1. Compute the NPV of the future cash flows. The maximum acceptable investment is this NPV.

2. Compute the NPV of all cash flows associated
with **A** using the MARR as the interest rate. If the NPV >= 0, accept
**A**.

3. Find the interest rate that causes the NPV to be zero. This is the ROR.

4. The ones near the present affect the decision because of the time value of money.

5. The cash flow repeats in 2 year cycles. One cycle is a payment of 100 at time 0 and a receipt of 120 at time 1. The NAW of the cycle is

NAW = [-100 + 120(P/F,i,1)](A/P,i,2)

6. In general calculate NAW with the MARR. Then calculate

P = NAW/MARR.

In the case of 20%, NAW = P = 0.

a. A = 1000(A/P,.01,24)

b. effective i = (1.01)^12 - 1

c. Payoff = 1000(F/P,0.01,12) - A(F/A,0.01,12)

or Payoff = A(P/A,0.01,12) present worth of remaining payments.

a. 1000 = 50(P/A,.01, 24) + x(P/G, 0.01, 24).

x = [1000 - 50(P/A,.01, 24)]/(P/G, 0.01, 24)

b. Payoff = 1000(F/P,0.01,12) - 50(F/A,0.01,12) - x(P/G,0.01,12)(F/P,0.01,12)

9. Let S be the selling price. The value after five years is

- 1000(F/P, i, 5) + 100(A/P, i, 5) + S = 0

S = 1000(F/P, i, 5) - 100(F/A, i, 5)

a. The NPV is equal to the sum of the future cash flows minus P.

b. The NPV is - P.

11. In both cases a and b, the present value decreases. The present worth factor is (1 + i)^(-n). The value of this factor decreases with either increasing i or n.

12. Using linear interpolation, an estimate is

i = 0.10 + 0.03(20/30) = 0.12 or 12%.

13. NAW of costs = 1000(A/P, 0.1, 10) + 100+ 100(A/G,0.1, 10) - 500(A/F, 0.1, 10)

14. Assumes annual costs: 100, 100, 100, 100, 100, 200, 300, 400, 500, 600

NAW of costs =1000(A/P, 0.1, 10) + 100 + 100(P/G, 0.1, 6)(P/F, 0.1, 4)(A/P, 0.1, 10) - 500(A/F, 0.1, 10)

15. Compute the NPW of costs for each alternative. Select the one with the smallest NPW of costs.

You can also do this by selecting the alternative with the smallest NAW of costs.

16. Compute the NAW of costs for each alternative. Select the one with the smallest NAW of costs.

Alternatively, select a study period of 12 years, and use the present worth method.

17. The interest rate is zero, since the payments equal exactly the loan.

18. Since you pay the entire principal at the end of the loan, you are paying 2% per month interest. The nominal rate is 24% per year. The effective rate is = (1.02)^12 - 1.