Question

5. A real estate investor is considering an investment in a building that will generate profits of $22,000 at the end of each year for the next 10 years. The investor requires a 22% return on the investment to compensate for the risk they are taking. a. How much should the investor pay today for the investment? b. How much should the investor pay today for the investment if profits at the then end of year 1 are $22,000, and are expected to grow 2.5% each following year?

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Answer 1

1.

Annual Profit Required = $22,000

Interest Rate = 22%

Time Period = 10 years

Calculating Value of Investment,

Present Value of Annuity = P[(1 - (1 + r)^-n)/r]

Present Value of Annuity = 22,000[(1 - (1.22)^-10)/0.22]

Present Value of Investment = $86,310.06

2.

Annual Profit Required = $22,000

Interest Rate = 22%

Time Period = 10 years

Growth Rate = 2.5%

Calculating Value of Investment,

Present Value of Growing Annuity = P/(r - g)[1 - ((1 + g)/(1 + r))ⁿ]

Present Value of Investment = 22,000/(0.22 - 0.025)[1 - (1.025/1.22)¹⁰]

Present Value of Investment = $93,049.52