Question

As manager of Precision Properties, you are considering the purchase of an apartment complex. The following assumptions are made:

• The purchase price is $2,000,000.

• Potential gross income (PGI) for the first year of operations is projected to be $320,000.

• PGI is expected to increase at 4 percent per year.

• No vacancies are expected.

• Operating expenses are estimated at 38 percent of effective gross income. Ignore capital expenditures.

• The market value of the investment is expected to increase 4 percent per year.

• Selling expenses will be 4 percent.

• The holding period is 4 years.

• The appropriate unlevered rate of return to discount projected NOIs and the projected NSP is 12 percent.

• The required levered rate of return is 14 percent.

• 70 percent of the acquisition price can be borrowed with a 30-year, monthly payment mortgage.

•   The annual interest rate on the mortgage will be 9.0 percent.

•   Financing costs will equal 2 percent of the loan amount.

•   There are no prepayment penalties.

1. Calculate the net present value of this investment, assuming no mortgage debt. Should you purchase? Why?

2. Calculate the internal rate of return of this investment, assuming no debt. Should you purchase? Why?

3. Calculate the amount of principal reduction achieved during each of the four years.

4. Calculate the total interest paid during each of the four years. (Note: Remember that debt service equals principal plus interest.)

5. Calculate the levered required initial equity investment.

6. Calculate the before-tax cash flow (BTCF) for each of the four years.

7. Calculate the before-tax equity reversion (BTER) from the sale of the property.

8. Calculate the levered net present value of this investment. Should you purchase? Why?

9. Calculate the levered internal rate of return of this investment (assuming no debt and no taxes). Should you purchase? Why?

10. Calculate, for the first year of operations, the: (1) overall (cap) rate of return, (2) equity dividend rate, (3) gross income multiplier, (4) debt coverage ratio.

Answer 1

1. Calculate the net present value of this investment, assuming no mortgage debt. Should you purchase? Why?

Answer:

a. Calculate net operating income (NOI) for each of the four years

Item	1	2	3	4
PGI	$320,000	332800	346112	359956
LESS: V&C	0	0	0	0
EGI	$320,000	332800	346112	359956
LESS: Operating Expenses	121600	126464	131523	136783
NOI	198400	206336	214589	223173

b. Calculate the net sale proceeds from the sale of the property

ITEM	AMOUNT
Selling Price [ 2000000 X (1.04)4 ]	2339717
less: selling expenses (4 % x SP)	93589
Net SP	2246128

c. Calculate the net present value of this investment

Item	Cashflow	Present Value @ 12%
Initial Outflow Yr. 0	- $2,000,000	-$2,000,000
NOI Yr. 1	198400	177143
NOI Yr. 2	206336	164490
NOI Yr. 3	214589	152740
NOI Yr. 4	223173	141830
Reversion Yr. 4	2246128	1427455
Net Present Value		63658

Yes, purchase the property because it is a positive NPV project.

2.  Calculate the internal rate of return of this investment, assuming no debt. Should you purchase? Why?

Answer: Internal rate of return = 14.22 %

Yes, purchase because unlevered required rate of return is 12 percent.