Study Questions

1. List three important ways in which DCF valuation models differ from direct capitalization models.

2. Why might a commercial real estate investor borrow to help finance an investment even if she could afford to pay 100 percent cash?

3. Using the "CFj" key of your financial calculator determine the IRR of the following series of annual cash flows: CF0= -$31,400; CF1 = $3,292; CF2 = $3,567; CF3 = $3,850; CF4 = $4,141; and CF5 = $50,659.

4. A retail shopping center is purchased for $2.1 million. During the next four years, the property appreciates at 4 percent per year. At the time of purchase, the property is financed with a 75 percent loan-to-value ratio for 30 years at 8 percent (annual) with monthly amortization. At the end of year 4, the property is sold with 8 percent selling expenses. What is the before-tax equity reversion?

5. State, in no more than one sentence, the condition for favorable financial leverage in the calculation of NPV.

6. State, in no more than one sentence, the condition for favorable financial leverage in the calculation of the IRR.

7. An office building is purchased with the following projected cash flows:
• NOI is expected to be $130,000 in year 1 with 5 percent annual increases.
• The purchase price of the property is $720,000.
• 100% equity financing is used to purchase the property
• The property is sold at the end of year 4 for $860,000 with selling costs of 4 percent.
• The required unlevered rate of return is 14 percent.

a. Calculate the unlevered internal rate of return (IRR).
b. Calculate the unlevered net present value (NPV).

8. With a purchase price of $350,000, a small warehouse provides for an initial before-tax cash flow of $30,000, which grows by 6 percent per year. If the before-tax equity reversion after four years equals $90,000, and an initial equity investment of $175,000 is required, what is the IRR on the project? If the required going-in levered rate of return on the project is 10 percent, should the warehouse be purchased?

9. You are considering the acquisition of a small office building. The purchase price is $775,000. Seventy-five percent of the purchase price can be borrowed with a 30-year, 7.5 percent mortgage. Payments will be made annually. Up-front financing costs will total three percent of the loan amount. The expected before-tax cash flows from operations--assuming a 5-year holding period-are as follows:

Year BTCF
1 $48,492
2 53,768
3 59,282
4 65,043
5 $71,058

The before-tax cash flow from the sale of the property is expected to be $295,050. What is the net present value of this investment, assuming a 12 percent required rate of return on levered cash flows? What is the levered internal rate of return?

10. You are considering the purchase of an apartment complex. The following assumptions are made:

• The purchase price is $1,000,000.
• Potential gross income (PGI) for the first year of operations is projected to be $171,000.
• PGI is expected to increase at 4 percent per year.
• No vacancies are expected.
• Operating expenses are estimated at 35 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 8.0 percent.
• Financing costs will equal 2 percent of the loan amount.
• There are no prepayment penalties.

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

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

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

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

e. Calculate the monthly mortgage payment. What is the total per year?

f. Calculate the loan balance at the end of years 1, 2, 3, and 4. (Note: the unpaid mortgage balance at any time is equal to the present value of the remaining payments, discounted at the contract rate of interest.)

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

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

i. Calculate the levered required initial equity investment.

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

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

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

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

n. 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.

11. The expected before-tax IRR on a potential real estate investment is 14 percent. The expected after-tax IRR is 10.5 percent. What is the effective tax rate on this investment?

12. An office building is purchased with the following projected cash flows:
• NOI is expected to be $130,000 in year 1 with 5 percent annual increases.
• The purchase price of the property is $720,000.
• 100% equity financing is used to purchase the property
• The property is sold at the end of year 4 for $860,000 with selling costs of 4 percent.
• The required unlevered rate of return is 14 percent.

a. Calculate the unlevered internal rate of return (IRR).

b. Calculate the unlevered net present value (NPV).