Question

Your division is considering two investment projects, each of which requires an up-front expenditure of $17 million. You estimate that the investments 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 projects' net present values, assuming the cost of capital is 5%, 10% and 15%?

What are the two projects' IRRs at these same costs of capital?

Answer 1

1]	NPV:	Cost of capital
		5%	10%	15%
	Project A	$      14,108,952	$     10,836,213	$       8,059,587
	Project B	$      16,300,939	$     13,954,170	$     11,897,838
2]	IRR:
	Project A	36.12%	36.12%	36.12%
	Project B	65.92%	65.92%	65.92%
	Note: IRR is the same as it is independent of the cost of capital. It is that discount rate for which NPV = 0.
	WORKINGS:
	PROJECT A:
	Year	Cash flow	PVIF at 5%	PV at 5%	PVIF at 10%	PV at 10%	PVIF at 15%	PV at 15%
	0	$    (17,000,000)	1	$   (17,000,000)	1.00000	$   (17,000,000)	1.00000	$   (17,000,000)
	1	$        5,000,000	0.95238	$       4,761,905	0.90909	$        4,545,455	0.86957	$        4,347,826
	2	$      10,000,000	0.90703	$       9,070,295	0.82645	$        8,264,463	0.75614	$        7,561,437
	3	$      20,000,000	0.86384	$     17,276,752	0.75131	$      15,026,296	0.65752	$     13,150,325
	NPV			$     14,108,952		$      10,836,213		$        8,059,587
	IRR is that discount rate for which NPV = 0. It has to be found out by trying different discount rates to get 0 NPV.
	Year	Cash flow	PVIF at 37%	PV at 37%	PVIF at 36%	PV at 36%
	0	$    (17,000,000)	1	$   (17,000,000)	1.00000	$   (17,000,000)
	1	$        5,000,000	0.72993	$       3,649,635	0.73529	$        3,676,471
	2	$      10,000,000	0.53279	$       5,327,934	0.54066	$        5,406,574
	3	$      20,000,000	0.38890	$       7,778,006	0.39754	$        7,950,845
	NPV			$         (244,424)		$              33,890
	IRR = 36%+1%*33890/(33890+244424) =	36.12%
	PROJECT B:
	Year	Cash flow	PVIF at 5%	PV at 5%	PVIF at 10%	PV at 10%	PVIF at 15%	PV at 15%
	0	$    (17,000,000)	1	$   (17,000,000)	1.00000	$   (17,000,000)	1.00000	$   (17,000,000)
	1	$      20,000,000	0.95238	$     19,047,619	0.90909	$      18,181,818	0.86957	$     17,391,304
	2	$      10,000,000	0.90703	$       9,070,295	0.82645	$        8,264,463	0.75614	$        7,561,437
	3	$        6,000,000	0.86384	$       5,183,026	0.75131	$        4,507,889	0.65752	$        3,945,097
	NPV			$     16,300,939		$      13,954,170		$     11,897,838
	IRR is that discount rate for which NPV = 0. It has to be found out by trying different discount rates to get 0 NPV.
	Year	Cash flow	PVIF at 65%	PV at 65%	PVIF at 66%	PV at 66%
	0	$    (17,000,000)	1	$   (17,000,000)	1.00000	$   (17,000,000)
	1	$      20,000,000	0.60606	$     12,121,212	0.60241	$      12,048,193
	2	$      10,000,000	0.36731	$       3,673,095	0.36290	$        3,628,974
	3	$        6,000,000	0.22261	$       1,335,671	0.21861	$        1,311,677
	NPV			$           129,977		$            (11,156)
	IRR = 65%+1%*129977/(129977+11156) =	65.92%