6 20 points You are going to invest in one of two projects T

6. (20 points) You are going to invest in one of two projects. Their streams of net benefits are given by Year Project A Project B 10 128 40 0 9 77 where year 1 is next year. (10 pts)(a) If you have a positive discount rate, which of these 2 projects would you prefer to invest in? Explain how you arrived at this conclusion

Solution

(a)

Let us assume an arbitrary positive discount rate of 1% and compute Present Worth (PW) for both projects.

Project A: 10 x P/F(1%, 1) + 12 x P/F(1%, 2) + 8 x P/F(1%, 3) + 4 x P/F(1%, 4) + 0 x P/F(1%, 5)

= 10 x 0.99 + 12 x 0.98 + 8 x 0.97 + 4 x 0.96

= 9.9 + 11.76 + 7.76 + 3.84

= 33.26

Project B: 0 x P/F(1%, 1) + 9 x P/F(1%, 2) + 11 x P/F(1%, 3) + 7 x P/F(1%, 4) + 7 x P/F(1%, 5)

= 0 + 9 x 0.98 + 8 x 0.97 + 7 x 0.96 + 7 x 0.95

= 8.82 + 7.76 + 6.72 + 6.65

= 29.95

Since PW_{Project A} > PW_{Project B}, I should invest in project A.

(b)

When discount rate is zero, PW is equal to the sum of all non-discounted cash flows.

PW, Project A = 10 + 12 + 8 + 4 + 0 = 34

PW, Project B = 0 + 9 + 11 + 7 + 7 = 34

Since PW_{Project A} = PW_{Project B}, I should be indifferent between the two projects.