknown, they should be solved for and if one has

to be solved for then the correct payment mode needs to be set)

3.

4.

5. Key in accelerated depreciation factor for the declining balance method and press

6.

7.

8.

9.

10.

11.

12.

Example 1: An apartment complex, purchased for $900,000 ten years ago, is sold for $1,750,000. The closing cost is 8% of the sale price, the income tax rate is 48% and the capital gains tax rate is 19.2%.

A $700,000 loan for 20 years at 9.5% annual interest was used to purchase the complex. When it was purchased the depreciable value was $750,000 with a useful life of 25 years. Using 125% declining balance depreciation, what are the After-Tax Net Cash Proceeds in year 10?

• Key in annual interest rate and press gC.

• Key in mortgage amount and press $.

• Key in monthly payment and press ÞP.

Key in depreciable value and press ?3. Key in depreciable life in years and press ?4.

?5. Key in your Marginal Tax Rate as a percentage and press ?6. Key in the Capital Gains Tax Rate as a percentage and press ?7. Key in the purchase price and press \(³). Key in the sale price and press \(³). Key in the % commission charged on the sale and press \(³).

RPN: If a dollar value is desired instead of a commission rate, key in gÂ, which does not affect the register values, at line 005 of the program.

ALG: If a dollar value is desired instead of a commission rate, key in gÂ, which does not affect the register values, at line 008 of the program.

Key in the number of years after purchase and press t. The ATNCPR is displayed.

To see the NCPR press :0 and to see the tax due press :1.

12c platinum / 12C

RPN Keystrokes

gÂ gÂ fCLEARH fCLEARH

700000$ 700000$

9.5gC 9.5gC

20gA 20gA

P PP 750000?3 750000?3

12c platinum

ALG Keystrokes

Display Comments

0.00 700,000.00

0.79

240.00

-6,524.92 750,000.00

Mortgage. Monthly interest. Number of payments. Monthly payment. Depreciable value.

Real Estate 23

A

12c platinum / 12C

RPN Keystrokes

25?4 25?4 125?5 125?5 48?6 48?6

19.2?7 19.2?7

12c platinum

ALG Keystrokes

Display Comments

25.00

125.00

48.00

19.20

Depreciable life. Factor. Marginal Tax Rate. Capital Gains Tax Rate.

900000\ 900000³ 1750000\ 1750000³ 8\ 8³ 10t 10t

:0 :0 :1 :1

900,000.00 1,750,000.00

8.00 911,372.04 1,105,746.74 194,374.70

Purchase price. Sale price. Commission rate.

TNCPR.

NCPR.

Tax due on resale.

Example 2: Now, re-do the previous example assuming all depreciation is treated as excess or unrecaptured depreciation, with MTR=25% and CGTR=15%.

First the fV in the program must be replaced with 0. This may be done as follows:

RPN: Press g(034 fs 0 fs. ALG: Press g(038 fs 0 fs.

The data stored in registers R

need not be re-entered.

3-R5

12c platinum / 12C

RPN Keystrokes

fCLEARG fCLEARG 700000$ 700000$

9.5gC 9.5gC 20gA 20gA

P PP 25?6 25?6 15?7 15?7

900000\ 900000³ 1750000\ 1750000³ 8\ 8³ 10t 10t

:0 :0 :1 :1

12c platinum

ALG Keystrokes

Display Comments

0.00 700,000.00

0.79

240.00

Mortgage. Monthly interest. Number of payments.

-6,524.92

25.00

15.00

Monthly payment. Marginal Tax Rate. Capital Gains Tax Rate.

900,000.00 1,750,000.00

8.00 924,009.92 1,105,746.74 181,736.83

Purchase price. Sale price. Commission rate.

TNCPR.

NCPR.

Tax due on resale.

Lending

Loan With a Constant Amount Paid Towards Principal

This type of loan is structured such that the principal is repaid in equal installments with the interest paid in addition. Therefore each periodic payment has a constant amount applied toward the principle and a varying amount of interest.

Loan Reduction Schedule

If the constant periodic payment to principal, annual interest rate, and loan amount are known, the total payment, interest portion of each payment, and remaining balance after each successive payment may be calculated as follows:

RPN Mode:

1.

Key in the constant periodic payment to principal and press ?0.

2.

Key in periodic interest rate and press \\\.

3. Key in the loan amount. If you wish to skip to another time period, press \. Then key in the number of payments to be skipped, and press :0§-.

4.

Press ~b to obtain the interest portion of the payment.

5.

Press :0+ to obtain the total payment.

6.

Press O:0- to obtain the remaining balance of the loan.

7. Return to step 4 for each successive payment.

ALG Mode:

1.

Key in the constant periodic payment to principal and press ?0.

2.

Key in the loan amount and press ?1.

3.

Key in periodic interest rate and press ?2.

If you wish to skip to another time period, key in the number of payments to be

skipped, and press §:0³?-1.

4.

Press :1§:2b+ to obtain the interest portion of the payment.

5.

Press :0?-1³ to obtain the total payment.

6.

Press :1 to obtain the remaining balance of the loan.

7. Return to step 4 for each successive payment.

24

Lending 25

Example 1: A $60,000 land loan at 10% interest calls for equal semi-annual principal payments over a 6-year maturity. What is the loan reduction schedule for the first year? (Constant payment to principal is $5000 semi-annually). What is the fourth year's schedule (skip 4 payments)?

12c platinum / 12C

RPN Keystrokes

5000?0 5000?0 10\2z\ 60000?1 \\ 60000~b :1§:2b+

:0+ :0?-1³ O:0- :1 ~b :0+ :0?-1³ O:0- :1

4:0§- 4§:0³?-1 ~b :0+ :0?-1³ O:0- :1 ~b :0+ :0?-1³ O:0- :1

12c platinum

ALG Keystrokes

10z2³?2

§:2b+

:1§:2b+

§:2b+

Display Comments

5.00 3,000.00 8,000.00 55,000.00 2,750.00 7,750.00 50,000.00

1,500.00 6,500.00 25,000.00 1,250.00 6,250.00 20,000.00

Semi-annual interest rate. First payment's interest. Total first payment. Remaining balance. Second payment's interest. Total second payment. Remaining balance after the first year.

Seventh payment's interest. Total seventh payment. Remaining balance. Eighth payment's interest. Total eighth payment. Remaining balance after fourth year.

Add-On Interest Rate Converted to APR

An add-on interest rate determines what portion of the principal will be added on for repayment of a loan. This sum is then divided by the number of months in a loan to determine the monthly payment. For example, a 10% add-on rate for 36 months on $3000 means add one-tenth of $3000 for 3 years (300 x 3) - usually called the "finance charge" for a total of $3900. The monthly payment is $3900/36.

This keystroke procedure converts an add-on interest rate to a annual percentage rate when the add-on rate and number of months are known.

26 Lending

RPN Mode:

1.

Press gÂ and press fCLEARG .

2.

Key in the number of months in the loan and press n\:gA .

3.

Key in the add-on rate and press §.

4.

Key in the amount of the loan and press $

5.

Press ~zÞP.

6.

Press ¼12§ to obtain the APR.

ALG Mode:

1.

Press gÂ and press fCLEARG .

2.

Key in the number of months in the loan and press n³:gA§ .

3.

Key in the add-on rate and press ³ .

4.

Key in the amount of the loan and press $

5.

Press ~³ÞP .

6.

Press ¼§12³ to obtain the APR.

Example 1: Calculate the APR and monthly payment of a 12% $1000 add-on loan which has a life of 18 months.

*

~b+.

*

+~bz .

12c platinum / 12C

RPN Keystrokes

gÂ gÂ fCLEARG fCLEARG 18n\ 18n³ :gA12§ :gA§12³ 1000$~b+ 1000$+~bz ~zÞP ~³ÞP ¼12§ ¼§12³

12c platinum

ALG Keystrokes

Display Comments

1,180.00

-65.56

21.64

Amount of loan. Monthly payment. Annual Percentage Rate.

APR Converted to Add-On Interest Rate

Given the number of months and annual percentage rate, this procedure calculates the corresponding add-on interest rate.

1.

Press gÂ and press fCLEARG .

*

Positive for cash received; negative for cash paid out.

Lending 27

2. Enter the following information:

a. Key in number of months of loan and press n . b. Key in APR and press gC . c. Key in 100 and press $P .

3.

RPN: Press :$:nz+Þ12§ to obtain the add-on rate.

3.

ALG: Press :$z:n+~§12³Þ to obtain the add-on rate.

Example 1: What is the equivalent add-on rate for an 18 month loan with an APR of

14%?

12c platinum / 12C

RPN Keystrokes

gÂ gÂ fCLEARG fCLEARG

18n14gC 18n14gC 100$P:$ 100$P:$ :nz+Þ z:n+~ 12§ §12³Þ

12c platinum

ALG Keystrokes

Display Comments

7.63

Add-On Interest Rate.

Add-On Rate Loan with Credit Life

This HP 12C Platinum program calculates the monthly payment amount, credit life amount (an optional insurance which cancels any remaining indebtedness at the death of the borrower), total finance charge, and annual percentage rate (APR) for an add-on interest rate (AIR) loan. The monthly payment is rounded (in normal manner) to the nearest cent. If other rounding techniques are used, slightly different results may occur.

12c platinum / 12C

RPN KEYSTROKES

fs fCLEARÎ gÂ

1 :0 1 2 0 0

z ?4 :2

DISPLAY

000, 001, 43 8 002, 1 003, 45 0 004, 1 005, 2 006, 0 007, 0 008, 10 009, 44 4 010, 45 2

12c platinum

ALG KEYSTROKES

fs fCLEARÎ gÂ :0 n :gA b ?4

§ :2 ³ :4

DISPLAY

000, 001, 43 8 002, 45 0 003, 11 004,45,43 11 005, 25 006, 44 4 007, 20 008, 45 2 009, 36 010, 45 4

28 Lending

12c platinum / 12C

RPN KEYSTROKES

§

-

gF :1

§

:4

§

-

:4 :1

§

1

+ ~ z :3

§

:0 z fB Þ P t :P :0

§

Þ $ :$ :2 b :0

§

1 2

z ?5 Æ

2

§

gT gm g(061 :5

DISPLAY

011, 20 012, 30 013, 43 40 014, 45 1 015, 20 016, 45 4 017, 20 018, 30 019, 45 4 020, 45 1 021, 20 022, 1 023, 40 024, 34 025, 10 026, 45 3 027, 20 028, 45 0 029, 10 030, 42 14 031, 16 032, 14 033, 31 034, 45 14 035, 45 0 036, 20 037, 16 038, 13 039, 45 13 040, 45 2 041, 25 042, 45 0 043, 20 044, 1 045, 2 046, 10 047, 44 5 048, 26 049, 2 050, 20 051, 43 24 052, 43 35 053,43,33,061 054, 45 5

12c platinum

ALG KEYSTROKES

§ :1 +

1

³ y

- ~

§ :0 z :3 ³ y fB Þ P t Þ

§ :0

§ :2

§ :4 ³ ?5

§ Æ

2

³ gT gm g(052

1

b + :5 ³ fB ?5 :5 t +

DISPLAY

011, 20 012, 45 1 013, 40 014, 1 015, 36 016, 22 017, 30 018, 34 019, 20 020, 45 0 021, 10 022, 45 3 023, 36 024, 22 025, 42 14 026, 16 027, 14 028, 31 029, 16 030, 20 031, 45 0 032, 20 033, 45 2 034, 20 035, 45 4 036, 36 037, 44 5 038, 20 039, 26 040, 2 041, 36 042, 43 24 043, 43 35 044,43,33,052 045, 1 046, 25 047, 40 048, 45 5 049, 36 050, 42 14 051, 44 5 052, 45 5 053, 31 054, 40

Lending 29

12c platinum / 12C

RPN KEYSTROKES

. 0 1

+ fB ?5 :5 t :$ ~

:3

Þ t :5 :3 + $ :0 n ¼ :gC g(000 fs

DISPLAY

055, 48 056, 0 057, 1 058, 40 059, 42 14 060, 44 5 061, 45 5 062, 31 063, 45 13 064, 34 065, 30 066, 45 3 067, 30 068, 16 069, 31 070, 45 5 071, 45 3 072, 40 073, 13 074, 45 0 075, 11 076, 12 077,45,43 12 078,43,33,000

12c platinum

ALG KEYSTROKES

:3 $ M Þ t

0

M ¼ :gC g(000 fs

DISPLAY

055, 45 3 056, 13 057, 15 058, 16 059, 31 060, 0 061, 15 062, 12 063,45,43 12 064,43,33,000

REGISTERS

n: N i: i PV: Used PMT: PMT FV: 0 R0: N R

: AIR R

1

: CL (%)

2

R3: Loan R4: N/1200 R5: Used R6-R9: Unused

Program Instructions:

1. Key in the program.

2.

Press fCLEARG.

3.

Key in the number of monthly payments in the loan and press ?0.

4.

Key in the annual add-on interest rate as a percentage and press ?1.

5.

Key in the credit life as a percentage and press ?2.

6.

Key in the loan amount and press ?3.

7.

Press t to find the monthly payment amount.

8.

Press t to obtain the amount of credit life.

30 Lending

9.

Press t to calculate the total finance charge.

10.

Press t to calculate the annual percentage rate.

11. For a new loan return to step 3.

Example 1: You wish to quote a loan on a $3100 balance, payable over 36 months at an add-on rate of 6.75%. Credit life (CL) is 1%. What are the monthly payment amount, credit life amount, total finance charge, and APR?

12c platinum / 12C

RPN Keystrokes

fCLEARG fCLEARG 36?0 36?0

6.75?1 6.75?1

1?2 1?2 3100?3 3100?3

t t t t t t t t

12c platinum

ALG Keystrokes

Display Comments

36.00

6.75

1.00

3100.00

-107.42

116.02

-651.10

12.39

Months. Add-on interest rate. Credit life (%). Loan. Monthly payment. Credit life. Total finance charge. APR.

Interest Rebate - Rule of 78's

This procedure finds the unearned interest rebate, as well as the remaining principal balance due for a prepaid consumer loan using the Rule of 78's. The known values are the current installment number, the total number of installments for which the loan was written, and the total finance charge (amount of interest). The information is entered as follows:

RPN Mode:

1.

Key in number of months in the loan and press ?1.

2.

Key in payment number when prepayment occurs and press -?2 1+.

3.

Key in total finance charge and press §:1\§:1+z:2§ to obtain the unearned interest (rebate).

4.

Key in periodic payment amount and press :2§~- to obtain the amount of principal outstanding.

ALG Mode:

1.

Key in number of months in the loan and press ?1-.

2.

Key in payment number when prepayment occurs and press³?2+1§.

3.

Key in total finance charge and press ³:1g’+:1z~~§:2 ³ to obtain the unearned interest (rebate).

4.

Key in periodic payment amount and press §:2-~³ to obtain the amount of principal outstanding.

Lending 31

Example 1: A 30 month $1000 loan having a finance charge of $180, is being repaid at $39.33 per month. What is the rebate and balance due after the 25th regular payment?

12c platinum / 12C

RPN Keystrokes

30?1 30?1 25-?2 -25³?2 1+180§ +1§180³

:1\ :1g’+:1

§:1+ z:2§ :2³

39.33:2§ 39.33§:2 ~- -~³

The following HP 12C Platinum program can be used to evaluate the previous example.

12c platinum / 12C

RPN KEYSTROKES

fs fCLEARÎ ?0 d ?2 d ?1 :2

?2

1

+ :0

§ :1 \

§ :1 + z :2

§ t :2

§ ~

-

12c platinum

ALG Keystrokes

z~~§

DISPLAY

000, 001, 44 0 002, 33 003, 44 2 004, 33 005, 44 1 006, 45 2 007, 30 008, 44 2 009, 1 010, 40 011, 45 0 012, 20 013, 45 1 014, 36 015, 20 016, 45 1 017, 40 018, 10 019, 45 2 020, 20 021, 31 022, 45 2 023, 20 024, 34 025, 30

Display Comments

5.81

190.84

12c platinum

ALG KEYSTROKES

fs fCLEARÎ ?0 d ~ ?1 ?2 ~ ?-2 :1 g’ + :1 ³ :2 g’ + :2 z ~

§ :0 ³ t

§ :2

-

Rebate.

Outstanding principal.

DISPLAY

000, 001, 44 0 002, 33 003, 34 004, 44 1 005, 44 2 006, 34 007,44 30 2 008, 45 1 009, 43 20 010, 40 011, 45 1 012, 36 013, 45 2 014, 43 20 015, 40 016, 45 2 017, 10 018, 34 019, 20 020, 45 0 021, 36 022, 31 023, 20 024, 45 2 025, 30

32 Lending

12c platinum / 12C

RPN KEYSTROKES

g(000 fs

REGISTERS

N: Unused i: Unused PV: Unused PMT: Unused FV: Unused R0: Fin. charge R1: # months R2: Payment # R3-R.6: Unused

Program Instructions:

1. Key in the program.

2.

Key in the number of months in the loan and press \(³).

3.

Key in the payment number when prepayment occurs and press \(³).

4.

Key in the total finance charge and press t to obtain the unearned interest (rebate).

5.

Key in the periodic payment amount and press t to find the amount of principal outstanding.

6. For a new case return to step 2.

12c platinum / 12C

RPN Keystrokes

30\ 30³ 25\ 25³ 180t 180t

39.33t 39.33t

DISPLAY

026,43,33,000

12c platinum

ALG Keystrokes

12c platinum

ALG KEYSTROKES

~ ³ g(000 fs

Display Comments

5.81

190.84

Rebate. Outstanding principal.

DISPLAY

026, 34 027, 36 028,43,33,000

Graduated Payment Mortgages

The Graduated Payment Mortgage is designed to meet the needs of young home buyers who currently cannot afford high mortgage payments, but who have the potential of increasing earning in the years to come.

Under the Graduated Payment Mortgage plan, the payments increase by a fixed percentage at the end of each year for a specified number of years. Thereafter, the payment amount remains constant for remaining life of the mortgage.

The result is that the borrower pays a reduced payment (a payment which is less than a traditional mortgage payment) in the early years, and in the later years makes larger payments than he would with a traditional loan. Over the entire term of the mortgage, the borrower would pay more than he would with conventional financing.

Lending 33

Given the term of the mortgage (in years), the annual percentage rate, the loan amount, the percentage that the payments increase, and the number of years that the payments increase, the following HP 12C Platinum program determines the monthly payments and remaining balance for each year until the level payment is reached.

12c platinum / 12C

RPN KEYSTROKES

fs fCLEARÎ gÂ ?2 ~

1 b 1

+ ?0 :n :2

gA :¼ gC :$ ?3

1

Þ P $ Þ M

1

gA :P :0 z P $ Þ M

1

?+1 :1 :2

-

DISPLAY

000, 001, 43 8 002, 44 2 003, 34 004, 1 005, 25 006, 1 007, 40 008, 44 0 009, 45 11 010, 45 2 011, 30 012, 43 11 013, 45 12 014, 43 12 015, 45 13 016, 44 3 017, 1 018, 16 019, 14 020, 13 021, 16 022, 15 023, 1 024, 43 11 025, 45 14 026, 45 0 027, 10 028, 14 029, 13 030, 16 031, 15 032, 1 033,44 40 1 034, 45 1 035, 45 2 036, 30

12c platinum

ALG KEYSTROKES

fs fCLEARÎ gÂ ?2 ~ b +

1

³ y ?0 :n

- :2 ³ gA :¼ gC :$ ?3 ?4

1

P $ Þ M

1

gA :P

§ :0 P $ Þ M

1

?+1 :1

DISPLAY

000, 001, 43 8 002, 44 2 003, 34 004, 25 005, 40 006, 1 007, 36 008, 22 009, 44 0 010, 45 11 011, 30 012, 45 2 013, 36 014, 43 11 015, 45 12 016, 43 12 017, 45 13 018, 44 3 019, 44 4 020, 1 021, 14 022, 13 023, 16 024, 15 025, 1 026, 43 11 027, 45 14 028, 20 029, 45 0 030, 14 031, 13 032, 16 033, 15 034, 1 035,44 40 1 036, 45 1

34 Lending

12c platinum / 12C

RPN KEYSTROKES

gm g(040 g(025 :3 :$ z ?4 :3 $

1

?3 :3 t :4

1

:0 :1 q z

§

Þ fB P t M M fB t Þ $

1

?+3 ?-1 :1 gm g(074 g(048 :4 Þ t g(076 fs

DISPLAY

037, 43 35 038,43,33,040 039,43,33,025 040, 45 3 041, 45 13 042, 10 043, 44 4 044, 45 3 045, 13 046, 1 047, 44 3 048, 45 3 049, 31 050, 45 4 051, 1 052, 45 0 053, 45 1 054, 21 055, 10 056, 20 057, 16 058, 42 14 059, 14 060, 31 061, 15 062, 15 063, 42 14 064, 31 065, 16 066, 13 067, 1 068,44 40 3 069,44 30 1 070, 45 1 071, 43 35 072,43,33,074 073,43,33,048 074, 45 4 075, 16 076, 31 077,43,33,076

12c platinum

ALG KEYSTROKES

- :2 ³ gm g(043 g(027 :$ ?z4 :3 $

1

?3 :3 t :0 q :1

§ :4 ³ fB t P M fB t Þ $

1

?+3 ?-1 :1 gm g(072 g(049 :4 t g(073 fs

DISPLAY

037, 30 038, 45 2 039, 36 040, 43 35 041,43,33,043 042,43,33,027 043, 45 13 044,44 10 4 045, 45 3 046, 13 047, 1 048, 44 3 049, 45 3 050, 31 051, 45 0 052, 21 053, 45 1 054, 20 055, 45 4 056, 36 057, 42 14 058, 31 059, 14 060, 15 061, 42 14 062, 31 063, 16 064, 13 065, 1 066,44 40 3 067,44 30 1 068, 45 1 069, 43 35 070,43,33,072 071,43,33,049 072, 45 4 073, 31 074,43,33,073

Lending 35

REGISTERS

n: Used i: i/12 PV: Used PMT: Used FV: Used R0: Used R1: Used R2: Used R3: Used R4: Level Pmt. R5-R9: Unused

Program Instructions:

1. Key in the program.

2.

Press fCLEARH.

3.

Key in the term of the loan and press n.

4.

Key in the annual interest rate and press ¼.

5.

Key in the total loan amount and press $.

6.

Key in the rate of graduation (as a percent) and press \(³).

7.

Key in the number of years for which the loan graduates and press t. The following information will be displayed for each year until a level payment is reached.

a. The current year.

Then press t to continue.

b. The monthly payment for the current year.

Then press t to continue.

c. The remaining balance to be paid on the loan at the end of the current year.

Then press t to return to step a. unless the level payment is reached. If the level payment has been reached, the program will stop, displaying the monthly payment over the remaining term of the loan.

8.

For a new case press g(000 and return to step 2.

Example: A young couple recently purchased a new house with a Graduated Payment Mortgage. The loan is for $50,000 over a period of 30 years at an annual interest rate of

12.5%. The monthly payments will be graduating at an annual rate of 5% for the first 5 years and then will be level for the remaining 25 years. What are the monthly payment amount for the first 6 years?

12c platinum / 12C

RPN Keystrokes

fCLEARH fCLEARH 30n 30n

12.5¼ 12.5¼ 50000$ 50000$ 5\ 5³ 5t 5t

t t t t

t t t t t t

12c platinum

ALG Keystrokes

Display Comments

0.00

30.00

12.50 50,000.00

5.00

1.00

-448.88

-50,914.67

2.00

-471.33

-51,665.07

Term Annual interest rate Loan amount Rate of graduation Year 1 1st year monthly payment. Remaining balance after 1st year. Year 2 2nd year monthly payment. Remaining balance after 2nd year.

36 Lending

12c platinum / 12C

RPN Keystrokes

t t t t t t

t t

12c platinum

ALG Keystrokes

Display Comments

3.00

-494.89

-52,215.34

4.00

-519.64

-52,523.86

5.00

-545.62

-52,542.97

-572.90

Year 3 3rd year monthly payment. Remaining balance after 3rd year. Year 4 4th year monthly payment. Remaining balance after 4th year. Year 5 5th year monthly payment. Remaining balance after 5th year. Monthly payment for remainder of term.

Variable Rate Mortgages

As its name suggests, a variable rate mortgage is a mortgage loan which provides for adjustment of its interest rate as market interest rates change. As a result, the current interest rate on a variable rate mortgage may differ from its origination rate (i.e., the rate when the loan was made). This is the difference between a variable rate mortgage and the standard fixed payment mortgage, where the interest rate and the monthly payment are constant throughout the term.

Under the agreement of the variable rate mortgage, the mortgage is examined periodically to determine any rate adjustments. The rate adjustment may be implemented in two ways:

1. Adjusting the monthly payment.

2. Modifying the term of the mortgage.

The period and limits to interest rate increases vary from state to state.

Each periodic adjustment may be calculated by using the HP 12C Platinum with the following keystroke procedure. The original terms of the mortgage are assumed to be known.

1.

Press gÂ and press fCLEARG.

2.

Key in the remaining balance of the loan and press $.

The remaining balance is the difference between the loan amount and the total

principal from the payments which have been made. To calculate the remaining balance, do the following:

a. Key in the previous remaining balance. If this is the first mortgage adjustment,

this value is the original amount of the loan. Press $.

b. Key in the annual interest rate before the adjustment (as a percentage) and press

gC.

Lending 37

c. Key in the number of years since the last adjustment. If this is the first mortgage

adjustment, then key in the number of years since the origination of the mortgage. Press gA.

d.

Key in the monthly payment over this period and press ÞP.

e.

Press M to find the remaining balance, then press fCLEARGÞ$.

3.

Key in the adjusted annual interest rate (as a percentage) and press gC.

To calculate the new monthly payment: a.

Key in the remaining life of the mortgage (years) and press gA.

b.

RPN: Press P to find the new monthly payment.

b.

ALG: Press PP to find the new monthly payment.

To calculate the revised remaining term of the mortgage:

a.

Key in the present monthly payment and press P.

b.

RPN: Press n12z to find the remaining term of the mortgage in years.

b.

ALG: Press nz12³ to find the remaining term of the mortgage in years.

Example: A homeowner purchased his house 3 years ago with a $50,000 variable rate

mortgage. With a 30 year term, his current monthly payment is $495.15. When the interest rate is adjusted from 11.5% to 11.75%, what will the monthly payment be? If the monthly payment remained unchanged, find the revised remaining term on the mortgage.

12c platinum / 12C

RPN Keystrokes

gÂ gÂ fCLEARG fCLEARG

50000$ 50000$

11.5gC 11.5gC 3gA 3gA

495.15ÞP 495.15ÞP

M M fCLEARG fCLEARG Þ$ Þ$

11.75gC 11.75gC 30\3- 30-3³

gA gA P PP

495.15ÞP 495.15ÞP n12z nz12³

12c platinum

ALG Keystrokes

Display Comments

50,000.00

0.96

36.00

-495.15

-49,316.74 49,316.74

0.98

27.00

324.00

-504.35

-495.15

31.67

Original amount of loan. Original monthly interest rate. Period. Previous monthly payment.

Remaining balance. Adjusted monthly interest. Remaining life of mortgage.

New monthly payment. Previous monthly payment. New remaining term (years).

38 Lending

Skipped Payments

Sometimes a loan (or lease) may be negotiated in which a specific set of monthly payments are going to be skipped each year. Seasonally is usually the reason for such an agreement. For example, because of heavy rainfall, a bulldozer cannot be operated in Oregon during December, January, and February, and the lessee wishes to make payments only when his machinery is being used. He will make nine payments per year, but the interest will continue to accumulate over the months in which a payment is not made.

To find the monthly payment amount necessary to amortize the loan in the specified amount of time, information is entered as follows:

1.

Press gÂ and press fCLEARG.

2. Key in the number of the last payment period before payments close the first time

and press n.

3.

Key in the annual interest rate as a percentage and press gC1PM.

RPN Mode:

4.

Press Þ$12:n-n0PM?0:n.

5.

Key in the number of payments which are skipped and press n1P0$M?+0.

6.

Press 0P12n100$M:$+ÞfCLEARG¼

7.

Key in the total number of years in the loan and press n.

8.

Key in the loan amount and press $P:0z to obtain the monthly payment amount when the payment is made at the end of the month.

9.

Press ÞM0P1n.

10.

Key in the annual interest rate as a percent and press gC$ to find the monthly payment amount when the payment is made at the beginning of the month.

ALG Mode:

4.

Press Þ$12-:nn0PM?0:n-.

5. Key in the number of payments which are skipped and press

n1P0$M?+0.

6.

Press 0P12n100$M+:$³ÞfCLEARG¼

7.

Key in the total number of years in the loan and press n.

8.

Key in the loan amount and press $Pz:0³ to obtain the monthly payment amount when the payment is made at the end of the month.

9.

Press ÞM0P1n.

10.

Key in the annual interest rate as a percent and press gC$$ to find the monthly payment amount when the payment is made at the beginning of the month.

Lending 39

Example: A bulldozer worth $100,000 is being purchased in September. The first payment is due one month later, and payments will continue over a period of 5 years. Due to the weather, the machinery will not be used during the winter months, and the purchaser does not wish to make payments during January, February, and March (months 4 thru 6). If the current interest rate is 14%, what is the monthly payment necessary to amortize the loan?

12c platinum / 12C

RPN Keystrokes

gÂ gÂ fCLEARG fCLEARG

3n 3n

14gC 14gC 1PMÞ$ 1PMÞ$ 12:n-n 12-:nn 0PM?0 0PM?0 :n3-n :n-3n 1P0$M 1P0$M ?+0 ?+0 0P12n 0P12n 100$M 100$M

:$+Þ +:$³Þ fCLEARG¼ fCLEARG¼ 5n100000$ 5n100000$ P:0z Pz:0³

12c platinum

ALG Keystrokes

Display Comments

3.00

1.17

-3.37

-6.18

14.93

3,119.89

Number of payments made before a group of payments is skipped. Monthly interest rate.

FV of 3 monthly unit PMTs.

FV of 6 monthly unit PMTs.

Effective annual interest rate

Monthly payment in arrears.

Savings

Initial Deposit with Periodic Deposits

Given an initial deposit into a savings account, and a series of periodic deposits coincident with the compounding period, the future value (or accumulated amount) may be calculated as follows:

1. Press gÂ and press fCLEARG.

2. Key in the initial investment and press Þ$.

3. Key in the number of additional periodic deposits and press n.

4. Key in the periodic interest rate and press ¼.

5. Key in the periodic deposit and press ÞP.

6. Press M to determine the value of the account at the end of the time period.

Example: You have just opened a savings account with a $200 deposit. If you deposit $50 a month, and the account earns 5 ¼ % compounded monthly, how much will you have in 3 years?

12c platinum / 12C

RPN Keystrokes

gÂ gÂ fCLEARG fCLEARG

200Þ$ 200Þ$ 3gA 3gA

5.25gC 5.25gC

50ÞPM 50ÞPM

Note: If the periodic deposits do not coincide with the compounding periods, the account

must be evaluated in another manner. First, find the future value of the initial deposits and store it. Then use the procedure for compounding periods different from payment periods to calculate the future value of the periodic deposits. Recall the future value of the initial deposit and add to obtain the value of the account.

40

12c platinum

ALG Keystrokes

Display Comments

2,178.94

Value of the account.

Savings 41

Number of Periods to Deplete a Savings Account or to Reach a Specified Balance

Given the current value of a savings account, the periodic interest rate, the amount of the periodic withdrawal, and a specified balance, this procedure determines the number of periods to reach that balance (the balance is zero if the account is depleted).

1. Press gÂ and press fCLEARG.

2. Key in the value of the savings account and press Þ$.

3. Key in the periodic interest rate and press ¼.

4. Key in the amount of the periodic withdrawal and press P.

5. Key in the amount remaining in the account and press M. This step may be omitted if the account is depleted (FV=0).

6. Press n to determine the number of periods to reach the desired balance.

Example: Your savings account presently contains $18,000 and earns 5 ½% compounded monthly. You wish to withdraw $300 a month until the account is depleted. How long will this take? If you wish to reduce the account to $5000, how many withdrawals can you make?

12c platinum / 12C

RPN Keystrokes

gÂ gÂ fCLEARG fCLEARG

18000Þ$ 18000Þ$

5.5gC 5.5gC 300Pn 300Pn 5000Mn 5000Mn

12c platinum

ALG Keystrokes

Display Comments

71.00

53.00

Months to deplete account. Months to reduce the account to $5000.

42 Savings

PV

FV

Periodic Deposits and Withdrawals

This section is presented as a guideline for evaluating a savings plan when deposits and withdrawals occur at irregular intervals. One problem is given, and a step by step method for setting up and solving the problem is presented:

Example: You are presently depositing $50 and the end of each month into a local savings and loan, earning 5 ½% compounded monthly. Your current balance is $1023.25. How much will you have accumulated in 5 months?

The cash flow diagram looks like this:

= ?

1 3 4 52

-50-50-50- 50 -50

= - 1023.25

12c platinum / 12C

RPN Keystrokes

gÂ gÂ fCLEARG fCLEARG

50ÞP 50ÞP

5.5gC 5.5gC

1023.25Þ$ 1023.25Þ$

5nM 5nM

Now suppose that at the beginning of the 6th month you withdrew $80.

What is the new balance?

12c platinum / 12C

RPN Keystrokes

80- -80³

12c platinum

ALG Keystrokes

12c platinum

ALG Keystrokes

Display Comments

1,299.22

Display Comments

1,219.22

Amount in account.

New balance.

Savings 43

PV

FV

PV

You increase your monthly deposit to $65. How much will you have in 3 months?

The cash flow diagram looks like this:

= ?

1 3 2

-65-65-65

= - 1219.22

12c platinum / 12C

RPN Keystrokes

Þ$ Þ$ 65ÞP 65ÞP 3nM 3nM

Suppose that for 2 months you decide not to make a periodic deposit. What is the balance in the account?

12c platinum

ALG Keystrokes

Display Comments

1,431.95

= ?

Account balance.

1 2

= - 1431.95

12c platinum / 12C

RPN Keystrokes

Þ$2n Þ$2n 0PM 0PM

12c platinum

ALG Keystrokes

Display Comments

1,445.11

Account balance.

44 Savings

This type of procedure may be continued for any length of time, and may be modified to meet the user's particular needs.

Savings Account Compounded Daily

This HP 12C Platinum program determines the value of a savings account when interest is compounded daily, based on a 365 day year. The user is able to calculate the total amount remaining in the account after a series of transactions on specified dates.

12c platinum / 12C

RPN KEYSTROKES

fs fCLEARÎ Þ $ d

3 6 5

z ¼ d ?0 :$ Þ t ?2 d ?1 :0 :1 gÒ n M fB M \ :$ + ?+3

:M :2 + Þ

DISPLAY

000, 001, 16 002, 13 003, 33 004, 3 005, 6 006, 5 007, 10 008, 12 009, 33 010, 44 0 011, 45 13 012, 16 013, 31 014, 44 2 015, 33 016, 44 1 017, 45 0 018, 45 1 019, 43 26 020, 11 021, 15 022, 42 14 023, 15 024, 36 025, 45 13 026, 40 027,44 40 3 028, 45 15 029, 45 2 030, 40 031, 16

12c platinum

ALG KEYSTROKES

fs fCLEARÎ Þ $ d z

3 6 5

¼ d ?0 :$ Þ t ?2 d ?1 :0 :1 gÒ n M fB M + :$ ³ ?+3

:M Þ

:2

DISPLAY

000, 001, 16 002, 13 003, 33 004, 10 005, 3 006, 6 007, 5 008, 12 009, 33 010, 44 0 011, 45 13 012, 16 013, 31 014, 44 2 015, 33 016, 44 1 017, 45 0 018, 45 1 019, 43 26 020, 11 021, 15 022, 42 14 023, 15 024, 40 025, 45 13 026, 36 027,44 40 3 028, 45 15 029, 16 030, 30 031, 45 2

Savings 45

12c platinum / 12C

RPN KEYSTROKES

$ :1 ?0 :$ Þ g(013 fs

REGISTERS

N: ∆days i: i/365 PV: Used PMT: 0 FV: Used R0: Initial date R1: Next date R2: $ amount R3: Interest R4-R.4: Unused

Program Instructions:

1. Key in the program.

2.

Press fCLEARH and press gÕ.

3.

Key in the date (MM.DDYYYY) of the first transaction and press \(³).

4.

Key in the annual nominal interest rate as a percentage and press \(³).

5.

Key in the amount of the initial deposit and press t.

6.

Key in the date of the next transaction and press \(³).

7. Key in the amount of the transaction (positive for money deposited, negative for cash

withdrawn) and press t to determine the amount in the account.

8. Repeat steps 6 and 7 for subsequent transactions.

9.

To see the total interest to date, press :3.

10.

For a new case press f(000 and go to step 2.

Example: Compute the amount remaining in this 5.25% account after the

following transactions:

1. January 19, 2003 deposit $125.00

2. February 24, 2003 deposit $60.00

3. March 16, 2003 deposit $70.00

4. April 6, 2003 withdraw $50.00

5. June 1, 2003 deposit $175.00

6 July 6, 2003 withdraw $100.00

DISPLAY

032, 13 033, 45 1 034, 44 0 035, 45 13 036, 16 037,43,33,013

12c platinum

ALG KEYSTROKES

$ :1 ?0 :$ Þ g(013 fs

DISPLAY

032, 13 033, 45 1 034, 44 0 035, 45 13 036, 16 037,43,33,013

46 Savings

12c platinum / 12C

RPN Keystrokes

fCLEARH fCLEARH gÕ gÕ

1.192003\ 1.192003³

5.25\ 5.25³

125t 125t

2.242003\ 2.242003³

60t 60t

3.162003\ 3.162003³

70t 70t

4.062003\ 4.062003³

50Þt 50Þt

6.012003\ 6.012003³

175t 175t

7.062003\ 7.062003³

100Þt 100Þt

:3 :3

12c platinum

ALG Keystrokes

Display Comments

125.00

185.65

256.18

206.95

383.62

285.56

5.56

Initial Deposit.

Balance in account, February 24, 2003.

Balance in account, March 16, 2003.

Balance in account, April 6, 2003.

Balance in account, June 1, 2003.

Balance in account, July 6, 2003. Total interest.

Compounding Periods Different From Payment Periods

In financial calculations involving a series of payments equally spaced in time with periodic compounding, both periods of time are normally equal and coincident. This assumption is preprogrammed into the HP 12C Platinum.

In savings plans however, money may become available for deposit or investment at a frequency different from the compounding frequencies offered. The HP 12C Platinum can easily be used in these calculations. However, because of the assumptions mentioned the periodic interest rate must be adjusted to correspond to an equivalent rate for the payment period.

Payments deposited for a partial compounding period will accrue simple interest for the remainder of the compounding period. This is often the case, but may not be true for all institutions.

These procedures present solutions for future value, payment amount, and number of payments. In addition, it should be noted that only annuity due (payments at the beginning of payment period) calculations are shown since this is the most common in savings plan calculations.

Savings 47

To calculate the equivalent payment period interest rate, information is entered as follows:

1.

Press g× and press fCLEARG.

RPN Mode:

2.

Key in the annual interest rate (as a percent) and press \.

3.

Key in the number of compounding periods per year and press nz¼.

ALG Mode:

2.

Key in the number of compounding periods per year and press n.

3.

Key in the annual interest rate (as a percent) and press z:n¼.

4.

Key in 1 and press $M.

5. Key in the number of payments (deposits) per year and press

n¼fCLEARG¼.

The interest rate which corresponds to the payment period is now in register "i" and you are ready to proceed.

Example 1: Solving for future value.

Starting today you make monthly deposits of $25 into an account paying 5% compounded daily (365-day basis). At the end of 7 years, how much will you receive from the account?

12c platinum / 12C

RPN Keystrokes

g× g× fCLEARG fCLEARG

5\ 365n 365nz¼ 5z:n¼ 1$M 1$M 12n¼ 12n¼ fCLEARG¼ fCLEARG¼

7gA 7gA 25ÞP 25ÞP M M

12c platinum

ALG Keystrokes

Display Comments

0.42

2,519.61

Equivalent periodic interest rate.

Future value.

48 Savings

Example 2: Solving for payment amount.

For 8 years you wish to make weekly deposits in a savings account paying 5.5% compounded quarterly. What amount must you deposit each week to accumulate $6000.

12c platinum / 12C

RPN Keystrokes

g× g× fCLEARG fCLEARG

5.5\ 4n

4nz¼ 5.5z:n¼ 1$M 1$M 52n¼ 52n¼ fCLEARG¼ fCLEARG¼

8\52§n 8§52n 6000MP 6000MP

Example 3: Solving for number of payment periods.

You can make weekly deposits of $10 in to an account paying 5.25% compounded daily (365-day basis). How long will it take you to accumulate $1000?

12c platinum

ALG Keystrokes

Display Comments

0.11

-11.49

Equivalent periodic interest rate.

Periodic payment.

12c platinum / 12C

RPN Keystrokes

g× g× fCLEARG fCLEARG

5.25\ 365n

365nz¼ 5.25z:n¼ 1$M 1$M 52n¼ 52n¼ fCLEARG¼ fCLEARG¼

10ÞP 10ÞP 1000Mn 1000Mn

12c platinum

ALG Keystrokes

Display Comments

0.10

96.00

Equivalent periodic interest rate.

Weeks.

Investment Analysis

Lease vs. Purchase

An investment decision frequently encountered is the decision to lease or purchase capital equipment or buildings. Although a thorough evaluation of a complex acquisition usually requires the services of a qualified accountant, it is possible to simplify a number of the assumptions to produce a first approximation. The following HP 12C Platinum program assumes that the purchase is financed with a loan and that the loan is made for the term of the lease. The tax advantages of interest paid, depreciation, and the investment credit which accrues from ownership are compared to the tax advantage of treating the lease payment as an expense. The resulting cash flows are discounted to the present at the firm's after-tax cost of capital.

12c platinum / 12C

RPN KEYSTROKES

fs fCLEARÎ

-

1

?+0 :3

-

§ ?8

1

f! ?1 :$ ?9 :P ?.0 :n ?.1 :¼ ?.2 :5 $ :6 n

49

DISPLAY

000, 001, 30 002, 1 003,44 40 0 004, 45 3 005, 30 006, 20 007, 44 8 008, 1 009, 42 11 010, 44 1 011, 45 13 012, 44 9 013, 45 14 014,44 48 0 015, 45 11 016,44 48 1 017, 45 12 018,44 48 2 019, 45 5 020, 13 021, 45 6 022, 11

12c platinum

ALG KEYSTROKES

fs fCLEARÎ

- ~ ³ ?8

1

?+0 f! ?1 :$ ?9 :¼ ?.2 :5 $ :6 n :7 ¼ :0 fÝ ?+1 :9

DISPLAY

000, 001, 30 002, 34 003, 36 004, 44 8 005, 1 006,44 40 0 007, 42 11 008, 44 1 009, 45 13 010, 44 9 011, 45 12 012,44 48 2 013, 45 5 014, 13 015, 45 6 016, 11 017, 45 7 018, 12 019, 45 0 020, 42 24 021,44 40 1 022, 45 9

50 Investment Analysis

12c platinum / 12C

RPN KEYSTROKES

:7 ¼ :0 fÝ ?+1 :9 $ :.0 P :.1 n :.2 ¼ :1 :3

§

:P

-

:8

-

:4 :0 q z ?+2 g(000 fs

DISPLAY

023, 45 7 024, 12 025, 45 0 026, 42 24 027,44 40 1 028, 45 9 029, 13 030,45 48 0 031, 14 032,45 48 1 033, 11 034,45 48 2 035, 12 036, 45 1 037, 45 3 038, 20 039, 45 14 040, 30 041, 45 8 042, 30 043, 45 4 044, 45 0 045, 21 046, 10 047,44 40 2 048,43,33,000

REGISTERS

12c platinum

ALG KEYSTROKES

$ :.2 ¼ :1

- :8

§ :3 + :8

- :P ³ :4 q :0 z ~ ~ ³ ?+2 g(000 fs

DISPLAY

023, 13 024,45 48 2 025, 12 026, 45 1 027, 30 028, 45 8 029, 20 030, 45 3 031, 40 032, 45 8 033, 30 034, 45 14 035, 36 036, 45 4 037, 21 038, 45 0 039, 10 040, 34 041, 34 042, 36 043,44 40 2 044,43,33,000

n: Used i: Used PV: Used PMT: Used FV: 0 R0: Used R1: Used R2: Purch. Adv. R3: Tax R4: Discount R5: Dep. Value R6: Dep. life R7: Factor (DB) R8: Used R9: Used R.0: Used R.1: Used R.2: Used R.3: Unused

Program Instructions:

1. Key in the program.

RPN: - Select the depreciation function and key in at line 26. ALG: - Select the depreciation function and key in at line 20.

2.

Press gÂ and press fCLEARH.

3. Input the following information for the purchase of the loan:

- Key in the number of years for amortization and press n.

Investment Analysis 51

- Key in the annual interest rate and press ¼.

- Key in the loan amount (purchase price) and press Þ$.

- Press P to find the annual payment.

4.

Key in the marginal effective tax rate

5.

RPN: Key in the discount rate or cost of capital

5.

ALG: Key in the discount rate or cost of capital

6.

Key in the depreciable value and press ?5.

7.

Key in the depreciable life and press ?6.

*

and press ?3.

*

and press \1+?4.

*

and press +1³?4.

8. For declining balance depreciation, key in the depreciation factor (as a percentage)

and press ?7.

9. RPN: Key in the total first lease payment (including any advance payments) and

press \1:3-§?2.

9. ALG: Key in the total first lease payment (including any advance payments) and

press ³1-:3§~³?2.

10. Key in the first year's maintenance expense that would be anticipated if the asset was

owned and press \(³) . If the lease contract does not include maintenance, then it is not a factor in the lease vs. purchase decision and 0 expense should be used.

11.

Key in the next lease payment and press t. During any year in which a lease payment does not occur (e.g. the last several payments of an advance payment contract) use 0 for the payment.

12. Repeat steps 10 and 11 for all maintenance expenses and lease payments over the term of the analysis.

Optional - If the investment tax credit is taken, key in the amount of the credit after

finishing steps 10 and 11 for the year in which the credit is taken and press g(043 (ALG:036) t . Continue steps 10 and 11 for the remainder of the term.

13. RPN: After all the lease payments and expenses have been entered (steps 10 and 11), key in the lease buy back option and press \1:3-§g(043t. If no buy back option exists, use the estimated salvage value of the purchased equipment at the end of the term.

13. ALG: After all the lease payments and expenses have been entered (steps 10 and 11), key in the lease buy back option and press ³1- :3§~³g(036t. If no buy back option exists, use the estimated salvage value of the purchased equipment at the end of the term.

14.

To find the net advantage of owning press :2. A negative value represents a net lease advantage.

Example: Home Style Bagel Company is evaluating the acquisition of a mixer which can be leased for $1700 a year with the first and last payments in advance and a $750 buy back option at the end of 10 years (maintenance is included). The same equipment could be purchased for $10,000 with a 12% loan amortized over 10 years. Ownership maintenance is estimated to be 2% of the purchase price per year for the first for years. A major overhaul is predicted for the 5th year at a cost of $1500. Subsequent yearly maintenance of 3% is estimated for the remainder of the 10 year term. The company would use sum of the years digits depreciation on a 10 year life with $1500

*

Key in as a decimal (e.g., 5% as .05).

52 Investment Analysis

salvage value. An accountant informs management to take the 10% capital investment tax credit at the end of the second year and to figure the cash flows at a 48% tax rate. The after tax cost of capital (discounting rate) is 5 percent. Because lease payments are made in advance and standard loan payments are made in arrears the following cash flow schedule is appropriate for a lease with the last payment in advance.

Year Maintenance Lease Payment Tax Credit Buy Back

0 1700+1700 1 200 1700 2 200 1700 1000 3 200 1700 4 200 1700 5 1500 1700 6 300 1700 7 300 1700 8 300 1700 9 300 0

10 300 0 750

12c platinum / 12C

RPN Keystrokes

gÂ gÂ fCLEARH fCLEARH

10n12¼ 10n12¼ 10000Þ$ 10000Þ$

12c platinum

ALG Keystrokes

Display Comments

0.00

-10,000.00

Always use negative loan amount.

P P .48?3 .48?3 .05\1+?4 .05+1³?4 10000\ 100001500-?5 1500³?5 10?6 10?6 1700\+ 1700+³ 1:3-§?2 1-:3§~

1,769.84

0.48

1.05

8,500.00

10.00 3,400.00 1,768.00

Purchase payment. Marginal tax rate. Discounting factor.

Depreciable value. Depreciable life. 1st lease payment. After-tax expense.

³?2 200\ 200³ 1700t 1700t

312.36

Present value of 1st year's net purchase.

200\ 200³ 1700t 1700t 1000g(043 1000g(036 t t 200\ 200³ 1700t 1700t 200\ 200³ 1700t 1700t

200.43 1,000.00

907.03

95.05

-4.38

2nd year's advantage. Tax credit. Present value of tax credit.

3rd year.

4th year.

Investment Analysis 53

12c platinum / 12C

RPN Keystrokes

1500\ 1500³ 1700t 1700t 300\ 300³ 1700t 1700t 300\ 300³ 1700t 1700t 300\ 300³ 1700t 1700t 300\0t 300³0t 300\0t 300³0t 750\ 750³ 1:3-§ 1-:3§~³

12c platinum

ALG Keystrokes

Display Comments

-628.09

-226.44

-309.48

-388.81

-1,034.72

-1,080.88

750.00

390.00

5th year.

6th year.

7th year.

8th year. 9th year. 10th year. Buy back. After tax buy back expense.

g(043t g(036t :2 :2

239.43

-150.49

Present value. Net lease advantage.

Break-Even Analysis

Break-even analysis is basically a technique for analyzing the relationships among fixed costs, variable costs, and income. Until the break-even point is reached at the intersection of the total sales revenue and total cost lines, the producer operates at a loss. After the break-even point each unit produced and sold makes a profit. Break-even analysis may be represented as follows.

Profit

Break-even Point

Fixed Costs

Variable

Costs

54 Investment Analysis

The variables are: fixed costs (F), Sales price per unit (P), variable cost per unit (V), number of units sold (U), and gross profit (GP). One can readily evaluate GP, U or P given the four other variables. To calculate the break-even volume, simply let the gross profit equal zero and calculate the number of units sold (U).

To calculate the break-even volume:

RPN Mode:

1.

Key in the fixed costs and press \.

2.

Key in the unit price and press \.

3.

Key in the variable cost per unit and press -.

4.

Press z to calculate the break-even volume.

ALG Mode:

1.

Key in the fixed costs and press ³.

2.

Key in the unit price and press -.

3.

Key in the variable cost per unit and press z.

4.

Press ~~³ to calculate the break-even volume.

To calculate the gross profit at a given volume:

RPN Mode:

1.

Key in the unit price and press \.

2.

Key in the variable cost per unit and press -.

3.

Key in the number of units sold and press §.

4.

Key in the fixed cost and press - to calculate the gross profit.

ALG Mode:

1.

Key in the unit price and press -.

2.

Key in the variable cost per unit and press §.

3.

Key in the number of units sold and press -.

4.

Key in the fixed cost and press ³ to calculate the gross profit.

To calculate the sales volume needed to achieve a specified gross profit:

RPN Mode:

1.

Key in the desired gross profit and press \.

2.

Key in the fixed cost and press +.

3.

Key in sales price per unit and press \.

4.

Key in the variable cost per unit and press -.

5.

Press z to calculate the sales volume.

Investment Analysis 55

ALG Mode:

1.

Key in the desired gross profit and press +.

2.

Key in the fixed cost and press ³.

3.

Key in sales price per unit and press -.

4.

Key in the variable cost per unit and press z.

5.

Press ~~³ to calculate the sales volume.

To calculate the required sales price to achieve a given gross profit at a specified sales volume:

RPN Mode:

1.

Key in the fixed costs and press \.

2.

Key in the gross desired and press +.

3.

Key in the specified sales volume in units and press z.

4.

Key in the variable cost per unit and press + to calculate the required sales price per unit.

ALG Mode:

1.

Key in the fixed costs and press +.

2.

Key in the gross desired and press z.

3.

Key in the specified sales volume in units and press +.

4.

Key in the variable cost per unit and press ³ to calculate the required sales price per unit.

Example 1: The E.Z. Sells company markets textbooks on salesmanship. The fixed cost involved in setting up to print the books are $12,000. The variable cost per copy, including printing and marketing the books are $6.75 per copy. The sales price per copy is $13.00. How many copies must be sold to break even?

12c platinum / 12C

RPN Keystrokes

12000\ 12000³ 13\ 13-

6.75-z 6.75z~~³

12c platinum

ALG Keystrokes

Display Comments

12,000.00

13.00 1,920.00

Fixed cost. Sales price. Break-even volume.

56 Investment Analysis

Find the gross profit if 2500 units are sold.

12c platinum / 12C

RPN Keystrokes

13\ 13-

6.75- 6.75§ 2500§ 250012000- 12000³

If a gross profit of $4500 is desired at a sales volume of 2500 units, what should the sales price be?

12c platinum / 12C

RPN Keystrokes

12000\ 12000+ 4500+ 4500z 2500z 2500+

6.75+ 6.75³

For repeated calculation the following HP 12C Platinum program can be used.

12c platinum

ALG Keystrokes

12c platinum

ALG Keystrokes

Display Comments

13.00

6.25 15,625.00 3,625.00

Sales price. Profit per unit.

Gross profit.

Display Comments

12,000.00 16,500.00

6.60

13.35

Fixed cost.

Sales price per unit to achieve desired gross profit.

12c platinum / 12C

RPN KEYSTROKES

fs fCLEARÎ :3 :2

g(000 :4

§ :1

g(000 :5 :1 + ~ z g(000 :1 :5 +

DISPLAY

000, 001, 45 3 002, 45 2 003, 30 004,43,33,000 005, 45 4 006, 20 007, 45 1 008, 30 009,43,33,000 010, 45 5 011, 45 1 012, 40 013, 34 014, 10 015,43,33,000 016, 45 1 017, 45 5 018, 40

12c platinum

ALG KEYSTROKES

fs fCLEARÎ :3

- :2 ³ g(000

§ :4

- :1 ³ g(000 :5 + :1 z ~ ³ g(000

DISPLAY

000, 001, 45 3 002, 30 003, 45 2 004, 36 005,43,33,000 006, 20 007, 45 4 008, 30 009, 45 1 010, 36 011,43,33,000 012, 45 5 013, 40 014, 45 1 015, 10 016, 34 017, 36 018,43,33,000

Investment Analysis 57

12c platinum / 12C

RPN KEYSTROKES

:4 z :2 + g(000 fs

DISPLAY

019, 45 4 020, 10 021, 45 2 022, 40 023,43,33,000

12c platinum

ALG KEYSTROKES

:1 + :5 z :4 + :2 ³ g(000 fs

DISPLAY

019, 45 1 020, 40 021, 45 5 022, 10 023, 45 4 024, 40 025, 45 2 026, 36 027,43,33,000

REGISTERS

n: Unused I: Unused PV: Unused PMT: Unused FV: Unused R0: Unused R1: F R R3: P R

: U R

4

: GP R

5

: V

2

6-R.6

: Unused

Program Instructions:

1. Key in the program and store the known variables as follows: a. b. c. d. e.

Key in the fixed costs, F and press ?1. Key in the variable costs per unit, V and press ?2. Key in the unit price, P (if known) and press ?3. Key in the sales volume, U, in units (if known) and press ?4. Key in the gross profit, GP, (if known) and press ?5.

2. To calculate the sales volume to achieve a desired gross profit: a. Store values as shown in 1a, 1b, and 1c. b. c. c.

Key in the desired gross profit (zero for break even) and press ?5.

RPN: Press tg(010t to calculate the required volume. ALG: Press tg(012t to calculate the required volume.

3. To calculate the gross profit at a given sales volume. a. Store values as shown in 1a, 1b, 1c, and 1d. b. b.

RPN: Press tg(005t to calculate gross profit. ALG: Press tg(006t to calculate gross profit.

4. To calculate the sales price per unit to achieve a desired gross profit at a specified sales volume:

a. Store values as shown in 1a, 1b, 1d, and 1e. b. b.

RPN: Press g(016t to calculate the required sales price. ALG: Press g(019t to calculate the required sales price.

58 Investment Analysis

Example 2: A manufacturer of automotive accessories produces rear view mirrors. A new line of mirrors will require fixed costs of $35,000 to produce. Each mirror has a variable cost of $8.25. The price of mirrors is tentatively set at $12.50 each. What volume is needed to break even?

12c platinum / 12C

RPN Keystrokes

35000?1 35000?1

8.25?2 8.25?2

12.5?3 12.5?3 0?5 0?5 tg(010t tg(012t

What would be the gross profit if the price is raised to $14.00 and the sales volume is 10,000 units?

12c platinum

ALG Keystrokes

Display Comments

35,000.00

8.25

12.50

0.00 8,235.29

Fixed cost. Variable cost. Sales price.

Break-even volume is between 8,235 and 8,236 units.

12c platinum / 12C

RPN Keystrokes

14?3 14?3

10000?4 10000?4 tg(005t tg(006t

12c platinum

ALG Keystrokes

Display Comments

14.00

10,000.00 22,500.00

Sales price. F and V are already stored. Volume. Gross Profit.

Investment Analysis 59

Operating Leverage

The degree of operating leverage (OL) at a point is defined as the ratio of the percentage change in net operating income to the percentage change in units sold. The greatest degree of operating leverage is found near the break-even point where a small change in sales may produce a very large increase in profits. Likewise, firms with a small degree of operating leverage are operating farther form the break-even point, and they are relatively insensitive to changes in sales volume.

The necessary inputs to calculate the degree of operating leverage and fixed costs (F), sales price per unit (P), variable cost per unit (V) and number of units (U).

The operating leverage may be readily calculated as follows:

RPN Mode:

1.

Key in the sales price per unit and press \.

2.

Key in the variable cost per unit and press -.

3.

Key in the number of units and press §\\.

4.

Key in the fixed cost and press -z to obtain the operating leverage.

ALG Mode:

1.

Key in the sales price per unit and press -.

2.

Key in the variable cost per unit and press §.

3.

Key in the number of units and press ³.

4.

Key in the fixed cost and press àbÞy to obtain the operating leverage.

Example 1: For the data given in example 1 of the Break-Even Analysis section, calculate the operating leverage at 2000 units and at 5000 units when the sales price is $13 a copy.

12c platinum / 12C

RPN Keystrokes

13\ 13-

6.75- 6.75§

2000§\ 2000³12000 \12000-z 13\ 13-

6.75- 6.75§

5000§\ 5000³12000 \12000-z

12c platinum

ALG Keystrokes

àbÞy

Display Comments

13.00

6.25

25.00

13.00

6.25

1.62

Price per copy. Profit per copy.

Close to break-even point. Price per copy. Profit per copy.

Operating further from the breakeven point and less sensitive to changes in sales volume.

60 Investment Analysis

For repeated calculations the following HP 12C Platinum program can be used:

12c platinum / 12C

RPN KEYSTROKES

fs fCLEARÎ :3 :2

-

§ \ \ :1

z g(000 fs

DISPLAY

000, 001, 45 3 002, 45 2 003, 30 004, 20 005, 36 006, 36 007, 45 1 008, 30 009, 10 010,43,33,000

12c platinum

ALG KEYSTROKES

fs fCLEARÎ :3

- :2

§ ~ ³ :1 à b Þ y g(000 fs

DISPLAY

000, 001, 45 3 002, 30 003, 45 2 004, 20 005, 34 006, 36 007, 45 1 008, 24 009, 25 010, 16 011, 22 012,43,33,000

REGISTERS

n: Unused i: Unused PV: Unused PMT: Unused FV: Unused R0: Unused R1: F R R3: P R

: Unused

4-R.8

2

: V

Program Instructions:

1. Key in the program.

2. Key in and store input variables F, V and P as described in the Break-Even Analysis program.

3.

Key in the sales volume and press t to calculate the operating leverage.

4. To calculate a new operating leverage at a different sales volume, key in the new sales volume and press t.

Example 2: For the figures given in example 2 of the Break-Even Analysis section, calculate the operating leverage at a sales volume of 9,000 and 20,000 units if the sales price is $12.50 per unit.

12c platinum / 12C

RPN Keystrokes

35000?1 35000?1

8.25?2 8.25?2

12.5?3 12.5?3

9000t 9000t

12c platinum

ALG Keystrokes

Display Comments

35,000.00

8.25

12.50

11.77

Fixed costs. Variable cost. Sales price. Operating leverage near breakeven.

20000t 20000t

1.70

Operating leverage further from break-even.

Investment Analysis 61

Profit and Loss Analysis

The HP 12C Platinum may be programmed to perform simplified profit and loss analysis using the standard profit income formula and can be used as a dynamic simulator to quickly explore ranges of variables affecting the profitability of a marketing operation.

The program operates with net income return and operating expenses as percentages. Both percentage figures are based on net sales price.

It may also be used to simulate a company wide income statement by replacing list price with gross sales and manufacturing cost with cost of goods sold.

Any of the five variables: a) list price, b) discount (as a percentage of list price), c) manufacturing cost, d) operating expense (as a percentage), e) net profit after tax (as a percentage) may be calculated if the other four are known.

Since the tax rage varies from company to company, provision is made for inputting your applicable tax rate. The example problem uses a tax rate of 48%.

12c platinum / 12C

RPN KEYSTROKES

fs fCLEARÎ :5 :6 z :4 + Þ :0 + :0 z g(000 :3 :1 :2 :0 z Þ

1

+

§ t z Þ

1

DISPLAY

000, 001, 45 5 002, 45 6 003, 10 004, 45 4 005, 40 006, 16 007, 45 0 008, 40 009, 45 0 010, 10 011,43,33,000 012, 45 3 013, 45 1 014, 45 2 015, 45 0 016, 10 017, 16 018, 1 019, 40 020, 20 021, 31 022, 10 023, 16 024, 1

12c platinum

ALG KEYSTROKES

fs fCLEARÎ :5 z :6 + :4

-

1

~ b ³ g(000 :3 :1 :2 ~

- ~ b ³ t g(027 ~ z ~

DISPLAY

000, 001, 45 5 002, 10 003, 45 6 004, 40 005, 45 4 006, 30 007, 1 008, 34 009, 25 010, 36 011,43,33,000 012, 45 3 013, 45 1 014, 45 2 015, 34 016, 30 017, 34 018, 25 019, 36 020, 31 021,43,33,027 022, 34 023, 10 024, 34

62 Investment Analysis

12c platinum / 12C

RPN KEYSTROKES

+ :0

§

g(000 z Þ :1 + :1 z :0

§

g(000 :5 :6 z

-

g(000 :4

-

:6

§

g(000 fs

REGISTERS

n: Unused i: Unused PV: Unused PMT: Unused FV: Unused R0: 100 R1: list price R2: % discount R3: mfg. cost R4: % op. exp. R5: % net profit R6: 1-% tax R7-R.3: Unused

Program Instructions:

1.

Key in the program and press fCLEARH, then key in 100 and press ?0.

2.

RPN: Key in 1 and press \, then key in your appropriate tax rate as a decimal and press -?6.

2.

ALG: Key in 1 and press -, then key in your appropriate tax rate as a decimal and press ³?6.

3. a.

Key in the list price in dollars (if known) and press ?1.

b.

Key in the discount in percent (if known) and press ?2.

c.

Key in the manufacturing cost in dollars (if known) and press ?3.

d.

Key in the operating expense in percent (if known) and press ?4.

e.

Key in the net profit after tax in percent (if known) and press ?5.

DISPLAY

025, 40 026, 45 0 027, 20 028,43,33,000 029, 10 030, 16 031, 45 1 032, 40 033, 45 1 034, 10 035, 45 0 036, 20 037,43,33,000 038, 45 5 039, 45 6 040, 10 041, 30 042,43,33,000 043, 45 5 044, 30 045, 45 6 046, 20 047,43,33,000

12c platinum

ALG KEYSTROKES

³ :1 ~ à Þ g(000 :5 z :6

- ~ ~ ³ g(000

- :4

§ :6 ³ g(000 fs

DISPLAY

025, 36 026, 45 1 027, 34 028, 24 029, 16 030,43,33,000 031, 45 5 032, 10 033, 45 6 034, 30 035, 34 036, 34 037, 36 038,43,33,000 039, 30 040, 45 4 041, 20 042, 45 6 043, 36 044,43,33,000

Investment Analysis 63

4. To calculate list price: a. Do steps 2 and 3b, c, d, e above.

b.

RPN: Press :3tz1g(014tzg(000.

b.

ALG: Press :3t~z~³1g(014t ~z~ ³g(000.

5. To calculate discount: a. Do steps 2 and 3a, c, d, e above.

b.

RPN: Press :3tg(029t.

b.

ALG: Press :3tg(022t.

6. To calculate manufacturing cost: a. Do steps 2 and 3a, b, d, e, above.

b.

RPN: Press g(013tg(001t§.

b.

ALG: Press g(013tg(001t§~³.

7. To calculate operating expense: a. Do steps 2 and 3a, b, c, e, above.

b.

RPN: Press g(012ttg(038t.

b.

ALG: Press g(012ttg(031t.

8. To calculate net profit after tax: a. Do steps 2 and 3a, b, c, d, above.

b.

RPN: Press g(012ttg(043t.

b.

ALG: Press g(012ttg(039t.

Example: What is the net return on an item that is sold for $11.98, discounted through

distribution an average of 35% and has a manufacturing cost of $2.50? The standard company operating expense is 32% of net shipping (sales) price and tax rate is 48%.

12c platinum / 12C

RPN Keystrokes

fCLEARH fCLEARH 100?0 100?0 1\.48-?6 1-.48³?6

11.98?1 11.98?1 35?2 35?2

2.50?3 2.50?3 32?4 32?4

g(012tt g(012tt g(043t g(039t

12c platinum

ALG Keystrokes

Display Comments

100.00

0.52

11.98

35.00

2.50

32.00

67.90

18.67

48% tax rate. List price ($). Discount (%). Manufacturing cost ($). Operating expenses (%).

Net profit (%).

64 Investment Analysis

If manufacturing expenses increase to $3.25, what is the effect on net profit?

12c platinum / 12C

RPN Keystrokes

3.25?3 3.25?3

g(012tt g(012tt g(043t g(039t

If the manufacturing cost is maintained at $3.25, how high could the overhead (operating expense) be before the product begins to lose money?

12c platinum

ALG Keystrokes

Display Comments

3.25

58.26

13.66

Manufacturing cost.

Net profit reduced to 13.66%

12c platinum / 12C

RPN Keystrokes

0?5 0?5 g(012tt g(012tt g(038t g(031t

At 32% operating expense and $3.25 manufacturing cost, what should the list price be to generate 20% net profit?

12c platinum

ALG Keystrokes

Display Comments

0.00

58.26

Maximum operating expense (%).

12c platinum / 12C

RPN Keystrokes

20?5 20?5 :3tz :3t~z~³ 1g(014tz 1g(014t~z~³

What reduction in manufacturing cost would achieve the same result without necessitating an increase in list price above $11.98?

12c platinum

ALG Keystrokes

Display Comments

20.00

11.00

16.93

List price ($).

12c platinum / 12C

RPN Keystrokes

g(013t g(013t g(001t§ g(001t§~³

12c platinum

ALG Keystrokes

Display Comments

7.79

2.30

Manufacturing cost ($).

Securities and Options

After-Tax Yield

The following HP 12C Platinum program calculates the after-tax yield to maturity of a bond held for more than one year. The calculation assumes an actual/actual day basis. For after-tax computations, the interest or coupon payments are considered income, while the difference between the bond's face value and its purchase price is considered capital gains.

12c platinum / 12C

RPN KEYSTROKES

fs fCLEARÎ fCLEARG ?7 d ?6 :2 :1

:4 b :2 ~

Æ

2

z ?0 :3 :5 b

:0 z P :1 :0 z $ :6 :7

65

DISPLAY

000, 001, 42 34 002, 44 7 003, 33 004, 44 6 005, 45 2 006, 45 1 007, 30 008, 45 4 009, 25 010, 45 2 011, 34 012, 30 013, 26 014, 2 015, 10 016, 44 0 017, 45 3 018, 45 5 019, 25 020, 30 021, 45 0 022, 10 023, 14 024, 45 1 025, 45 0 026, 10 027, 13 028, 45 6 029, 45 7

12c platinum

ALG KEYSTROKES

fs fCLEARÎ fCLEARG ?7 d ?6 :2

- :1

- :4 b + :1 ³ b ?0 :3

- :5

b z :0 P :1 z :0 $ :6 :7 fS

DISPLAY

000, 001, 42 34 002, 44 7 003, 33 004, 44 6 005, 45 2 006, 30 007, 45 1 008, 30 009, 45 4 010, 25 011, 40 012, 45 1 013, 36 014, 25 015, 44 0 016, 45 3 017, 30 018, 45 5 019, 25 020, 10 021, 45 0 022, 14 023, 45 1 024, 10 025, 45 0 026, 13 027, 45 6 028, 45 7 029, 42 22

66 Securities and Options

12c platinum / 12C

RPN KEYSTROKES

fS g(000 fs

DISPLAY

030, 42 22 031,43,33,000

REGISTERS

12c platinum

ALG KEYSTROKES

g(000 fs

DISPLAY

030,43,33,000

n: Unused i: Yield PV: Used PMT: Used FV: 0 R0: Used R1: Purchase price R2: Sales price R3: Coupon rate R4: Capital rate R5: Income rate R6: Used R7: Used R8-R.5: Unused

Program Instructions:

1. Key in the program.

2.

Key in the purchase price and press ?1.

3.

Key in the sales price and press ?2.

4.

Key in the annual coupon rate (as a percentage) and press ?3.

5.

Key in capital gains tax rate (as a percentage) and press ?4.

6.

Key in the income tax rate (as a percentage) and press ?5.

7.

Press gÕ.

8.

Key in the purchase date (MM.DDYYYY) and press \(³).

9.

Key in the assumed sell date (MM.DDYYYY) and press t to find the after-tax yield (as a percentage).

10. For the same bond but different date return to step 8.

11. For a new case return to step 2.

Example: You can buy a 7% bond on October 1, 2003 for $70 and expect to sell it in 5 years for $90. What is your net (after-tax) yield over the 5-year period if interim coupon payments are considered as income, and your tax bracket is 50%?

(One-half of the long term capital gain is taxable at 50%, so the tax on capital gains alone is 25%)

12c platinum / 12C

RPN Keystrokes

70?1 70?1 90?2 90?2 7?3 7?3 25?4 25?4 50?5 50?5 gÕ gÕ

10.012003\ 10.012003³

10.012008t 10.012008t

12c platinum

ALG Keystrokes

Display Comments

70.00

90.00

7.00

25.00

50.00

10.01

8.53

Purchase price. Selling price. Annual coupon rate. Capital gains tax rate. Income tax rate.

Purchase Date. % after tax yield.

Securities and Options 67

Discounted Notes

A note is a written agreement to pay a sum of money plus interest at a certain rate. Notes do not have periodic coupons, since all interest is paid at maturity.

A discounted note is a note that is purchased below its face value. The following HP 12C Platinum program finds the price and/or yield

12c platinum / 12C

RPN KEYSTROKES

fs fCLEARÎ :1 :2 gÒ :3 z :5 b

1

~

:4

§ ?5 t :1 :2 gÒ :3 ~

z :4 :5 z

1

-

§ Æ

2

§ g(000 fs

DISPLAY

000, 001, 45 1 002, 45 2 003, 43 26 004, 45 3 005, 10 006, 45 5 007, 25 008, 1 009, 34 010, 30 011, 45 4 012, 20 013, 44 5 014, 31 015, 45 1 016, 45 2 017, 43 26 018, 45 3 019, 34 020, 10 021, 45 4 022, 45 5 023, 10 024, 1 025, 30 026, 20 027, 26 028, 2 029, 20 030,43,33,000

*

The yield is a reflection of the return on an investment.

*

of a discounted note.

12c platinum

ALG KEYSTROKES

fs fCLEARÎ :1 :2 gÒ z :3

§ :5 ³ :4

- ~ b ³ ?5 t :1 :2 gÒ :5

:4 à ~ d z ~

§ :3 ³ g(000 fs

DISPLAY

000, 001, 45 1 002, 45 2 003, 43 26 004, 10 005, 45 3 006, 20 007, 45 5 008, 36 009, 45 4 010, 30 011, 34 012, 25 013, 36 014, 44 5 015, 31 016, 45 1 017, 45 2 018, 43 26 019, 45 5 020, 45 4 021, 24 022, 34 023, 33 024, 10 025, 34 026, 20 027, 45 3 028, 36 029,43,33,000

68 Securities and Options

n: Unused i: Unused PV: Unused PMT: Unused FV: Unused R0: Unused R1: Settl. date R2: Mat. Date R3: 360 or 360 R4: redemp. Value R5: dis./price R6-R.5: Unused

Program Instructions:

1. Key in the program.

2.

Press gÕ.

3.

Key in the settlement date (MM.DDYYYY) and press ?1.

4.

Key in the maturity date (MM.DDYYYY) and press ?2.

5.

Key in the number of days in a year (360 or 365) and press ?3.

6.

Key in the redemption value per $100 and press ?4.

7. To calculate the purchase price: a. Key in the discount rate and press ?5. b. Press t to calculate the purchase price. c. Press t to calculate the yield.

d. For a new case, go to step 3.

8. To calculate the yield when the price is known: a. Key in the price and press ?5. b. RPN: Press g(015t to calculate the yield. b. ALG: Press g(016t to calculate the yield.

c. For a new case, go to step 3.

Example 1: Calculate the price and yield on this bill: settlement date October 8, 2002; maturity date March 21, 2003; discount rate 7.80%. Compute on a 360 day basis.

REGISTERS

12c platinum / 12C

RPN Keystrokes

gÕ gÕ

10.082002?1 10.082002?1

3.212003?2 3.212003?2

360?3 360?3 100?4 100?4

7.8?5 7.8?5

t t t t

12c platinum

ALG Keystrokes

Display Comments

10.08

3.21

360.00

100.00

7.80

96.45

8.09

Settlement date. Maturity date. 360 day basis. Redemption value per $100. Discount rate. Price. Yield.

Securities and Options 69

Example 2: Determine the yield of this security; settlement date June 25, 2002; maturity date September 10, 2002; price $99.45; redemption value $101.33. Assume 360 day basis.

12c platinum / 12C

RPN Keystrokes

6.252002?1 6.252002?1

9.102002?2 9.102002?2 360?3 360?3

101.33?4 101.33?4

99.45?5 99.45?5 g(015t g(016t

12c platinum

ALG Keystrokes

Display Comments

6.25

9.10

360.00

101.33

99.45

8.84

Settlement date. Maturity date. 360 day basis. Redemption value per $100. Price. Yield.

Black-Scholes Formula for Valuing European Options

This program implements the Black-Scholes formula which has been used extensively in option markets worldwide since its publication in the early 1970’s. The five inputs are simply keyed into the five financial variables and then t displays the call option value, and ~ shows the put option value. The option values produced are accurate to at least the nearest cent for asset and strike prices under $100.

Reference: Hutchins, 2003, Black-Scholes takes over the HP12C, HPCC (www.hpcc.org) DataFile,V22,N3 pp13-21.

12c platinum / 12C

RPN KEYSTROKES

fs fCLEARÎ :n :¼ b Þ g> :M

§ ?4 ~ gr :P b ?3 :$ :4 z

DISPLAY

000, 001, 45 11 002, 45 12 003, 25 004, 16 005, 43 22 006, 45 15 007, 20 008, 44 4 009, 34 010, 43 21 011, 45 14 012, 25 013, 44 3 014, 45 13 015, 45 4 016, 10

12c platinum

ALG KEYSTROKES

fs fCLEARÎ :n

§ :¼ b ³ Þ g>

§ :M ³ ?4 :n gr

§ :P b

DISPLAY

000, 001, 45 11 002, 20 003, 45 12 004, 25 005, 36 006, 16 007, 43 22 008, 20 009, 45 15 010, 36 011, 44 4 012, 45 11 013, 43 21 014, 20 015, 45 14 016, 25

70 Securities and Options

12c platinum / 12C

RPN KEYSTROKES

g° ~ z gF

2

?5 z + ?6 :3

-

?3 \

§

gr gF

2

z Þ g> ~

3 . 0 0 6 z 1

+ y

§

gF gF

1 8 7

§

2 4

-

§

8 7

+

DISPLAY

017, 43 23 018, 34 019, 10 020, 43 40 021, 2 022, 44 5 023, 10 024, 40 025, 44 6 026, 45 3 027, 30 028, 44 3 029, 36 030, 20 031, 43 21 032, 43 40 033, 2 034, 10 035, 16 036, 43 22 037, 34 038, 3 039, 48 040, 0 041, 0 042, 6 043, 10 044, 1 045, 40 046, 22 047, 20 048, 43 40 049, 43 40 050, 1 051, 8 052, 7 053, 20 054, 2 055, 4 056, 30 057, 20 058, 8 059, 7 060, 40

12c platinum

ALG KEYSTROKES

³ ?3 :$ z :4 ³ g° z ~ ³ :3 z

2

?5 + ~

- ?6 :3 ³ ?3 g’ z

2

³ Þ g> :3 g’ gr z

3 . 0 0 6 + 1

³ y ?2

§ ~ ³

DISPLAY

017, 36 018, 44 3 019, 45 13 020, 10 021, 45 4 022, 36 023, 43 23 024, 10 025, 34 026, 36 027, 45 3 028, 10 029, 2 030, 44 5 031, 40 032, 34 033, 30 034, 44 6 035, 45 3 036, 36 037, 44 3 038, 43 20 039, 10 040, 2 041, 36 042, 16 043, 43 22 044, 45 3 045, 43 20 046, 43 21 047, 10 048, 3 049, 48 050, 0 051, 0 052, 6 053, 40 054, 1 055, 36 056, 22 057, 44 2 058, 20 059, 34 060, 36

Securities and Options 71

12c platinum / 12C

RPN KEYSTROKES

§ .

2

b :3 ~ ?3 O ~ go g(077

1

?-3 Þ ?§3 ~ :5 gm g(089 :6 :3 :4

§ ?6 O ?5 ~ g(028 ~ :3 :$ ?-4

§ :6

- ?+4 :4 ~ ?5 fs

DISPLAY

061, 20 062, 48 063, 2 064, 25 065, 45 3 066, 34 067, 44 3 068, 35 069, 34 070, 43 34 071,43,33,077 072, 1 073,44 30 3 074, 16 075,44 20 3 076, 34 077, 45 5 078, 43 35 079,43,33,089 080, 45 6 081, 45 3 082, 45 4 083, 20 084, 44 6 085, 35 086, 44 5 087, 34 088,43,33,028 089, 34 090, 45 3 091, 45 13 092,44 30 4 093, 20 094, 45 6 095, 30 096,44 40 4 097, 45 4 098, 34 099, 44 5

12c platinum

ALG KEYSTROKES

1 8 7

§ :2

-

2 4

§ :2 +

8 7

§ ~

§ .

2

b ³ :3 ~ ?3 O ~ go g(093

1

?-3 Þ ?§3 ~ :5 gm g(106 :6 :3

§ :4 ³

DISPLAY

061, 1 062, 8 063, 7 064, 20 065, 45 2 066, 30 067, 2 068, 4 069, 20 070, 45 2 071, 40 072, 8 073, 7 074, 20 075, 34 076, 20 077, 48 078, 2 079, 25 080, 36 081, 45 3 082, 34 083, 44 3 084, 35 085, 34 086, 43 34 087,43,33,093 088, 1 089,44 30 3 090, 16 091,44 20 3 092, 34 093, 45 5 094, 43 35 095,43,33,106 096, 45 6 097, 45 3 098, 20 099, 45 4 100, 36

72 Securities and Options

12c platinum / 12C

RPN KEYSTROKES

n: Term to expiry i: Interest rate (%) PV: Stock price PMT: Volatility (%) FV: Strike price R0: Unused R1: Unused R2: Unused R3: N(d1) R4: Put value R5: Call value R6: Q·N(d2) R7-R.9: Unused

Note: The n, i and PMT values must all be based on the same time unit (for example: n is

measured in years or months and i and PMT are rates per year or per month). i is a continuous percentage rate. PMT is the standard deviation of the continuous percentage stock return (as observed over the time unit). For sensible output, all inputs should be positive. The PMT=0 case can be simulated by using a PMT arbitrarily close to 0.

Program Instructions

1. Key in the program.

2. Enter the five inputs into the five financial registers. These values are preserved by the program. a. Key in the unexpired term of the option and press n. b. Key in the risk-free interest rate as a percentage and press ¼. c. Key in the current (or spot) stock price and press $. d. Key in the volatility assumption as a percentage and press P. e. Key in the strike price and press M.

3.

Press R/S. The Call value is displayed. Press ~ to see the Put value.

DISPLAY

REGISTERS

12c platinum

ALG KEYSTROKES

?6 O ?5 ~ g(037 ~ :$ ?-4

§ :3

- :6 ³ ?+4 :4 ~ ?5 g(000 fs

DISPLAY

101, 44 6 102, 35 103, 44 5 104, 34 105,43,33,037 106, 34 107, 45 13 108,44 30 4 109, 20 110, 45 3 111, 30 112, 45 6 113, 36 114,44 40 4 115, 45 4 116, 34 117, 44 5 118,43,33,000

Securities and Options 73

Example 1: An option has 6 months to run and a strike price of $45. Find Call and Put values assuming a spot price of $52, return volatility of 20.54% per month and a risk-free interest rate of ½% per month. Show how to re-scale n, i and PMT to use a yearly time unit, and how to re-scale them back again to the original monthly basis.

12c platinum / 12C

RPN Keystrokes

6n 6n .5¼ .5¼ 52$ 52$

20.54P 20.54P 45M 45M

t t ~ ~ :gAn :gAn :gC¼ :gC¼ :P 12gr§P t t :ngA :ngA :¼gC :¼gC :P 12grzP

The next example is Example 12.7 from Options, Futures, and Other Derivatives (5th Edition) by John C. Hull (Prentice Hall, 2002).

Example 2: The stock price six months from the expiration of an option is $42, the exercise price of the option is $40, the risk-free interest rate is 10% per annum, and the volatility is 20% per annum. Find Call and Put values.

12c platinum / 12C

RPN Keystrokes

.5n .5n 10¼ 10¼ 42$ 42$ 20P 20P 40M 40M

t t ~ ~

12c platinum

ALG Keystrokes

:P§ 12grP

:Pz 12grP

12c platinum

ALG Keystrokes

Display Comments

6.00

0.50

52.00

20.54

45.00

14.22

5.89

0.50

6.00

71.15

14.22

6.00

0.50

20.54

Display Comments

0.50

10.00

42.00

20.00

40.00

4.76

0.81

Time to expiry (months). Interest rate (% per month). Stock price. Volatility (% per month). Strike price. Call value. Put value. Years to expiry. Yearly interest rate %.

Yearly volatility %. Call value (unchanged). Months to expiry. Monthly interest rate %.

Monthly volatility %.

Time to expiry (years). Interest rate (% per year). Stock price. Volatility (% per year). Strike price. Call value. Put value.

Forecasting

Simple Moving Average

Moving averages are often useful in recording of forecasting sales figures, expenses or manufacturing volume. There are many different types of moving average calculations. An often used, straightforward method of calculation is presented here.

In a moving average a specified number of data points are averaged. When there is a new piece of input data, the oldest piece of data is discarded to make room for the latest input. This replacement scheme makes the moving average a valuable tool in following trends. The fewer the number of data points, the more trend sensitive the average becomes. With a large number of data points, the average behaves more like a regular average, responding slowly to new input data.

A simple moving average may be calculated with your HP 12C Platinum as follows.

1.

Press fCLEARH.

2. Key in the first m data points (where m is the number of data points in the average) and press _ after each entry.

3.

Press gÖ to obtain the first average.

4.

Key in the oldest (first value) entered in step 2 and press g^.

5.

Key in the newest data point (m + 1) and press _.

6.

Press gÖ to obtain the next value of the moving average.

7. Repeat steps 4 through 5 for the remaining data.

Example 1: An electronics sales firm wished to calculate a 3-month moving average for the dollar volume of components sold each month. Sales for the first six months of this year were:

January $211,570 April 131,760 February 112,550 May 300,500 March 190,060 June 271,120

12c platinum / 12C

RPN Keystrokes

fCLEARH fCLEARH 211570_ 211570_ 112550_ 112550_ 190060_ 190060_ gÖ gÖ

74

12c platinum

ALG Keystrokes

Display Comments

0.00

1.00

2.00

3.00 171,393.33

3-month average for March.

Forecasting 75

12c platinum / 12C

RPN Keystrokes

211570g^ 211570g^ 131760_ 131760_ gÖ gÖ 112550g^ 112550g^ 300500_ 300500_ gÖ gÖ 190060g^ 190060g^ 271120_ 271120_ gÖ gÖ

For repeated calculations the following HP 12C Platinum program can be used for up to a 12 element moving average:

12c platinum

ALG Keystrokes

Display Comments

2.00

3.00 144,790.00

2.00

3.00 207,440.00

2.00

3.00 234,460.00

3-month average for April.

3-month average for May.

3-month average for June.

12c platinum / 12C

RPN KEYSTROKES

fs fCLEARÎ :1 :2 ?1 + :3 ?2 +3 :4 ?3 +4 :5 ?4 +5 :6 ?5 +6 :7 ?6 +7 :8 ?7 +8 :9 ? +9 :.0

DISPLAY

000, 001, 45 1 002, 45 2 003, 44 1 004, 40 005, 45 3 006, 44 2 007, 40 008, 45 4 009, 44 3 010, 40 011, 45 5 012, 44 4 013, 40 014, 45 6 015, 44 5 016, 40 017, 45 7 018, 44 6 019, 40 020, 45 8 021, 44 7 022, 40 023, 45 9 024, 44 8 025, 40 026,45 48 0

12c platinum

ALG KEYSTROKES

fs fCLEARÎ :1 + :2 ?1 + :3 ?23 + :4 ?34 + :5 ?45 + :6 ?56 + :7 ?67 + :8 ?78 + :9 ?89 +

DISPLAY

000, 001, 45 1 002, 40 003, 45 2 004, 44 1 005, 40 006, 45 3 007, 44 2 008, 40 009, 45 4 010, 44 3 011, 40 012, 45 5 013, 44 4 014, 40 015, 45 6 016, 44 5 017, 40 018, 45 7 019, 44 6 020, 40 021, 45 8 022, 44 7 023, 40 024, 45 9 025, 44 8 026, 40

76 Forecasting

12c platinum / 12C

RPN KEYSTROKES

?9 +10 :.1 ?.0 +11 :.2 ?.1 +12 :0 z t ?m* g(001 fs

DISPLAY

027, 44 9 028, 40 029,45 48 1 030,44 48 0 031, 40 032,45 48 2 033,44 48 1 034, 40 035, 45 0 036, 10 037, 31 038, 44 -039,43,33,001

12c platinum

ALG KEYSTROKES

:.0 ?910 + :.1 ?.011 + :.2 ?.112 z :0 ³ t

*

?m g(001 fs

DISPLAY

027,45 48 0 028, 44 9 029, 40 030,45 48 1 031,44 48 0 032, 40 033,45 48 2 034,44 48 1 035, 10 036, 45 0 037, 36 038, 31 039, 44 -040,43,33,001

REGISTERS

n: Unused i: Unused PV: Unused PMT: Unused FV: Unused R0: m R R3: X3 R R7: X7 R R.1: X11 R

: X4 R

4

: X8 R

8

: X12 R

.2

: X1 R

1

: X5 R

5

: X9 R

9

: Unused

.3-R.4

: X2

2

: X6

6

.0

: X.0

This program can be used for a moving average of 2 to 12 elements. It may be shortened considerably for moving averages with less than 12 elements. To do this, key in the program, as shown, from line 01 until you reach a + (ALG: a ? command) superscripted with the number of elements you desire. Key in this line, then skip the rest of the program down to line 35. Then key in lines 035 through 039 (ALG:040), being sure to specify the register number at line 038 (ALG:039), ? m, corresponding to the number of elements you are using. (For instance, for a 5 element moving average, key in lines 01 through 13 then go to line 35 in the listing and key in the balance of the program. Obviously the program listing line 38 (ALG:039), ? m becomes the displayed line 017, ?5 in RPN and 018, ?5 in ALG).

*

At step 038 (ALG:039), m=number of elements in the moving average, i.e. for a 5 element moving

average line 038 (ALG:039) would be ?5 and for a 12 element average line 38 (ALG:039) would be ?.2

Forecasting 77

Program Instructions:

1. Key in the program.

2.

Press fCLEARH. Key in the number of elements, m, and press ?0.

3.

Key in the first data point and press ?1.

4.

Key in the second data point and press ?2.

5. Continue as above, keying in and storing each data point in its appropriate register until m data points have been stored.

6.

Press g(000t to calculate the first moving average.

7.

Key in the next data point and press t to calculate the next moving average.

8. Repeat step 7 for each new data point.

Example 2: Calculate the 3-element moving average for the data given in example 1. Your modified program listing will look like this:

12c platinum / 12C

RPN KEYSTROKES

fs fCLEARÎ :1 :2 ?1 + :3 ?2 + :0 z

t ?3 g(001 fs

12c platinum / 12C

RPN Keystrokes

fCLEARH fCLEARH 3?0 3?0 211570?1 211570?1 112550?2 112550?2 190060?3 190060?3 g(000t g(000t 131760t 131760t

DISPLAY

000, 001, 45 1 002, 45 2 003, 44 1 004, 40 005, 45 3 006, 44 2 007, 40 008, 45 0 009, 10 010, 31 011, 44 3 012,43,33,001

12c platinum

ALG Keystrokes

12c platinum

ALG KEYSTROKES

fs fCLEARÎ :1 + :2 ?1 + :3 ?2 z :0

³ t ?3 g(001 fs

Display Comments

0.00

3.00 211,570.00 112,550.00 190,060.00 171,393.33 144,790.00

3-month average for March. 3-month average for April.

DISPLAY

000, 001, 45 1 002, 40 003, 45 2 004, 44 1 005, 40 006, 45 3 007, 44 2 008, 10 009, 45 0 010, 36 011, 31 012, 44 3 013,43,33,001

78 Forecasting

12c platinum / 12C

RPN Keystrokes

300500t 300500t 271120t 271120t

12c platinum

ALG Keystrokes

Display Comments

207,440.00 234,460.00

3-month average for May. 3-month average for June.

Seasonal Variation Factors Based on Centered Moving Averages

Seasonal variation factors are useful concepts in many types of forecasting. There are several methods of developing seasonal moving averages, on the of more common ways being to calculate them as a ratio of the periodic value to a centered moving average for the same period.

For instance, to determine the sales for the 3rd quarter of a given year a centered moving average for that quarter would be calculated from sales figures from the 1st, 2nd, 3rd and 4th quarters of the year and the 1st quarter of the following year. The seasonal variation factor for that 3rd quarter would then be the ratio of the actual sales in the 3rd quarter to the centered moving average for that quarter.

While quarterly seasonal variations are commonly used, the HP 12C Platinum can also be programmed to calculate monthly seasonal variations using a centered 12 month moving average. Programs for both of these calculations are represented here:

An HP 12C Platinum program to calculate the quarterly seasonal variations based on a centered 4-point moving average is:

12c platinum / 12C

RPN KEYSTROKES

fs fCLEARÎ :1

2

z :2 ?1 + :3 ?2 + :4 ?3 + :5 ?4

2

z +

DISPLAY

000, 001, 45 1 002, 2 003, 10 004, 45 2 005, 44 1 006, 40 007, 45 3 008, 44 2 009, 40 010, 45 4 011, 44 3 012, 40 013, 45 5 014, 44 4 015, 2 016, 10 017, 40

12c platinum

ALG KEYSTROKES

fs fCLEARÎ :1 z

2

+ :2 ?1 + :3 ?2 + :4 ?3 ³ :5 ?4 z

2

DISPLAY

000, 001, 45 1 002, 10 003, 2 004, 40 005, 45 2 006, 44 1 007, 40 008, 45 3 009, 44 2 010, 40 011, 45 4 012, 44 3 013, 36 014, 45 5 015, 44 4 016, 10 017, 2

Forecasting 79

12c platinum / 12C

RPN KEYSTROKES

4

z t :2

Z t ?5 g(001 fs

DISPLAY

018, 4 019, 10 020, 31 021, 45 2 022, 23 023, 31 024, 44 5

025,43,33,001

12c platinum

ALG KEYSTROKES

+ ~ z

4

³ t :2 Z t ?5 g(001 fs

DISPLAY

018, 40 019, 34 020, 10 021, 4 022, 36 023, 31 024, 45 2

025, 23 026, 31 027, 44 5 028,43,33,001

REGISTERS

n: Unused i: Unused PV: Unused PMT: Unused FV: Unused R0: n R R3: X3 R

: X4 R

4

: X1 R

1

: X5 R

5

: X2

2

6-R.6

: Unused

Program Instructions:

1. Key in the program.

2.

Press fCLEARH.

3. Key in the quarterly sales figures starting with the first quarter: a. Key in 1st quarter sales and press ?1. b. Key in 2nd quarter sales and press ?2. c. Key in 3rd quarter sales and press ?3. d. Key in 4th quarter sales and press ?4. e. Key in the 1st quarter sales for the next year and press ?5.

4.

Press g(000t to calculate the centered moving average for the 3rd quarter of the first year.

5.

Press t to calculate the seasonal variation for this quarter.

6.

Key in the next quarter's sales and press t to calculate the moving average for the next quarter.

7.

Press t to calculate the seasonal variation.

8. Repeat steps 6 and 7 for the balance of the data.

80 Forecasting

Example: Econo-Wise Home Appliance Company had quarterly sales for the years 2000 thru 2002 as follows:

Sales (IN $K)

Quarterly 1st 2nd 3rd 4th

2000 397 376 460 501 2001 455 390 530 560 2002 513 434 562 593

Find the centered 4-quarter moving average and seasonal variation factor for each quarter.

12c platinum / 12C

RPN Keystrokes

fCLEARH fCLEARH 397?1 397?1 376?2 376?2 460?3 460?3 501?4 501?4 455?5 455?5

g(000t g(000t

t t 390t 390t t t 530t 530t t t 560t 560t t t 513t 513t t t 434t 434t t t 562t 562t t t 593t 593t t t

Now, what is the average of each quarter's seasonal variation for the two years?

12c platinum

ALG Keystrokes

Display Comments

0.00

397.00

376.00

460.00

501.00

455.00

440.75

Centered 4-element average for 3rd quarter, 2000.

104.37

449.75

111.40

460.25

98.86

476.38

81.87

491.00

107.94

503.75

111.17

513.25

99.95

521.38

83.24

Seasonal variation factor. 4th quarter, 2000.

1st quarter, 2001.

2nd quarter, 2001.

3rd quarter, 2001.

4th quarter, 2001.

1st quarter, 2002.

2nd quarter, 2002.

12c platinum / 12C

RPN Keystrokes

fCLEAR² fCLEAR²

98.86_ 98.86_

99.95_ 99.95_ gÖ gÖ

12c platinum

ALG Keystrokes

Display Comments

0.00

1.00

2.00

99.41

1st quarter average seasonal variation, %.

Forecasting 81

12c platinum / 12C

RPN Keystrokes

fCLEAR² fCLEAR²

81.87_ 81.87_

83.24_ 83.24_

gÖ gÖ

fCLEAR² fCLEAR²

104.37_ 104.37_

107.94_ 107.94_

gÖ gÖ

fCLEAR² fCLEAR²

111.4_ 111.4_

111.17_ 111.17_

gÖ gÖ

An HP 12C Platinum program to calculate a centered 12 month moving average and seasonal variation factor is as follows:

12c platinum

ALG Keystrokes

Display Comments

0.00

1.00

2.00

82.56

0.00

1.00

2.00

106.16

0.00

1.00

2.00

111.29

2nd quarter average seasonal variation, %.

3rd quarter average seasonal variation, %.

4th quarter average seasonal variation, %.

12c platinum / 12C

RPN KEYSTROKES

fs fCLEARÎ :1

2

z :2 ?1 + :3 ?2 + :4 ?3 + :5 ?4 + :6 ?5 + :7 ?6

DISPLAY

000, 001, 45 1 002, 2 003, 10 004, 45 2 005, 44 1 006, 40 007, 45 3 008, 44 2 009, 40 010, 45 4 011, 44 3 012, 40 013, 45 5 014, 44 4 015, 40 016, 45 6 017, 44 5 018, 40 019, 45 7 020, 44 6

12c platinum

ALG KEYSTROKES

fs fCLEARÎ :1 z

2

+ :2 ?1 + :3 ?2 + :4 ?3 + :5 ?4 + :6 ?5 + :7

DISPLAY

000, 001, 45 1 002, 10 003, 2 004, 40 005, 45 2 006, 44 1 007, 40 008, 45 3 009, 44 2 010, 40 011, 45 4 012, 44 3 013, 40 014, 45 5 015, 44 4 016, 40 017, 45 6 018, 44 5 019, 40 020, 45 7

82 Forecasting

12c platinum / 12C

RPN KEYSTROKES

+ :8 ?7 + :9 ?8 + :.0 ?9 + :.1 ?.0 + :.2 ?.1 + :.3 ?.2

2

z + :0 z t :6 Z t ?.3 g(001 fs

DISPLAY

021, 40 022, 45 8 023, 44 7 024, 40 025, 45 9 026, 44 8 027, 40 028,45 48 0 029, 44 9 030, 40 031,45 48 1 032,44 48 0 033, 40 034,45 48 2 035,44 48 1 036, 40 037,45 48 3 038,44 48 2 039, 2 040, 10 041, 40 042, 45 0 043, 10 044, 31 045, 45 6 046, 23 047, 31 048,44 48 3 048,43,33,001

12c platinum

ALG KEYSTROKES

?6 + :8 ?7 + :9 ?8 + :.0 ?9 + :.1 ?.0 + :.2 ?.1 ³ :.3 ?.2 z

2

+ ~ z :0 ³ t :6 Z t ?.3 g(001 fs

DISPLAY

021, 44 6 022, 40 023, 45 8 024, 44 7 025, 40 026, 45 9 027, 44 8 028, 40 029,45 48 0 030, 44 9 031, 40 032,45 48 1 033,44 48 0 034, 40 035,45 48 2 036,44 48 1 037, 36 038,45 48 3 039,44 48 2 040, 10 041, 2 042, 40 043, 34 044, 10 045, 45 0 046, 36 047, 31 048, 45 6 049, 23 050, 31 051,44 48 3 052,43,33,001

REGISTERS

n: Unused i: Unused PV: Unused PMT: Unused FV: Unused R0: n R R3: X3 R R7: X7 R R.1: X11 R

: X4 R

4

: X8 R

8

: X12 R

.2

: X1 R

1

: X5 R

5

: X9 R

9

: X13

.3

: X2

2

: X6

6

: X10

.0

Forecasting 83

Program Instructions:

1. Key in the program.

2.

Press fCLEARH.

3.

Key in 12 and press ?0.

4. Key in the values for the first 13 months, storing them one at a time in registers 1 through .3; i.e. Key in the 1st month and press ?1. Key in the 2nd month and press ?2, etc., Key in the 10th month and press ?.0, etc., Key in the 13th month and press ?.3.

5.

Press g(000t to calculate the centered moving average for the 7th month.

6.

Press t to calculate the seasonal variation for that month.

7.

Key in the value for the next month (14th) and press t to calculate the moving average for the next month (8th).

8. Repeat steps 6 and 7 for the balance of the data.

These programs may be customized by the user for different types of centered moving averages. Inspection of the programs will show how they can be modified.

Gompertz Curve Trend Analysis

A useful curve for evaluating sales trends, etc., is the Gompertz curve. This is a "growth" curve having a general "S" shape and may be used to describe series of data where the early rate of growth is small, then accelerates for a period of time and then slows again as the time grows long. The sales curve for many products follow this trend during the introductory, growth and maturity phases.

The data points to be fit to a Gompertz curve should be equally spaced along the x (or time) axis and all the data points must be positive. The points are divided serially into 3 groups for data entry.

The following HP 12C Platinum program processes the data, fits it to a Gompertz curve and calculates estimated values for future data points. The 3 constants which characterize the curve are available to the user if desired.

12c platinum / 12C

RPN KEYSTROKES

fs fCLEARÎ g° ?+3 d

DISPLAY

000, 001, 43 23 002,44 40 3 003, 33

12c platinum

ALG KEYSTROKES

fs fCLEARÎ g° ?+3 d

DISPLAY

000, 001, 43 23 002,44 40 3 003, 33

84 Forecasting

12c platinum / 12C

RPN KEYSTROKES

g° ?+2 d g° ?+1

1

?+4 :4 g(000 :3 :2

:2 :1

z :4 y q ?6 :1 :3

§ :2 \

§

:1 :3 + :2

2

§

z :4 z g> ?7 :6

1

:6

DISPLAY

004, 43 23 005,44 40 2 006, 33 007, 43 23 008,44 40 1 009, 1 010,44 40 4 011, 45 4 012,43,33,000 013, 45 3 014, 45 2 015, 30 016, 45 2 017, 45 1 018, 30 019, 10 020, 45 4 021, 22 022, 21 023, 44 6 024, 45 1 025, 45 3 026, 20 027, 45 2 028, 36 029, 20 030, 30 031, 45 1 032, 45 3 033, 40 034, 45 2 035, 2 036, 20 037, 30 038, 10 039, 45 4 040, 10 041, 43 22 042, 44 7 043, 45 6 044, 1 045, 30 046, 45 6

12c platinum

ALG KEYSTROKES

g° ?+2 d g° ?+1

1

?+4 :4 g(000 :2

- :1 ³ ?8 :3

- :2 z ?9 ~ ³ q :4 y ³ ?6 :9

- :8 ³ :1

§ :3

- :2 g’ z ~ z :4 ³ g> ?7

DISPLAY

004, 43 23 005,44 40 2 006, 33 007, 43 23 008,44 40 1 009, 1 010,44 40 4 011, 45 4 012,43,33,000 013, 45 2 014, 30 015, 45 1 016, 36 017, 44 8 018, 45 3 019, 30 020, 45 2 021, 10 022, 44 9 023, 34 024, 36 025, 21 026, 45 4 027, 22 028, 36 029, 44 6 030, 45 9 031, 30 032, 45 8 033, 36 034, 45 1 035, 20 036, 45 3 037, 30 038, 45 2 039, 43 20 040, 10 041, 34 042, 10 043, 45 4 044, 36 045, 43 22 046, 44 7

Forecasting 85

12c platinum / 12C

RPN KEYSTROKES

:4 q

1

-

\

§

z :6 z :2 :1

-

§

g> ?5 t :6 ~ q :5 ~ q :7

§

g(062 fs

DISPLAY

047, 45 4 048, 21 049, 1 050, 30 051, 36 052, 20 053, 10 054, 45 6 055, 10 056, 45 2 057, 45 1 058, 30 059, 20 060, 43 22 061, 44 5 062, 31 063, 45 6 064, 34 065, 21 066, 45 5 067, 34 068, 21 069, 45 7 070, 20 071,43,33,062

12c platinum

ALG KEYSTROKES

:6 q :4

-

1

³ g’

1

- :6 y

§ :8 z ~ ³ g> ?5 t :6 q ~ ³ :5 q ~

§ :7 ³ g(065 fs

DISPLAY

047, 45 6 048, 21 049, 45 4 050, 30 051, 1 052, 36 053, 43 20 054, 1 055, 30 056, 45 6 057, 22 058, 20 059, 45 8 060, 10 061, 34 062, 36 063, 43 22 064, 44 5 065, 31 066, 45 6 067, 21 068, 34 069, 36 070, 45 5 071, 21 072, 34 073, 20 074, 45 7 075, 36 076,43,33,065

REGISTERS

n: Unused i: Unused PV: Unused PMT: Unused FV: Unused R0: Unused R1: S1 R R3: S3 R R7: c R

: n R

4

: Unused

8-R.0

: a R

5

: S2

2

: b

6

Program Instructions:

1.

Key in the program and press fCLEARH.

2. Divide the data points to be input into 3 equal consecutive groups. Label them Groups I, II and III for convenience.

86 Forecasting

3.

Key in the first point of group I and press \(³)

4.

Key in the first point of group II and press \(³).

5.

Key in the first point of group III and press t.

6. Repeat steps 3, 4, and 5 for the balance of the data in each group. After executing step 5 the display shows how many sets of data have been entered.

7.

To fit the data to a Gompertz curve, press g(013t . The resultant display is the curve constant "a". Constants "b" and "c" may be obtained by pressing :6 and :7 respectively. The display may need adjusting to see significant digits.

8.

To calculate a projected value, key in the number of the period and press t.

9. Repeat step 8 for each period desired.

Example: The X-presso Company marked a revolutionary new coffee brewing machine in 1990. Sales grew at a steady pace for several years, then began to slow. The sales records for the first 9 years of the product's life were as follows.

Year Sales($K) Year Sales($K)

1 18 6 260 2 41 7 282 3 49 8 322 4 151 9 340 5 188

What are the projected sales volumes for this product in its 10th and 12th year? What is the maximum yearly sales volume for this product if the present trend continues? What annual sales rate would the curve have predicted for the 5th year of the product's life? (Arrange the data as follows:)

Group I Group II Group III

18 151 282 41 188 322 49 260 340

12c platinum / 12C

RPN Keystrokes

fCLEARH fCLEARH 18\ 18³ 151\ 151³ 282t 282t 41\ 41³ 188\ 188³ 322t 322t 49\ 49³ 260\ 260³ 340t 340t

12c platinum

ALG Keystrokes

Display Comments

0.00

18.00

151.00

1.00

41.00

188.00

2.00

49.00

260.00

3.00

Total number of entries.

Forecasting 87

12c platinum / 12C

RPN Keystrokes

g(013t g(013t :6 :6 :7 :7

10t 10t 12t 12t 100t 100t

5t 5t

12c platinum

ALG Keystrokes

Display Comments

0.004

0.65

373.92

349.09

363.36

373.92

202.60

a b c Sales in 10th year, (in $K). Sales in 12th year, (in $K). Maximum annual sales (after very long product life). Sales in 5th year (actual sales were $188K).

Forecasting with Exponential Smoothing

A common method for analyzing trends in sales, inventory and securities is the moving average. Exponential smoothing is a version of the weighted moving average which is readily adaptable to programmable calculator forecasting.

Exponential smoothing is often used for short term sales and inventory forecasts. Typical forecast periods are monthly or quarterly. Unlike a moving average, exponential smoothing does not require a great deal of historical data. However , it should not be used with data which has more than a moderate amount of up or down trend.

When using exponential smoothing, a smoothing factor is chosen which affects the sensitivity of the average much the same way as the length of the standard moving average period. The correspondence between the two techniques can be represented by the formula:

α

where α is the exponential smoothing factor (with values from 0 to 1) and n is the length of the standard moving average. As the equation shows, the longer the moving average period, the smaller the equivalent and the less sensitive the average becomes to fluctuations in current values.

12+=n

88 Forecasting

Forecasting with exponential smoothing involves selecting the best smoothing factor based on historical data and then using the factor for updating subsequent data and forecasting. This procedure uses the following HP 12C Platinum program:

12c platinum / 12C

RPN KEYSTROKES

fs fCLEARÎ \ \ :6

-

\

§

?+4 gF t d d :0

§

:2 :1

§

+ :2 Þ ~ ?2 + :0

§

:1 :3

§

+ ?3 :1

§

:0 z :2 + ?5 :3

DISPLAY

000, 001, 36 002, 36 003, 45 6 004, 30 005, 36 006, 20 007,44 40 4 008, 43 40 009, 31 010, 33 011, 33 012, 45 0 013, 20 014, 45 2 015, 45 1 016, 20 017, 40 018, 45 2 019, 16 020, 34 021, 44 2 022, 40 023, 45 0 024, 20 025, 45 1 026, 45 3 027, 20 028, 40 029, 44 3 030, 45 1 031, 20 032, 45 0 033, 10 034, 45 2 035, 40 036, 44 5 037, 45 3

12c platinum

ALG KEYSTROKES

fs fCLEARÎ ?7

- :6 ³ t g’ ?+4 :7

§ :0 ³ :2

§ :1 + ~

- :2

§ ?+2 :0 ³ :3

§ :1 + ~ z ?3 :0 + :2

- ?6 :3 ³ ?5

DISPLAY

000, 001, 44 7 002, 30 003, 45 6 004, 36 005, 31 006, 43 20 007,44 40 4 008, 45 7 009, 20 010, 45 0 011, 36 012, 45 2 013, 20 014, 45 1 015, 40 016, 34 017, 30 018, 45 2 019, 20 020,44 40 2 021, 45 0 022, 36 023, 45 3 024, 20 025, 45 1 026, 40 027, 34 028, 10 029, 44 3 030, 45 0 031, 40 032, 45 2 033, 30 034, 44 6 035, 45 3 036, 36 037, 44 5

Forecasting 89

12c platinum / 12C

RPN KEYSTROKES

:0 z :2 + ?6 g(000 fs

DISPLAY

038, 45 0 039, 10 040, 45 2 041, 40 042, 44 6 043,43,33,000

12c platinum

ALG KEYSTROKES

:6 g(000 fs

DISPLAY

038, 45 6 039,43,33,000

REGISTERS

n: Unused i: Unused PV: Unused PMT: Unused FV: Unused R0: α R

R3: T

R

t-1

: Σe2 R

4

: 1-α R

1

: Dt

5

: S

2

t-1

ˆ

: D

R

t+1

6

R7-R.4: Unused

Program Instructions: Selecting the "best" smoothing constant (α ):

1.

Key in the program and press fCLEARH.

RPN Mode:

2.

Key in the number 1 and press \.

3.

Key in the "trial " and press ?0-?1.

ALG Mode:

2.

Key in the number 1 and press -.

3.

Key in the "trial " and press ?0³?1.

4.

Key in the first historical value (X

5.

Key in the second historical value (X

between the forecast value

6.

Press

t; the display shows the next forecast D

7.

Optional: Press

:5 to display the smoothed estimate of current demand.

8. Continue steps 5 and 6 for X When doing step 5 merely key in the value and press

9.

Press

:4. This value represents the cumulative forecasting error (∑e

value and the following additional values; press

10.

S

t-1

Press

), :3 (trend T

fCLEARH.

) and :6 (forecast D

t-1

) and press ?2.

1

) and press ?6t. The result is the error

2

Dˆ(

) and the true value (X

t+1

ˆ

(

, X4, ... Xn until all historical values have been entered.

3

t+2

).

t+1

).

t (do not press ?6).

2

). Record the

:0 (α), :2 (smoothed average

ˆ

).

t+1

11. Repeat steps 2 through 10 until a "best" α is selected based on the lowest cumulative forecasting error (Register 4).

90 Forecasting

Forecasting:

RPN Mode:

1.

Key in the number 1 and press

2.

Key in the selected α and press

ALG Mode:

1.

Key in the number 1 and press

2.

Key in the selected α and press

\.

?0-?1.

-. ?0³?1.

3. From the selection routine or from a previous forecast:

Key in the smoothed average S

Key in the trend T

Key in the forecast

4.

Key in the current data value and press

and press ?3.

t-1

ˆ

D

and press ?6.

t+1

and press ?2.

t-1

t. The output is the error in forecasting the

value just entered.

5.

Press

t. The displayed value represents the forecast for the next period.

6.

Record the following values:

use as initial values in the next forecast. You may also wish to record

:0 (α), :2 (S

), :3 (T

t-1

) and :6 Dˆ(

t-1

:5 (D

t

t+1

).

) for

7. Repeat steps 4, 5, and 6 for the next forecast if available.

Example: Select the best smoothing constant based on sales (in thousands of dollars) of

22, 23, 23, 25, 23, 27, 25. Given the current sales in month 8 of 26, forecast the following month.

Select the smoothing constant (α ):

12c platinum / 12C

RPN Keystrokes

fCLEARH fCLEARH 1\ 1.5?0- .5?0³ ?1 ?1 22?2 22?2 23?6t 23?6t t t 23tt 23tt 25tt 25tt 23tt 23tt 27tt 27tt 25tt 25tt

:4 :4 :0 :0

12c platinum

ALG Keystrokes

Display Comments

0.00

1.00

0.50

22.00

0.00

23.00

23.25

25.25

23.69

27.13

25.95

23.61

0.50

Cumulative error (∑e2). Smoothing constant (α ).

Forecasting 91

12c platinum / 12C

RPN Keystrokes

:2 :2 :3 :3

:6 :6

12c platinum

ALG Keystrokes

Display Comments

25.11

0.42

25.95

Smoothing average (S Trend (T

).

t-1

Last forecast Dˆ(

t+1

).

t-1

).

α

The procedure is repeated for several

's.

Smoothing Constant (α) .5 .1 .25 .2

Cumulative Error (Σe

For the selected α = .25 S

T

2

) 23.61 25.14 17.01 18.03

= 24.28

t+1

= 0.34

t-1

25.64

ˆ

D

=

t+1

Forecasting:

12c platinum / 12C

RPN Keystrokes

fCLEARH fCLEARH 1\ 1.25?0- .25?0³ ?1 ?1

24.28?2 24.28?2 .34?3 .34?3

25.64?6 25.64?6 26t 26t

t t :5 :5

12c platinum

ALG Keystrokes

Display Comments

0.00

1.00

0.75

24.28

0.34

25.64

0.36

26.16

25.80

Forecast for month 9, ( D

ˆ

Expected usage for current

t+1

(month 8) period, (Smoothed

).

D

:0 :0 :2 :3 :6

:2 :3 :6

0.25

24.71

0.36

26.16

t

α

Record for initial values when month 9 actual figures become available.

Note: At least 4 periods of current data should be entered before forecasting is attempted.

).

Pricing Calculations

Markup and Margin Calculations

Sales work often involves calculating the various relations between markup, margin, selling price and costs. Markup is defined as the difference between selling price and cost, divided by the cost. Margin is defined as the difference between selling price and cost, divided by selling price. In other words, markup is based on cost and margin is based on selling price.

The following keystroke sequences are given to readily make these calculations on the

HP 12C Platinum.

CALCULATE GIVEN RPN KEYSTROKES ALG KEYSTROKES

Selling Price Cost & Markup

Selling Price Cost & Margin Key in cost,

Cost Selling Price & Markup Key in selling price,

Cost Selling Price & Margin Key in selling price,

Markup Cost and Selling Price

Markup

Margin

Margin Markup Key in markup,

Margin Key in margin,

Selling Price & Cost Key in selling price,

Key in cost, key in markup (in %),

\1\

key in margin (in %),

b-z.

\1\,

key in markup (in %),

b+z.

\,

key in margin (in %), Key in cost, key in selling price,

à.

\\1 ~b-z.

\, key in cost, àÞ.

\\1 ~b+z.

\,

b+.

b-.

\,

Key in cost, key in markup (in %), Key in cost,

y-,

key in margin (in %),

b³y.

Key in selling price,

y+,

key in markup (in %),

b³y.

Key in selling price,

-,

key in margin (in %), Key in cost, key in selling price,

à.

Key in margin,

-y ~b³y.

Key in selling price,

³, key in cost, àÞ.

Key in markup,

+y ~b³y.

+,

b³.

³,

92

Pricing Calculations 93

Example 1:

If the cost of an item is $160 and the margin is 20%, what is the selling

price? What is the markup?

12c platinum / 12C

RPN Keystrokes

160\1\20 160y-20 b-z b³y

20\\ 20- 1~b-z

Example 2:

If an item sells for $21.00 and has a markup of 50%, what is its cost? What is

12c platinum

ALG Keystrokes

y~b³y

Display Comments

20.

200.00

20.00

25.00

Margin(%). Selling price. Margin(%) Markup (%).

the margin?

12c platinum / 12C

RPN Keystrokes

21\1\50 21y+50 b+z b³y

50\\ 50+ 1~b+z

12c platinum

ALG Keystrokes

y~b³y

Display Comments

50.00

14.00

50.00

33.33

Markup (%). Cost. Markup(%) Margin (%).

The following HP 12C Platinum program may be helpful for repetitive calculations of selling price and costs as well as conversions between markup and margin.

12c platinum / 12C

RPN KEYSTROKES

fs fCLEARÎ \ g(004 Þ

1

~ b + z t gF

§ gF

§ g(000 fs

DISPLAY

000, 001, 36 002,43,33,004 003, 16 004, 1 005, 34 006, 25 007, 40 008, 10 009, 31 010, 43 40 011, 20 012, 43 40 013, 20 014,43,33,000

12c platinum

ALG KEYSTROKES

fs fCLEARÎ ³ g(004 Þ ~ + ~ b ³ gF g’ z ~ ³ t gF g(000 fs

DISPLAY

000, 001, 36 002,43,33,004 003, 16 004, 34 005, 40 006, 34 007, 25 008, 36 009, 43 40 010, 43 20 011, 10 012, 34 013, 36 014, 31 015, 43 40 016,43,33,000

94 Pricing Calculations

REGISTERS

n: Unused i: Unused PV: Unused PMT: Unused FV: Unused R0-R.8: Unused

Program Instructions:

1. Key in the program.

2.

To calculate selling price, given the markup, key in the cost, press the markup and press

3.

To calculate cost, given the markup, key in the selling price, press the markup and press

4,

To calculate selling price, given the margin, key in the cost, press the margin and press

5.

To calculate cost, given the margin, key in the selling price, press the margin and press

RPN Mode:

6. To calculate markup from the margin, key in the margin and press

\g(003t.

7. To calculate margin from the markup, key in the markup and press

\g(000t.

ALG Mode:

6.

To calculate markup from the margin, key in the margin and press

g(003t.

7.

To calculate margin from the markup, key in the markup and press markup,

Example: Find the cost of an item selling for $38.00 with a margin of 30%. What is the

markup on the item? If the markup is raised to 50%, what will the selling price be?

g(000t.

\(³), key in

g(000tt.

\(³), key in

g(000t.

\(³), key in

g(003t.

\(³), key in

g(003tt.

³, re-key margin,

³, re-key

12c platinum / 12C

RPN Keystrokes

38\ 38³ 30g(003 30g(003 tt tt 30\ 30³ g(003t 30g(003t

26.6\ 26.6³ 50g(000 50g(000 tt tt

12c platinum

ALG Keystrokes

Display Comments

38.00

30.00

26.60

30.00

42.86

26.60

50.00

39.90

Selling price. Margin (%). Cost. Margin (%). Markup (%). Cost. New markup. New selling price.

Pricing Calculations 95

Calculations of List and Net prices With Discounts

It is often useful to be able to quickly calculate a list or net price when the other price and a series of discount rates are known. Alternatively, if the list and net price and several discounts are known it may be desirable to calculate a missing discount. The following series of keystrokes may be used:

RPN Mode:

1.

Key in 1, press

2.

Key in the first discount (as a percentage) and press

3. Repeat step 2 for each of the remaining known discount rates.

4.

To calculate the list price, key in the net price and press

5.

To calculate the net price, key in the list price and press

6. To calculate an unknown discount rate, immediately after step 3 (display should show

1.00), key in the net price, press

7.

Press

:1§z-100§.

ALG Mode:

1.

Key in 1, press

2.

Key in 1

3. Repeat step 2 for each of the remaining known discount rates.

4.

To calculate the list price, key in the net price and press

5.

To calculate the net price, key in the list price and press

6. To calculate an unknown discount rate, immediately after doing step 3 , key in the list price, press

7.

Press

àÞ.

Example:

rates are 48% and 5%. What is the third discount rate?

The list price of an item is $3.28 and the net price is $1.45. Two of the discount

12c platinum / 12C

RPN Keystrokes

1\\ ?1 ?1 48b-?§1 1-48b³?§1 d 5b-?§11-5b³?§1 d1.45\

3.28:1 3.28§:1

§z-100§ ³1.45àÞ

\\?1.

b-?§1d.

:1z. :1§.

\ and key in the list price.

?1.

-, key in the first discount (as a percentage) and press b³?§1.

z:1³.

§:1³.

§:1³, then key in the net price.

12c platinum

ALG Keystrokes

1

Display Comments

1.00

0.52

0.95

0.49

10.51

3rd discount rate (%).

96 Pricing Calculations

The following program for the HP 12C Platinum will be helpful in performing the calculations:

12c platinum / 12C

RPN KEYSTROKES

fs fCLEARÎ

1

~ b

?§1 g(000 :1

§ z

1

~

Æ

2

§ g(000 fs

DISPLAY

000, 001, 1 002, 34 003, 25 004, 30 005,44 20 1 006,43,33,000 007, 45 1 008, 20 009, 10 010, 1 011, 34 012, 30 013, 26 014, 2 015, 20 016,43,33,000

12c platinum

ALG KEYSTROKES

fs fCLEARÎ

1

- ~ b ³ ?§1 g(000 :1

§ ~ ³ ~ à Þ g(000 fs

DISPLAY

000, 001, 1 002, 30 003, 34 004, 25 005, 36 006,44 20 1 007,43,33,000 008, 45 1 009, 20 010, 34 011, 36 012, 34 013, 24 014, 16 015,43,33,000

REGISTERS

n: Unused i: Unused PV: Unused PMT: Unused FV: Unused R0: Unused R1: D’1xD’2... R2-R7: Unused

Program Instructions:

1. Key in the program.

2.

Key in 1 and press

3.

Key in the first discount rate (as a percentage) and press

?1.

t.

4. Repeat step 2 for each of the remaining discount rates.

RPN Mode:

5.

To calculate the list price, key in the net price and press

6.

To calculate the net price, key in the list price and press

7.

To calculate the unknown discount rate, key in the net price, press price and press

g(007t.

:1z. :1§.

\, key in the list

Pricing Calculations 97

ALG Mode:

5.

To calculate the list price, key in the net price and press

6.

To calculate the net price, key in the list price and press

7.

To calculate the unknown discount rate, key in the net price, press price and press

Example: Calculate the unknown discount rate for the previous example. If the list price

is now raised to $3.75 what is the new net price?

g(008t.

z:1³.

§:1³. ³, key in the list

12c platinum / 12C

RPN Keystrokes

1?1 1?1 48t 48t 5t 5t

1.45\ 1.45³

3.28g(007t 3.28g(008t t t

3.75:1§ 3.75§:1³

12c platinum

ALG Keystrokes

Display Comments

1.00

0.52

0.95

10.51

0.89

1.66

3rd discount rate (%). Include 3rd discount rate in calculation. New net price.

Statistics

Curve Fitting

Exponential Curve Fit

Using the ° function of the HP 12C Platinum, a least squares exponential curve fit may be easily calculated according to the equation y=Ae technique is often used to determine the growth rate of a variable such as a stock's value over time, when it is suspected that the performance is non-linear. The value for B is the decimal value of the continuous growth rate. For instance, assume after keying in several end-of-month price quotes for a particular stock it is determined that the value of B is

0.10. This means that over the measured growth period the stock has experienced a 10% continuous growth rate.

If B>0, you will have a growth curve. If B<0, you will have a decay curve.

Examples of these are given below.

Bx

. The exponential curve fitting

GROWTH CURVE

(B>0)

Quantity

Time

The procedure is as follows:

1.

2.

3.

98

fCLEARH .

Press

For each input pair of values, key in the y-value and press corresponding x-value and press

After all data pairs are input, press (between ln y and x).

_ .

Quantity

gR~ to obtain the correlation coefficient

DECAY CURVE

(B<0)

Time

g°, key in the

Statistics 99

4.

Press 1

gRg>0gRg> to obtain A in the equation above.

RPN Mode:

5.

Press

~dzg° to obtain B.

6.

Press

g>1- to obtain the effective growth rate (as a decimal).

ALG Mode:

5.

Press

z~d³g° to obtain B.

6.

Press

g>-1³ to obtain the effective growth rate (as a decimal).

7.

To make a y-estimate, key in the x-value and press

Example 1: A stock's price in history is listed below. What effective growth rate does this

represent? If the stock continues this growth rate, what is the price projected to be at the end of 2004 (year 7)?

gRg>.

End of Year Price

1998(1) 45 1999(2) 51.5 2000(3) 53.75 2001(4) 80 2002(5) 122.5 2003(6) 210 2004(7) ?

12c platinum / 12C

RPN Keystrokes

fCLEARH fCLEARH 45g°1_ 45g°1_

51.5g°2_ 51.5g°2_

53.75g°3_ 53.75g°3_ 80g°4_ 80g°4_

122.5g°5_ 122.5g°5_ 210g°6_ 210g°6_ gR~ gR~

1gRg> 1gRg> 0gRg> 0gRg>

~dzg° z~d³g° g>1- g>-1³ 7gRg> 7gRg>

12c platinum

ALG Keystrokes

Display Comments

1.00

2.00

3.00

4.00

5.00

6.00

0.95

27.34

0.31

0.36

232.35

First data pair input. Second data pair input. Third data pair input. Fourth data pair input. Fifth data pair input. Sixth data pair input. Correlation coefficient (between ln y and x).

A B Effective growth rate. Projected price at end of year 7 (2004).

100 Statistics

For repeated use of this routine, the following HP 12C Platinum program will be useful.

12c platinum / 12C

RPN KEYSTROKES

fs fCLEARÎ ~ g° ~ _ g(000 gR ~ t

1

gR g>

0

gR g> t ~ d z g° t g>

1

t gR g> g(000 fs

DISPLAY

000, 001, 34 002, 43 23 003, 34 004, 49 005,43,33,000 006, 43 2 007, 34 008, 31 009, 1 010, 43 2 011, 43 22 012, 0 013, 43 2 014, 43 22 015, 31 016, 34 017, 33 018, 10 019, 43 23 020, 31 021, 43 22 022, 1 023, 30 024, 31 025, 43 2 026, 43 22 027,43,33,000

REGISTERS

n: Unused i: Unused PV: Unused PMT: Unused FV: Unused R0: Unused R1: n R R3: Σx2 R

: Σy R

4

R7-R.6: Unused

12c platinum

ALG KEYSTROKES

fs fCLEARÎ ~ g° ~ _ g(000 gR ~ t

0

gR g> t

1

gR g> ~ d z ~ ³ g° t g>

-

1

³ t gR g> g(000 fs

000, 001, 34 002, 43 23 003, 34 004, 49 005,43,33,000 006, 43 2 007, 34 008, 31 009, 0 010, 43 2 011, 43 22 012, 31 013, 1 014, 43 2 015, 43 22 016, 34 017, 33 018, 10 019, 34 020, 36 021, 43 23 022, 31 023, 43 22 024, 30 025, 1 026, 36 027, 31 028, 43 2 029, 43 22 030,43,33,000

: Σx

: Σy2 R

5

2

: Σxy

6

DISPLAY

HP 12C PLANTINUM User Manual

Specifications and Main Features

Frequently Asked Questions

User Manual

Introduction

About This Handbook

Presentation of Algebraic and RPN

Using the RPN Programs on the HP-12C

Contents

Real Estate

Refinancing

Wrap-Around Mortgage

Income Property Cash Flow Analysis

Before-Tax Cash Flows

Before-Tax Reversions (Resale Proceeds)

After-Tax Cash Flows

After-Tax Net Cash Proceeds of Resale

Lending

Loan With a Constant Amount Paid Towards Principal

Add-On Interest Rate Converted to APR

APR Converted to Add-On Interest Rate

Add-On Rate Loan with Credit Life

Interest Rebate - Rule of 78's

Graduated Payment Mortgages

Variable Rate Mortgages

Skipped Payments

Savings

Initial Deposit with Periodic Deposits

Number of Periods to Deplete a Savings Account or to Reach a Specified Balance

Periodic Deposits and Withdrawals

Savings Account Compounded Daily

Compounding Periods Different From Payment Periods

Investment Analysis

Lease vs. Purchase

Break-Even Analysis

Operating Leverage

Profit and Loss Analysis

Securities and Options

After-Tax Yield

Discounted Notes

Black-Scholes Formula for Valuing European Options

Forecasting

Simple Moving Average

Seasonal Variation Factors Based on Centered Moving Averages

Gompertz Curve Trend Analysis

Forecasting with Exponential Smoothing

Pricing Calculations

Markup and Margin Calculations

Calculations of List and Net prices With Discounts

Statistics

Curve Fitting

Exponential Curve Fit