Question

1. (10 pts) You want to create an investment that will provide $5,000 annually in perpetuity. What amount needs to be invested today at 4% interest to provide $5000/yr perpetually? (Chapter 5)
2. (10 pts) Assume we receive $500 at the end of each year for 8 years. What is the equivalent value of the cash flows at time period 0 assuming 7% interest? What is the equivalent value at the end of time period 8 assuming 7% interest? (Chapter 4)
3. (10 pts) Use Present Worth Analysis to determine the present cost of each investment and determine which investment is best (which has the lowest present cost). Assume a 10% interest rate. (Chapter 5)

Year	Alt A	Alt B
0	-$4,000	-$1,000
1	-$500	-$500
2	-$500	-$800
3	-$500	-$1,100
4	-$500	-$1,400
5	-$500	-$1,700
6	-$500	-$2,000

Answer 1

Q1.

Given,

Required annual amount for perpetuity = $5,000

Interest rate = 4%

Amount to be invested today = PW of the given annuity = $5,000(P/A, 4%, ∞0 = $5,000 * 1/(4%) = $5,000*1/(0.04) = $125,000

Ans: $125,000

Q2. Amount received at the end of each year for 8 years = $500

Interest rate = 7%

From the compound interest table, we obtain

(P/A, 7%, 8) = 5.971

(F/A, 7%, 8) = 10.260

Equivalent present value = $500(P/A, 7%, 8) = $500*5.971 = $2,985.50

Equivalent future value at the end of 8 years = $500(F/A, 7%, 8) = $500*10.260 = $5,130

Q3. Interest rate = 10%

From the compound interest table, we obtain

(P/A, 10%, 6) = 4.355

(P/G, 10%, 6) = 9.684

Present worth of the Alternative A = -$4,000 -$500(P/A, 10%, 6) = -$1,000 -$500*4.355 = -$6,177.5

Alternative B can be split into a initial cost of -$1,000 in year 0, a uniform annual cost of -$500 for 6 years and a gradient series with G = -$300 for 6 years

Present worth of the Alternative A = -$1,000 -$500(P/A, 10%, 6) -$300(P/G, 10%, 6) =-$1,000 -$500*4.355 -$300*9.684 = -$6,082.7

As the PW of alternative B is higher than that of alternative A (alternately, it could be said that the alternative B has lower cost than alternative A), select alternative B