HP 12C Bedienungsanleitung

Introduction

This Solutions Handbook has been designed to supplement the HP-12C

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.

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 1: 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 abount 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?

Keystrokes Display

CLEAR

6.5

133190

-1,080.33 Monthly payment on existing

mortgage received by lender.

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?

9.5

200000 1,979.56 Monthly payment on new mortgage.

0 899.23 Net monthly payment (to lender).

133190 0

-66,810.00 Net amount of cash advanced (by

lender).

11.5 -80,425.02 Present value of net

0 -13,615.02 NPV to lender of net cash advanced

14.83 % nominal yield (IRR).

15.25 -65,376.72 Present value of net monthly

payment at 15.25%.

0 1,433.28 NPV to borrower.

Keystrokes Display

144.00 Total number of months remaining in

original load (into n).

Sometimes the wrap around mortgage will have a longer payback period

than the original mortgage, or a balloon payment may exist.

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

CLEAR

6.75 0.56 Monthly interest rate (into i).

200132.06 200,132.06 Loan amount (into PV).

0 -2,031.55 Monthly payment on existing

mortgage (calculated).

10 0.83 Monthly interest on wrap-around.

300000 -300,000.00 Amount of wrap-around (into PV).

3,585.23 Monthly payment on wrap-around

(calculated).

0 1,553.69 Net monthly payment received (into

PMT).

200132.06

-99,867.94 Net cash advanced (into PV).

12 15.85 Nominal yield (IRR) to lender

(calculated).

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 1/2% 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?

Keystrokes Display

CLEAR

200000

125010

-74,990.00 Net investment.

1051.61

1681.71

630.10 Net cash flow received by lender.

The above cash flow occurs 200

times.

1,681.71 Next cash flow received by lender.

39 39.00 Cash flow occurs 39 times.

129963.35

131,645.06 Final cash flow.

12 11.84 Rate of return to lender.

$125010

$1681.71 $1681.71 $1681.71

$-1051.61 $-1051.61

200mos.

$-200000

$129963.35

240 mos.

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 and press CLEAR .

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

3. Key in the desired annual yield and press .

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

mortgage and press .

5. Press .

6. Key in the net amount of cash advanced and press .

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

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

9. Press to obtain the payment amount necessary to achieve the

desired yield.

10. Key in the amount of the wrap-around mortgage and press

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?

Keystrokes Display

CLEAR

200 12

Number of periods and monthly

interest rate.

1051.61

74990

-165,776.92 Present value of payments plus cash

advanced.

240

129963.35

1,693.97 Monthly payment received by lender

2000 9.58 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 payments 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.

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?

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 are as follows:

1. Forecast or estimate Sales Price. Deduct sales and Transaction Costs.

The result is the Proceeds of Resale.

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

Keystrokes Display

CLEAR

250 12

180,000.00 Potential Gross Income.

5 9,000.00 Vacancy Loss.

171,000.00 Effective Gross Income.

76855 94,145.00 Net Operating Income.

11.5

700000

-89,580.09 Annual Debt Service.

4,564.91 Cash Throw-Off.

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?

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.

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 program. This program calculates the

Net Operating Income using the Potential Gross Income, operational cost

and vacancy rate. The Net Operating 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 at

line 32 of the program in place of .

Keystrokes Display

CLEAR

240.00 Mortgage term.

11.5 0.96 Mortgage rate.

700000 Property value.

-7,465.01 Monthly payment.

10 120.00 Projection period.

-530,956.57 Mortgage balance in 10 years.

800000 Estimated resale.

7 56,000.00 Transaction costs.

744,000.00 Cash Proceeds of Resale.

213,043.43 Net Cash Proceeds of Resale.

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