Question

There are two alternative ways of building and operating a project.

A. The government borrows, builds, and operates the project. Because it is considered the risk-free borrower, the government has a comparative advantage in borrowing, and it can borrow at the risk-free rate of 1%. It will cost the government $200 million to build the project in Year 0 and the project will generate a cash flow of $3 million for infinity.

B. A private enterprise, whose weighted average cost of capital is 5%, has a comparative advantage in building and operating the project. It can build the project for $150 million in Year 0 and generate a cash flow of $12.5 million for infinity.

Questions:

1. (10 points) How much are the NPV and IRR of Alternative A? How much are the NPV and IRR of Alternative B?

2 (10 points) If only one of the two alternatives can be chosen, which one should be chosen? Explain fully, with supporting calculations.

3. (10 points) Suggest a way of building and operating the project that would be even better than choosing either A or B. Explain fully, with supporting calculations.

Answer 1

1.

Alternative A

Year	0	1	2	……..
Cash flows of Government	-200	3	3	3
Discounted cash flows	-200/(1+.01)0	3/(1+.01)1	3/(1+.01)2	……

The NPV shall be sum of discounted cash flows of all the years which will included $- 200 m in the first year and the sum of future discounted cash flows.

The series of future discounted cash flows forms a Geometric Progression series from year 1 whose

sum is = 3/(1+0.01)/[1-(1/(1+0.01)] = 300

Hence the NPV of Cash flows of Government = -200 + 300 = $100 m

IRR of series -200 ,300 = 50%

Alternative B

Year	0	1	2	……
Cash flows of Private Enterprise	-150	12.5	12.5	12.5
Discounted cash flows	-150	11.90476	11.33787	10.79797

Similarly NPV of alternative B = $ 100 m

IRR of alternative B = 67%

2. The NPV of both the alternatives is $100 m but the IRR of alternative B is 67% which is more than alternative A. Alternative B should be chosen since the returns on investment are better in alternative B.

3. If project can be done with Government and private partnership where Government invests $ 100 m and Private Enterprise invests $ 50 m, the cash flows will be in following manner:

Year	0	1	2
Cash flows of Government	-100	1.5	1.5
Discounted cash flows	-100	1.485149	1.470444
NPV	50
IRR	50%

Year	0	1	2
Cash flows of Private enterprise	-50	6.25	6.25
Discounted cash flows	-50	5.952381	5.668934
NPV	75
IRR	150%

The combined IRR of cash flows will be 83% and combined NPV is $ 125 m.