Question

Your division is considering two investment projects, each of which requires an up-front expenditure of $14 million. You estimate that the investments will produce the following net cash flows:

Year

Year	$5,000,000	$20,000,000
1	10,000,000	10,000,000
2	20.000.000	6,000,000
3

a. What are the two project’s NPVs assuming the cost of capital is 4%, 11%, 16%?

b. What are the two projects’ IRRs at those same costs of capital?

Answer 1

answer a)
		Present value computation							Present value computation
		Year	Project A		PVIF @ 4%	PVIF @ 11%	PVIF @ 16%		PV @ 4%	PV @ 11%	PV @ 16%
		0	-14000000		1	1	1		(14,000,000)	(14,000,000)	(14,000,000)
		1	5000000		0.96154	0.9009	0.86207		4,807,692	4,504,505	4,310,345
		2	10000000		0.92456	0.81162	0.74316		9,245,562	8,116,224	7,431,629
		3	20000000		0.889	0.73119	0.64066		17,779,927	14,623,828	12,813,153
								NPV =	17,833,182	13,244,556	10,555,127
		Year	Project B		PVIF @ 4%	PVIF @ 11%	PVIF @ 16%		PV @ 4%	PV @ 11%	PV @ 16%
		0	-14000000		1	1	1		(14,000,000)	(14,000,000)	(14,000,000)
		1	20000000		0.96154	0.9009	0.86207		19,230,769	18,018,018	17,241,379
		2	10000000		0.92456	0.81162	0.74316		9,245,562	8,116,224	7,431,629
		3	6000000		0.889	0.73119	0.64066		5,333,978	4,387,148	3,843,946
								NPV=	19,810,310	16,521,391	14,516,954
answer b)		IRR : we have to use trial and error method to compute IRR. IRR is the rate at which NPV = ZERO
		Lets use 48% and 49% for project A
		Year	Project A		PVIF @ 48%	PVIF @ 49%		PV @ 48%	PV @ 49%
		0	-14000000		1	1		(14,000,000)	(14,000,000)
		1	5000000		0.67568	0.67114		3,378,378	3,355,705
		2	10000000		0.45654	0.45043		4,565,376	4,504,302
		3	20000000		0.30847	0.3023		6,169,427	6,046,042
								113,182	(93,951)
		IRR =
		Lower rate +(Lower rate NPV/(Lower rate NPV-Higher rate NPV))*Difference in rate
		=48%+(113182/(113182--93951))*1%
		48.55%
		Lets use 91% and 92% for project B
		Year	Project A		PVIF @ 91%	PVIF @ 92%		PV @ 91%	PV @ 92%
		0	-14000000		1	1		(14,000,000)	(14,000,000)
		1	20000000		0.52356	0.52083		10,471,204	10,416,667
		2	10000000		0.27412	0.27127		2,741,153	2,712,674
		3	6000000		0.14352	0.14129		861,095	847,711
								73,452	(22,949)
		IRR =
		Lower rate +(Lower rate NPV/(Lower rate NPV-Higher rate NPV))*Difference in rate
		=91%+(73452/(73452--22949))*1%
		91.76%