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.

HP 12C PLANTINUM 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