HP 12C User manual

© Hewlett-Packard Development Company, L.P. rev. 03.04
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.

2
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

Introduction 3
itself and the ALG alternative is then indicated parenthetically.
5. Usage of \(³)
To activate the ³key 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 ³is 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.

4
Contents
Introduction ........................................................................................................................ 2
About This Handbook..................................................................................................... 2
Presentation of Algebraic and RPN ................................................................................2
Using the RPN Programs on the HP-12C .......................................................................3
Contents..............................................................................................................................4
Real Estate..........................................................................................................................7
Refinancing.....................................................................................................................7
Wrap-Around Mortgage .................................................................................................8
Income Property Cash Flow Analysis........................................................................... 12
Before-Tax Cash Flows ............................................................................................ 12
Before-Tax Reversions (Resale Proceeds)................................................................ 13
After-Tax Cash Flows............................................................................................... 14
After-Tax Net Cash Proceeds of Resale.................................................................... 19
Lending............................................................................................................................. 24
Loan With a Constant Amount Paid Towards Principal ............................................... 24
Add-On Interest Rate Converted to APR...................................................................... 25
APR Converted to Add-On Interest Rate...................................................................... 26
Add-On Rate Loan with Credit Life ............................................................................. 27
Interest Rebate - Rule of 78's........................................................................................ 30
Graduated Payment Mortgages..................................................................................... 32
Variable Rate Mortgages .............................................................................................. 36
Skipped Payments......................................................................................................... 38
Savings ............................................................................................................................. 40
Initial Deposit with Periodic Deposits .......................................................................... 40
Number of Periods to Deplete a Savings Account or to Reach a Specified Balance ....41
Periodic Deposits and Withdrawals .............................................................................. 42
Savings Account Compounded Daily ........................................................................... 44
Compounding Periods Different From Payment Periods.............................................. 46
Investment Analysis.......................................................................................................... 49
Lease vs. Purchase ........................................................................................................ 49
Break-Even Analysis .................................................................................................... 53
Operating Leverage ...................................................................................................... 59
Profit and Loss Analysis............................................................................................... 61
Securities and Options ...................................................................................................... 65
After-Tax Yield ............................................................................................................ 65
Discounted Notes.......................................................................................................... 67
Black-Scholes Formula for Valuing European Options................................................ 69

Contents 5
Forecasting........................................................................................................................74
Simple Moving Average ...............................................................................................74
Seasonal Variation Factors Based on Centered Moving Averages ...............................78
Gompertz Curve Trend Analysis...................................................................................83
Forecasting with Exponential Smoothing .....................................................................87
Pricing Calculations ..........................................................................................................92
Markup and Margin Calculations..................................................................................92
Calculations of List and Net prices With Discounts......................................................95
Statistics............................................................................................................................98
Curve Fitting .................................................................................................................98
Exponential Curve Fit ...............................................................................................98
Logarithmic Curve Fit.............................................................................................102
Power Curve Fit ......................................................................................................104
Standard Error of the Mean.........................................................................................105
Mean, Standard Deviation, Standard Error for Grouped Data ....................................106
Chi-Square Statistics...................................................................................................109
Normal Distribution ....................................................................................................112
Covariance ..................................................................................................................114
Permutations ...............................................................................................................116
Combinations ..............................................................................................................117
Random Number Generator ........................................................................................119
Personal Finance .............................................................................................................121
Homeowners Monthly Payment Estimator .................................................................121
Tax-Free Individual Retirement (IRA) or Keogh Plan................................................124
Stock Portfolio Evaluation and Analysis.....................................................................127
Canadian Mortgages .......................................................................................................131
Periodic Payment Amount ..........................................................................................131
Number of Periodic Payments to Fully Amortize a Mortgage ....................................132
Effective Interest Rate (Yield) ....................................................................................132
Balance Remaining at End of Specified Period...........................................................132
Miscellaneous .................................................................................................................134
Learning Curve for Manufacturing Costs ...................................................................134
Queuing and Waiting Theory......................................................................................138
Appendix A : Programs from Part III of the Owner's Handbook ....................................145
About this Appendix ...................................................................................................145
Algebraic Mode Programs ..........................................................................................146
Section 12: The Rent or Buy Decision....................................................................146
Section 13: Straight-Line Depreciation...................................................................147
Section 13: Declining-Balance Depreciation ..........................................................148
Section 13: Sum-of-the-Years-Digits Depreciation.................................................149
Section 13: Full- and Partial- Year Depreciation with Crossover ...........................150
Section 14: Lease with Advance Payments - Solving For Payment........................151
Section 14: Lease with Advance Payments - Solving For Yield .............................151
Section 14: Advance Payments With Residual - Solving for Payment ...................152

6 Contents
Section 15: Nominal Rate Converted to Effective Rate......................................... 152
Section 16: 30/360 Day Basis Bonds ..................................................................... 153
Section 16: Annual Coupon Bonds......................................................................... 154
Appendix B: Formulas Used........................................................................................... 155
Real Estate .................................................................................................................. 155
Wrap-Around Mortgage ......................................................................................... 155
After-Tax Cash Flows............................................................................................. 155
After-Tax Net Cash Proceeds of Resale.................................................................. 155
Lending....................................................................................................................... 156
Loans With a Constant Amount Paid Towards Principal........................................ 156
Add-On Interest Rate to APR ................................................................................. 156
Add-On to APR with Credit Life............................................................................ 156
Rule of 78's Rebate ................................................................................................. 156
Graduated Payment Mortgage ................................................................................ 157
Skipped Payments................................................................................................... 157
Savings ....................................................................................................................... 158
Compounding Periods Different From Payment Periods........................................ 158
Investment Analysis.................................................................................................... 158
Lease vs. Purchase .................................................................................................. 158
Break-Even Analysis and Operating Leverage ....................................................... 158
Profit and Loss Analysis ......................................................................................... 158
Securities and Options ................................................................................................ 159
Discounted Notes.................................................................................................... 159
Black-Scholes Formula for Valuing European Options.......................................... 159
Forecasting ................................................................................................................. 160
Simple Moving Average......................................................................................... 160
Seasonal Variation Factors Based on a Centered Moving Average ........................ 160
Gompertz Curve Trend Analysis ............................................................................ 160
Forecasting With Exponential Smoothing .............................................................. 161
Pricing Calculations.................................................................................................... 161
Markup and Margin Calculations ........................................................................... 161
Calculations of List and Net Prices with Discounts ................................................ 162
Statistics...................................................................................................................... 162
Exponential Curve Fit............................................................................................. 162
Logarithmic Curve Fit ............................................................................................ 163
Power Curve Fit...................................................................................................... 163
Standard Error of the Mean..................................................................................... 163
Mean, Standard Deviation, Standard Error for Grouped Data ................................ 163
Personal Finance......................................................................................................... 164
Tax-Free Retirement Account (IRA) or Keogh Plan .............................................. 164
Stock Portfolio Evaluation and Analysis ................................................................ 164
Portfolio beta coefficient: ....................................................................................... 164
Canadian Mortgages ................................................................................................... 164
Miscellaneous ............................................................................................................. 165
Learning Curve for Manufacturing Cost................................................................. 165
Queuing and Waiting Theory.................................................................................. 165
Subject Index .................................................................................................................. 166

7
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 $200,000, 17 year, level-monthly-payment loan at 9.5%
interest.
What are the NPV and effective yield to the lender on the net amount of cash actually
advanced?
What is the NPV to the borrower on this amount if he can earn a 15.25% equity yield rate
on the net proceeds of the loan?
12c platinum / 12C
RPN Keystrokes 12c platinum ALG Keystrokes Display Comments
gÂ
fCLEARG
17gA
6.5gC
133190$
P?0
gÂ
fCLEARG
17gA
6.5gC
133190$
P?0
-1,080.33
Monthly payment on
existing mortgage
received by lender.

8 Real Estate
12c platinum / 12C
RPN Keystrokes 12c platinum ALG Keystrokes Display Comments
9.5gC
200000Þ$
P
9.5gC
200000Þ$
P
1,979.56
Monthly payment on
new mortgage.
:0+P +:0P899.23 Net monthly payment (to
lender).
:$ :$
133190+?0 +133190³?0 -66,810.00 Net amount of cash
advanced (by lender).
11.5gC$ 11.5gC$$ -80,425.02 Present value of net
monthly payment.
:0--:0³-13,615.02 NPV to lender of net
cash advanced.
:0$¼ :0$¼
12§§12³14.83 % nominal yield (IRR).
15.25gC$ 15.25gC$$ -65,376.72 Present value of net
monthly payment at
15.25%.
:0--:0³1,433.28 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
12c platinum / 12C
RPN Keystrokes 12c platinum ALG Keystrokes Display Comments
gÂ
fCLEARG
20\
8-gA
gÂ
fCLEARG
20-
8³gA
144.00
Total number of months
remaining in original loan
(into n).
6.75gC 6.75gC 0.56 Monthly interest rate (into i).
200132.06$200132.06$200,132.06 Loan amount (into PV).
P?0 P?0 -2,031.55 Monthly payment on existing
mortgage (calculated).
10gC 10gC 0.83 Monthly interest on wrap-
around.
300000Þ$ 300000Þ$ -300,000.00 Amount of wrap-around (into
PV).
PP3,585.23 Monthly payment on wrap-
around (calculated).
:0+P +:0P1,553.69 Net monthly payment
received (into PMT).
:$ :$
200132.06+$ +200132.06$-99,867.94 Net cash advanced (into PV).
¼12§¼§12³15.85 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.
PV
1
P
M
T
2for n2Years
B
AL
(+)
PV
2
P
M
T
1for n1Years
(–)
... ...

10 Real Estate
Where:
n1= number of years remaining in original mortgage
PMT1= yearly payment of original mortgage
PV1= remaining balance of original mortgage
n2= number of years in wrap-around mortgage
PMT2= yearly payment of wrap-around mortgage
PV2= total amount of wrap-around mortgage
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?
12c platinum / 12C
RPN Keystrokes 12c platinum ALG Keystrokes Display Comments
g gÂ
fCLEARGfCLEARG
200000Þ\ 200000Þ
125010+gJ +125010gJ -74,990.00 Net investment.
1051.61Þ\ 1051.61Þ
1681.71++1681.71gK 630.10 Net cash flow
received by lender.
$125010
$ -200000
240 mos.
200 mos.
$ 129963.35
$1681.71 $1681.71 $1681.71
$ -1051.61 $ -1051.61
... ...

Real Estate 11
12c platinum / 12C
RPN Keystrokes 12c platinum ALG Keystrokes Display Comments
gK99ga
~gK
~ga
~gK
2ga
99ga
~gK
~ga
~gK
2ga
The above cash flow
occurs 200 times.
gFgK 1681.71gK 1,681.71 Next cash flow
received by lender.
39ga 39ga 39.00 Cash flow occurs 39
times.
~129963.35+~+129963.35
gK gK 131,645.06 Final cash flow.
fL12§fL§12³11.84 Rate of return to
lender.
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 g 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$.
7. Key in the total term of the wrap-around mortgage and press n.
8. If a balloon payment exists, key it in and press M.
9. Press Pto obtain the payment amount necessary to achieve the desired yield.
10. Key in the amount of the wrap-around mortgage and press Þ$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?

12 Real Estate
12c platinum / 12C
RPN Keystrokes 12c platinum ALG Keystrokes Display Comments
g gÂ
fCLEARGfCLEARG
200n12gC 200n12gC Number of periods and
monthly interest rate.
1051.61ÞP 1051.61ÞP Monthly payment.
$74990+$+74990³
Þ$ Þ$ -165,776.92 Present value of
payments plus cash
advanced.
240n240n
129963.35MP 129963.35MP 1,693.97 Monthly payment
received by lender.
200000Þ$¼ 200000Þ$¼
12§§12³9.58 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?
c. What is the Cash Throw-Off to Equity?
12c platinum / 12C
RPN Keystrokes 12c platinum ALG Keystrokes Display Comments
gÂ
fCLEARG
60\
gÂ
fCLEARG
60§
250§12§250§12-180,000.00 Potential Gross Income.
5b- 5b- 171,000.00 Effective Gross Income.
76855-76855³94,145.00 Net Operating Income.
20gA 20gAd
11.5gC 11.5gCd
700000$700000$
P12§P§12+-89,580.09 Annual Debt Service.
+~³ 4,564.91 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 12c platinum ALG Keystrokes Display Comments
g gÂ
fCLEARGfCLEARG
20gA 20gA 240.00 Mortgage term.
11.5gC 11.5gC 0.96 Mortgage rate.
700000$700000$Property value.
PP-7,465.01 Monthly payment.
10gA 10gA 120.00 Projection period.
MMM -530,956.57 Mortgage balance in 10 years.
800000\800000-Estimated resale.
7b- 7b+ 744,000.00 Cash Proceeds of Resale.
+~³ 213,043.43 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 DISPLAY 12c platinum ALG KEYSTROKES DISPLAY
fs fs
fCLEARÎ000, fCLEARÎ000,
0 001, 0 0 001, 0
n002, 11 n002, 11
?1 003, 44 1 1 003, 1
:7 004, 45 7 2 004, 2
Æ005, 26 f! 005, 42 11
2 006, 2 ?0 006, 44 0
z007, 10 :5 007, 45 5
?7 008, 44 7 n008, 11
1 009, 1 :¼ 009, 45 12
?+1 010,44 40 1 :6 010, 45 6
1 011, 1 ¼011, 12
2 012, 2 d012, 33
f! 013, 42 11 ?6 013, 44 6
?0 014, 44 0 d014, 33
:5 015, 45 5 :$ 015, 45 13
n016, 11 :4 016, 45 4
:¼ 017, 45 12 $017, 13
:6 018, 45 6 d018, 33
¼019, 12 ?4 019, 44 4
d020, 33 d020, 33
?6 021, 44 6 gm 021, 43 35
d022, 33 g(030 022,43,33,030
:$ 023, 45 13 1 023, 1
:4 024, 45 4 ?+1 024,44 40 1
$025, 13 :1 025, 45 1
d026, 33 f# 026, 42 25
?4 027, 44 4 ?-0 027,44 30 0
d028, 33 0 028, 0
gm 029, 43 35 g(009 029,43,33,009
g(036 030,43,33,036 :2 030, 45 2
:1 031, 45 1 -031, 30
f# 032, 42 25 :.0 032,45 48 0
?-0 033,44 30 0 b033, 25
0 034, 0 -034, 30
g(017 035,43,33,017 :3 035, 45 3

16 Real Estate
12c platinum / 12C
RPN KEYSTROKES DISPLAY 12c platinum
ALG KEYSTROKES DISPLAY
n036, 11 ³036, 36
:2 037, 45 2 ?+0 037,44 40 0
:8 038, 45 8 +038, 40
b039, 25 :P 039, 45 14
?+2 040,44 40 2 gA 040, 43 11
d041, 33 ³041, 36
:.0 042,45 48 0 :7 042, 45 7
b043, 25 b043, 25
-044, 30 ?§0 044,44 20 0
:3 045, 45 3 d045, 33
:9 046, 45 9 -046, 30
b047, 25 :0 047, 45 0
?+3 048,44 40 3 ³048, 36
d049, 33 :1 049, 45 1
-050, 30 gu 050, 43 31
1 051, 1 ~051, 34
:7 052, 45 7 t052, 31
?§0 053,44 20 0 :2 053, 45 2
-054, 30 +054, 40
§055, 20 :8 055, 45 8
:P 056, 45 14 b056, 25
1 057, 1 ³057, 36
2 058, 2 ?2 058, 44 2
§059, 20 :3 059, 45 3
+060, 40 +060, 40
:0 061, 45 0 :9 061, 45 9
-062, 30 b062, 25
:1 063, 45 1 ³063, 36
gu 064, 43 31 ?3 064, 44 3
~065, 34 g(001 065,43,33,001
t066, 31 fs
g(009 067,43,33,009
fs
REGISTERS
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.

Real Estate 17
Program Instructions:
1. Press g 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 tto 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
$20 years. Assuming a 125% declining balance depreciation, what are the After-Tax Cash
Flows for the first 10 years if the investors Marginal Tax Rate is 35%?
12c platinum / 12C
RPN Keystrokes 12c platinum ALG Keystrokes Display Comments
g gÂ
fCLEARHfCLEARH
100000\100000-
20b-$ 20b$ 80,000.00 Mortgage amount.
12.25gC 12.25gC 1.02 Monthly interest rate.
30gA 30gA 360 Mortgage term.
PPP -838.32 Monthly payment.
9900?2 9900?2 9,900.00 Potential Gross Income.

18 Real Estate
12c platinum / 12C
RPN Keystrokes 12c platinum ALG Keystrokes Display Comments
3291.75?3 3291.75?3 3,291.75 1st year operating cost.
75000?4 75000?4 75,000.00 Depreciable value.
20?5 20?5 20.00 Useful life.
125?6 125?6 125.00 Declining balance factor.
35?7 35?7 35.00 Marginal Tax Rate.
6?8 6?8 6.00 Potential Gross Income
growth rate.
2.5?9 2.5?9 2.50 Operating cost growth.
5?.0 5?.0 5.00 Vacancy rate.
tt1.00 Year 1
-1,020.88
A
TC
F
1
tt2.00 Year 2
-822.59
A
TC
F
2
tt3.00 Year 3
-598.85
A
TC
F
3
tt4.00 Year 4
-348.94
A
TC
F
4
tt5.00 Year 5
-72.16
A
TC
F
5
tt6.00 Year 6
232.35
A
TC
F
6
tt7.00 Year 7
565.48
A
TC
F
7
tt8.00 Year 8
928.23
A
TC
F
8
tt9.00 Year 9
1,321.62
A
TC
F
9
tt10.00 Year 10
1,746.81
A
TC
F
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 12c platinum ALG Keystrokes Display Comments
gÂ
fCLEARH
1050000$
9173.81ÞP
9.5gC
25gA
gÂ
fCLEARH
1050000$
9173.81ÞP
9.5gC
25gA
175200?2 175200?2 175,200.00 Potential Gross
Income.
40296?3 40296?3 40,296.00 1st year operating
cost.
1200000?4 1200000?4 1,200,000.00 Depreciable value.
35?5 35?5 35.00 Depreciable life.
50?7 50?7 50.00 Marginal tax rate.
3.5?8 3.5?8 3.50 Potential Gross
Income growth rate.
1.6?9 1.6?9 1.60 Operating cost
growth rate.
7?.0 7?.0 7.00 Vacancy rate.
g(031 g(025 7.00 Go to dep. step.
fsfV fsfV 032, 42 23
026, 42 23 RPN:Change to SL
ALG:depreciation
fst fst 1.00 Year 1
18,021.07 ATCF1
tt2.00 Year 2
20,014.26 ATCF2
tt3.00 Year 3
22,048.90 ATCF3
tt4.00 Year 4
24,123.14 ATCF4
tt5.00 Year 5
26,234.69 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 DISPLAY 12c platinum
ALG KEYSTROKES DISPLAY
fs fs
fCLEARÎ000, fCLEARÎ000,
g 001, 43 8 g 001, 43 8
?2 002, 44 2 ?2 002, 44 2
gA 003, 43 11 gA 003, 43 11
d004, 33 d004, 33
b005, 25 ~005, 34
-006, 30 -006, 30
?0 007, 44 0 ~007, 34
~008, 34 b008, 25
-009, 30 -009, 30
:7 010, 45 7 ?0 010, 44 0
b011, 25 ~011, 34
?1 012, 44 1 §012, 20
:P 013, 45 14 :7 013, 45 7
fB 014, 42 14 ³014, 36
P015, 14 ?1 015, 44 1
M016, 15 :P 016, 45 14
?+0 017,44 40 0 fB 017, 42 14
fCLEARG018, 42 34 P018, 14
:3 019, 45 3 M019, 15
$020, 13 ?+0 020,44 40 0
:4 021, 45 4 fCLEARG021, 42 34
n022, 11 :3 022, 45 3
:5 023, 45 5 $023, 13
¼024, 12 :4 024, 45 4
:2 025, 45 2 n025, 11
f# 026, 42 25 :5 026, 45 5
d027, 33 ¼027, 12