Question

5. A project requires an investment of $100m in two years. It is expected to yield $25m after the third year, $25m after the fourth year; in the fifth year it will yield $7m, which will grow at 1% per year over the next five years. What is the project’s NPV at a cost of capital of 15%?

Answer 1

Solution :- NPV of Project = Present value of cash inflows - Present value of cash outflow.

Present value of cash outflow (made in year 2) = 100 Million / (1 + 0.15)2

= 100 Million / (1.15)2

= 100 Million / 1.3225

= $ 75.614 Million (approx) (Value of cash outflow in present terms = $ 75.614 Million)

Calculation of Present value of cash inflows:-

Year end	Cash inflow	Present value factors (See Note)	Present value of cash inflow (Column 2 * Column 3)
3	25 M (M denotes Million)	0.658	16.45 M
4	25 M	0.572	14.30 M
5	7 M	0.497	3.479 M
6	7.07 M (7 M + 1 % of 7 M)	0.432	3.054 M
7	7.14 M (7.07 M + 1 % of 7.07 M)	0.380	2.713 M
8	7.21 M (7.14 M + 1 % of 7.14 M)	0.327	2.358 M
9	7.28 M (7.21 M + 1 % of 7.21 M)	0.284	2.068 M
10	7.35 M (7.28 M + 1 % of 7.28 M)	0.247	1.815 M
Total			46.237 M (Rounded off to 46.24 Million)

(Note :- Present value factors at 15 % for Year 3, Year4, Year 5, Year 6, Year 7, Year 8, Year 9 and Year 10 are 0.658, 0.572, 0.497, 0.432, 0.380, 0.327, 0.284 and 0.247 respectively using the present value table)

Accordingly, NPV of Project = 46.24 M - 75.614 M (M denotes Million).

= (-) 29.374 M (Rounded off to - 29.37 Million)

Conclusion :- NPV of Project = (-) 29.37 Million dollars. (Project should not be accepted as NPV is negative).