Question

You have the following information on a project's cash flows. The cost of capital is 12.5%.

Year	Cash flows
0	-$123,000
1	28,000
2	31,000
3	36,000
4	41,000
5	49,000

The NPV of the project is $______ (round to two decimal places); The IRR is ______ percent (round to two decimal places); the payback is _______ years (round to two decimal places)

Answer 1

Present value of inflows=cash inflow*Present value of discounting factor(rate%,time period)

=28000/1.125+31000/1.125^2+36000/1.125^3+41000/1.125^4+49000/1.125^4

=$127454.28

NPV=Present value of inflows-Present value of outflows

=$127454.28-$123000

=$4454.28

Year	Cash flows	Cumulative Cash flows
0	(123000)	(123000)
1	28000	(95000)
2	31000	(64000)
3	36000	(28000)
4	41000	13000
5	49000	62000

Payback period=Last period with a negative cumulative cash flow+(Absolute value of cumulative cash flows at that period/Cash flow after that period).

=3+(28000/41000)=3.68 YEARS(APPROX).

Let irr be x%

At irr,present value of inflows=present value of outflows.

123000=28000/1.0x+31000/1.0x^2+36000/1.0x^3+41000/1.0x^4+49000/1.0x^5

Hence x=irr=13.83%(Approx).