An investor has paid you to analyze what he might do with a small plot of land on the edge of town that he has already purchased for 30,000. There are four alternative uses for the

land. “Total Investment”, represents the year zero development costs. “Uniform Net Annual Benefit”, is what the investor will receive for operating the enterprise for the next 20 years, and, “Terminal Value”, is what the property may be sold for in year 20.

Alternative | Total investment | Unifom Net Annual Benefit | Terminal Value |

A. Do Nothing | 0 | 0 | 0 |

B. Vegetable Market | 50,000 | 5,100 | 30,000 |

C. Gas Station | 95,000 | 10,500 | 30,000 |

D. Small Motel | 350,000 | 36,000 | 150,000 |

Use a MARR of 8%.

1. What is the present worth of asset C?

Solution:

The present worth of asset C is the initial investment of $95,000 plus the annual benefits plus the terminal value. The MARR is 8% and the investor receives the benefits for 20 years and then sells the gas station. So N = 20, i = 8% = 0.08 and the formula for present worth is

PW(C) = -$95,000 + $10,500(P/A,8%,20) + $30,000(P/F,8%,20) = $14,526.99.

2. What is the annual worth of asset D?

Solution:

To solve this problem we first need to compute the PW of asset D and then compute the annual worth using the formula AW=PW(A|P,i,N). The PW of asset D is the initial investment plus the annual benefits plus the terminal value. Again the investor receives the annual benefits for 20 years and then sells the property in year 20 so we use the same N and i as above and so

PW(D) = -$350,000 + $36,000(P/A,8%,20) + $150,000(P/F,8%,20)= $35,635.54

and

AW(D) = $35,635.54(.10185) = $3,629.56.

3. Using the present worth criteria which asset would you choose?

Solution:

We already know the PW of asset C and D from problem 1 and 2 and since the PW of asset A is clearly zero, this problem reduces to determining the PW of asset B and then using the present worth criteria to select the best option.

PW(B) = -$50,000 + $5,100(P/A,8%,20) + $30,000(P/F,8%,20)= $6,508.99

Now we compare the 3 assets and select the one with the highes PW:

PW(A) = $0.

PW(B) = $6,508.99.

PW(C) = $14,526.99.

PW(D) = $35,635.54.

Asset D has the highest PW so we choose asset D.