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AGEC 432 – Real Estate and Finance: Part I

Practice Problem Set #3

  1. Suppose a firm is considering undertaking one of the two following projects. Which one would you recommend? Why? Assume a required rate of return of 7 percent and a 34 percent tax bracket. Also assume no change in the price of the assets acquired under both projects.

______Project A______Project B______

YearNet InvestmentNet CashNet InvestmentNet Cash

Flow Flow

0$2,000$2,000

1 $ 550 $400

2 550 400

3 550 400

4 550 400

5 550 400

6400

7400

8400

9400

10400

NPVA = - 2,000 + 550(EPIF.07,10) – 2,000(PIF.07,5)

NPVA = – 2,000 + 550(7.0236) – 2,000(0.7130) = $436.98

NPVB = – 2,000 + 400(7.0236) = $809.44

Prefer project B over project A since NPVB > NPVA

  1. Suppose land is currently selling for $1,000 an acre and that you expect land prices to continue to go up at an annual rate of 7% over the next 10 years.

Ignoring the net cash revenue generated by this land for the moment and assuming you would sell it 10 years from now, can you justify purchasing land at this price if your discount rate is 5% and your capital gains income will be taxed at a 20% rate?

Step 1: FV = 1,000(1/PIF.07,10) = 1,000(1/.508) = $1,968.50

Step 2: PV = 0 + 1,968.50(PIF.05,10) - .20(1,968.50-1,000)(PIF.05,10)

= 0 + 1,968.50(.614) - .20(968.50)(.614) = $1,089.73

Yes, sell 10 years from now since $1,089.73 > $1,000

  1. Suppose you are considering investing in a $40,000 capital improvement to your business, which has an economic life of 25 years. Assume further that you plan to sell this improvement 10 years from now. If the expected net cash revenue generated by this investment is $5,000 annually and you choose a discount rate of 8%, would you make this investment if:
  2. The market value of the purchased improvement was only $20,000 ten years from now?
  3. What would this market value have to be 10 years from now before you would be indifferent between making and not making this investment?

Part a:

NPV = 5,000(EPIF.08,10) – 40,000 +20,000(PIF.08,10)

= 5,000(6.710) – 40,000 + 20,000(0.463)

NPV = 33,550 – 40,000 + 9,260 = $2,810

Yes, the NPV is positive. There is no capital gain associated with the eventual sale of the assets.

Part b:

Set NPV equation equal to zero and solve for the terminal value

0 = 33,550 – 40,000 + T(0.463)

T = 6,450  0.463 = $13,930.88 is breakeven or value if indifferent

Check by substituting solution for T into first equation:

33,550 – 40,000 + 13,930.88(0.463) = 0

  1. A farmer is considering a new confinement feeding system, which costs $65,000. He figures that reduced labor costs and better feeding efficiency will result in additional net cash revenue of $8,000 annually.

If his required rate of return is 8 percent and the economic life of the project is 10 years, should he make the investment?

C= 65,000

NCF = 8,000

Discount rate = 8%

N = 10 years

NPV = NCF(EPIF.08,10) – C

NPV = 8,000(6.7101) – 65,000

NPV = -11,319.20 No, since NPV is negative

  1. Suppose farmland in your county is selling for $850 per acre. What will its value be 24 years from now if this land increased in value at a rate of 6 percent annually?

FIF.06,24 = 1/(PIF.06,24)

FV = PV(FIF.06,24)

FV = 850(1/.247)

FV = $3,441.29

6.Suppose someone has offered to buy 30 acres of your farm for subdivision purposes and has offered you $1,500 an acre. You estimate, however, that you can hold out and sell this land 5 years from now for $2,500 an acre. If your required rate of return is 8 %, should you sell now or wait 5 years? Hint: this analysis ignores possibility of annual net cash flows generated by land over the next five years.

R = 8%

N = 5 years

PV = 2,500(PIF.08,5)

PV = 2,500(0.681)

PV = $1,702.50

Prefer waiting 5 years since $1,702.50 > $1,500.