Question

3. Your division is considering two investment projects, each of which requires an up-front expenditure of 20 million. You estimate that the investment will produce the following net cash flows:

Year          Project A                       Project B

1 $5,000,000 $20,000,000

2                10,000,000                    10,000,000

3 20,000,000                    6,000,000

• What are the two project’s net present values, assuming the cost of capital is 5%? 10%? 15%?
• What are the two projects’ IRRs at these same costs of capital?

Show your work.

Answer 1

Answer:-

Initial investment = $ 20 million

NPV when cost of capital = 5 %
NPV of A = - $ 20 m + $ 5 m / 1.05 + $ 10 m / 1.05² + $ 20 m / 1.05³
NPV of A = - $ 20 m + $ 4.76 m + $ 9.07 m + $ 17.27 m
NPV of A = - $ 20 m + $ 31.1 m
NPV of A = $ 11.1 million

NPV of B = - $ 20 m + $ 20 m / 1.05 + $ 10 m / 1.05² + $ 6 m / 1.05³
NPV of B = - $ 20 m + $ 19.05 + $ 9.07 m + $ 5.18 m
NPV of B = - $ 20 m + $ 33.3
NPV of B = $ 13.3 million

NPV when cost of capital = 10 %
NPV of A = - $ 20 m + $ 5 m / 1.1 + $ 10 m / 1.1² + $ 20 m / 1.1³
NPV of A = - $ 20 m + $ 4.54 m + $ 8.26 m + $ 15.02 m
NPV of A = - $ 20 m + $ 27.82 m
NPV of A = $ 7.82 million

NPV of B = - $ 20 m + $ 20 m / 1.1 + $ 10 m / 1.1² + $ 6 m / 1.1³
NPV of B = - $ 20 m + $ 18.18 + $ 8.26 m + $ 4.51 m
NPV of B = - $ 20 m + $ 30.95 m
NPV of B = $ 10.95 million

NPV when cost of capital = 15 %
NPV of A = - $ 20 m + $ 5 m / 1.15 + $ 10 m / 1.15² + $ 20 m / 1.15³
NPV of A = - $ 20 m + $ 4.35 m + $ 7.56 m + $ 13.15 m
NPV of A = - $ 20 m + $ 25.06 m
NPV of A = $ 5.06 million

NPV of B = - $ 20 m + $ 20 m / 1.15 + $ 10 m / 1.15² + $ 6 m / 1.15³
NPV of B = - $ 20 m + $ 17.39 m + $ 7.56 m + $ 3.94 m
NPV of B = - $ 20 m + $ 28.89
NPV of B = $ 8.89 million

IRRs

IRR of A , NPV is set at zero
0 = - $ 20 m + $ 5 m / (1+ IRR) + $ 10 m / ( 1 + IRR )² + $ 20 m / (1+ IRR)³
IRR of A = 26.72 %

IRR of B , NPV is set at zero
0 = - $ 20 m + $ 20 m / (1+ IRR) + $ 10 m / ( 1 + IRR )² + $ 6 m / (1+ IRR)³
IRR of B = 47.63 %