Question

A project has expected cash flows of -$1,000, $2,500, and -$1,540 in years 0, 1, and 2, respectively. The cost of capital is 15%.

a. Construct an NPV profile using interest rates of 0, 10, 20, 30, 40, 50, and 60%.

b. What is the IRR of the project?

Answer 1

a.

Discount rate	0.0000%
Cash flows	Year	Discounted CF= cash flows/(1+rate)^year	Cumulative cash flow
(1,000.000)	0	(1,000.00)	(1,000.00)
2,500.000	1	2,500.00	1,500.00
(1,540.000)	2	(1,540.00)	(40.000)

NPV at 0% = 40

Discount rate	10.0000%
Cash flows	Year	Discounted CF= cash flows/(1+rate)^year	Cumulative cash flow
(1,000.000)	0	(1,000.00)	(1,000.00)
2,500.000	1	2,272.73	1,272.73
(1,540.000)	2	(1,272.73)	-

NPV at 10% = 0

Discount rate	20.0000%
Cash flows	Year	Discounted CF= cash flows/(1+rate)^year	Cumulative cash flow
(1,000.000)	0	(1,000.00)	(1,000.00)
2,500.000	1	2,083.33	1,083.33
(1,540.000)	2	(1,069.44)	13.889

NPV at 20% = 13.889

Discount rate	30.0000%
Cash flows	Year	Discounted CF= cash flows/(1+rate)^year	Cumulative cash flow
(1,000.000)	0	(1,000.00)	(1,000.00)
2,500.000	1	1,923.08	923.08
(1,540.000)	2	(911.24)	11.834

NPV at 30% = 11.834

Discount rate	40.0000%
Cash flows	Year	Discounted CF= cash flows/(1+rate)^year	Cumulative cash flow
(1,000.000)	0	(1,000.00)	(1,000.00)
2,500.000	1	1,785.71	785.71
(1,540.000)	2	(785.71)	-

NPV at 40% = 0

Discount rate	50.0000%
Cash flows	Year	Discounted CF= cash flows/(1+rate)^year	Cumulative cash flow
(1,000.000)	0	(1,000.00)	(1,000.00)
2,500.000	1	1,666.67	666.67
(1,540.000)	2	(684.44)	(17.778)

NPV at 50% = -17.778

Discount rate	60.0000%
Cash flows	Year	Discounted CF= cash flows/(1+rate)^year	Cumulative cash flow
(1,000.000)	0	(1,000.00)	(1,000.00)
2,500.000	1	1,562.50	562.50
(1,540.000)	2	(601.56)	(39.062)

NPV at 60% = -39.062

IRR = 10% and 40% since NPV is 0