Question

(IRR calculation) Determine to the nearest percent the IRR on the following projects:

a. An initial outlay of $9,000 resulting in a free cash flow of $3,000 at the end of year 1, $6 ,000 at the end of year 2, and $8,500 at the end of year 3

b. An initial outlay of $9,000 resulting in a free cash flow of $8,500 at the end of year 1, ?$6,000 at the end of year 2, and $ 3,000 at the end of year 3

c. An initial outlay of $9,000 resulting in a free cash flow of $3,000 at the end of years 1 through 5 and $6,000 at the end of year 6

 

 

Answer 1

				IRR
		Project A		36%
		Project B		55%
		Project C		28%
Working:
Project A:
	IRR is the rate, at which net present value is zero.
	Net Present Value at 20%					Net Present Value at 40%
	Year	Cash flow	Discount factor	Present Value		Year	Cash flow	Discount factor	Present Value
	a	b	c=1.20^-a	d=b*c		a	b	c=1.40^-a	d=b*c
	0	$            -9,000	1.0000	$       -9,000		0	$   -9,000	1.0000	$   -9,000
	1	3,000	0.8333	2,500		1	3,000	0.7143	2,143
	2	6,000	0.6944	4,167		2	6,000	0.5102	3,061
	3	8,500	0.5787	4,919		3	8,500	0.3644	3,098
		Net Present Value		2,586			Net Present Value		-698
	IRR	=	20%+(40%-20%)*(2586/(2586+698))
		=	36%
Project B:
	IRR is the rate, at which net present value is zero.
	Net Present Value at 20%					Net Present Value at 60%
	Year	Cash flow	Discount factor	Present Value		Year	Cash flow	Discount factor	Present Value
	a	b	c=1.20^-a	d=b*c		a	b	c=1.60^-a	d=b*c
	0	$            -9,000	1.0000	$       -9,000		0	$   -9,000	1.0000	$   -9,000
	1	8,500	0.8333	7,083		1	8,500	0.6250	5,313
	2	6,000	0.6944	4,167		2	6,000	0.3906	2,344
	3	3,000	0.5787	1,736		3	3,000	0.2441	732
		Net Present Value		3,986			Net Present Value		-611
	IRR	=	20%+(60%-20%)*(3986/(3986+611))
		=	55%
Project C:
	IRR is the rate, at which net present value is zero.
	Net Present Value at 20%					Net Present Value at 30%
	Year	Cash flow	Discount factor	Present Value		Year	Cash flow	Discount factor	Present Value
	a	b	c=1.20^-a	d=b*c		a	b	c=1.30^-a	d=b*c
	0	$            -9,000	1.0000	$       -9,000		0	$   -9,000	1.0000	$   -9,000
	1	3,000	0.8333	2,500		1	3,000	0.7692	2,308
	2	3,000	0.6944	2,083		2	3,000	0.5917	1,775
	3	3,000	0.5787	1,736		3	3,000	0.4552	1,365
	4	3,000	0.4823	1,447		4	3,000	0.3501	1,050
	5	3,000	0.4019	1,206		5	3,000	0.2693	808
	6	6,000	0.3349	2,009		6	6,000	0.2072	1,243
		Net Present Value		1,981			Net Present Value		-450
	IRR	=	20%+(30%-20%)*(1981/(1981+450))
		=	28%