1．An investor made the following purchase:

§ Bought an office building for $500,000 using 90% financing.

§ The borrowing cost was 10%.

§ They received $29,000 at year-end from rentals.

§ They sold the building for $520,000 at the end of the year.

Assuming a flat tax rate on income and capital gains of 25% what was the return on equity?

A)   +10%.

B)   +6%.

C)   0%.

D)   -3%.

2.A real estate analysis estimates the market value of an income-producing property at $2,560,000. The annual gross potential rental income is $596,000, the annual property operating expenses and taxes are $178,800, and the annual vacancy and collection losses are $89,400. What capitalization rate was used by the analysis to assess the property at $2,560,000.

A)   0.128.

B)   0.1275.

C)   0.129.

 D)    0.127.

3.An investor purchases an office building for $2,500,000. He puts 10 percent down and finances the remainder at a 9 percent rate of interest. Calculate the first year’s after-tax cash flow for the investment using the following information:

A)  $11,160.

B)   $0.

C)  $20,660.

D)  $18,000.

4.An investor purchases a property for $1,000,000, financing 92 percent of the purchase price. He plans to sell the property four years later for $1,200,000. The expected net cash flows for the investment are as follows:

Assuming a 9 percent cost of equity, the net present value (NPV) of the cash flows at the time the property is purchased is:

A)   $249,564.

B)   $338,091.

C)   $169,564.

D)   $258,091.

5.A real estate speculator is considering an investment in a piece of raw land that will be developed. He expects to invest $150,000 in the land. It will not be developed for three years, but at the end of year 3, he expects a cash flow of $25,000. In years 4 and 5, the cash flow will increase to $35,000, and at the end of year 5 he expects to sell the land for $185,000. Due to the risky nature of the investment, he requires an 18 percent return.

The net present value of this investment is closest to:

A)   $30,222.

B)   -$32,903.

C)   $13,046.

D)   -$20,568.

6.The internal rate of return (IRR) is closest to:

A)   12.6%.

B)   26.6%.

C)   14.3%.

D)   18.1%.

7.Ron Biggs is considering a real estate investment. In the first year, the property is expected to generate revenue of $65,000. The expense in the first year is $25,000 and the depreciation allowance will be 2.6 percent of the $350,000 initial investment. Assuming all cash flows occur at the end of the year and Biggs expects to be in a 35 percent marginal tax bracket, the after-tax cash flow in year 1 is closest to:

A)   $20,085.

B)   $29,185.

C)   $30,900.

D)   $19,915.

1．An investor made the following purchase:

§ Bought an office building for $500,000 using 90% financing.

§ The borrowing cost was 10%.

§ They received $29,000 at year-end from rentals.

§ They sold the building for $520,000 at the end of the year.

Assuming a flat tax rate on income and capital gains of 25% what was the return on equity?

A)   +10%.

B)   +6%.

C)   0%.

D)   -3%.

The correct answer was B)

Equity = 500,000(0.10) = 50,000

Interest cost = 450,000 (0.10) = 45,000

Capital Gain = 520,000 - 500,000 = 20,000

ATCF = (Income + Capital Gain - Interest)(1 - tax rate)

ATCF = (29,000 + 20,000 - 45,000)(1 - 0.25) = $3,000

ROE = ATCF / Equity = 3,000 / 50,000 = 0.06 or 6%

2.A real estate analysis estimates the market value of an income-producing property at $2,560,000. The annual gross potential rental income is $596,000, the annual property operating expenses and taxes are $178,800, and the annual vacancy and collection losses are $89,400. What capitalization rate was used by the analysis to assess the property at $2,560,000.

A)   0.128.

B)   0.1275.

C)   0.129.

D)    0.127.

The correct answer was A)

3.An investor purchases an office building for $2,500,000. He puts 10 percent down and finances the remainder at a 9 percent rate of interest. Calculate the first year’s after-tax cash flow for the investment using the following information:

A)  $11,160.

B)   $0.

C)  $20,660.

D)  $18,000.

The correct answer was C)

The first year’s interest payment is the amount borrowed ($2,250,000) times the rate of interest (9%), which equals $202,500. After-tax net income, which is NOI minus depreciation minus interest, net of taxes, is ($243,000 - $25,000 - $202,500) × (1 - .28) = $11,160. After-tax cash flow is after-tax net income, plus depreciation and minus the principal component of the mortgage payment ($218,000-$202,500): $11,160 + $25,000 - $15,500 = $20,660.

4.An investor purchases a property for $1,000,000, financing 92 percent of the purchase price. He plans to sell the property four years later for $1,200,000. The expected net cash flows for the investment are as follows:

Assuming a 9 percent cost of equity, the net present value (NPV) of the cash flows at the time the property is purchased is:

A)   $249,564.

B)   $338,091.

C)   $169,564.

D)   $258,091.

The correct answer was C)

The present value of the cash flows is: $23,450 / 1.09 + $25,312 / 1.09² + $27,879 / 1.09³ + 261,450 / 1.09⁴ = $249,563.83. The NPV is the present value of the cash flows minus the initial investment: $249,564 – $80,000 = $169,564.

5.A real estate speculator is considering an investment in a piece of raw land that will be developed. He expects to invest $150,000 in the land. It will not be developed for three years, but at the end of year 3, he expects a cash flow of $25,000. In years 4 and 5, the cash flow will increase to $35,000, and at the end of year 5 he expects to sell the land for $185,000. Due to the risky nature of the investment, he requires an 18 percent return.

The net present value of this investment is closest to:

A)   $30,222.

B)   -$32,903.

C)   $13,046.

D)   -$20,568.

The correct answer was D)

CF₀ = –150,000
CF₁ = 0
CF₂ = 0
CF₃ = 25,000
CF₄ = 35,000
CF₅ = (35,000 + 185,000) = 220,000
I/Y = 18; Compute NPV = –$20,567.90

6.The internal rate of return (IRR) is closest to:

A)   12.6%.

B)   26.6%.

C)   14.3%.

D)   18.1%.

The correct answer was C)

CF₀ = –150,000
CF₁ = 0
CF₂ = 0
CF₃ = 25,000
CF₄ = 35,000
CF₅ = 220,000
Compute IRR = 14.3%.

7.Ron Biggs is considering a real estate investment. In the first year, the property is expected to generate revenue of $65,000. The expense in the first year is $25,000 and the depreciation allowance will be 2.6 percent of the $350,000 initial investment. Assuming all cash flows occur at the end of the year and Biggs expects to be in a 35 percent marginal tax bracket, the after-tax cash flow in year 1 is closest to:

A)   $20,085.

B)   $29,185.

C)   $30,900.

D)   $19,915.

The correct answer was B)

After-tax cash flow = (revenue – cost – depreciation)(1 – t) + depreciation.
Depreciation = 0.026 x $350,000 = $9,100.
CF = ($65,000 – $25,000 – $9,100)(1 – 0.35) + $9,100 = $29,185.