Question

"The initial investment for a project is $91,000. The project will last for 5 years and can be salvaged for $7,280 at the end of 5 years. The annual expenses for the project are $5,500 in year 1 and increase at an annual rate of 5% in each year of the project. Assume the annual revenue remains the same in each of the 5 years. What does the annual revenue need to be in order for the internal rate of return of the project to equal 24.8%? "

Answer 1

Internal rate of return (IRR) is 24.8%, which means that Present value (PV) of all costs must equal PV of revenues. PV of costs, discounted at 2.8%, is computed as follows. In year 5, salvage value is deducted from cost.

PV factor for year N = (1.248)^-N

Year	Cost ($)	PV Factor @24.8%	Discounted Cost ($)
	(A)	(B)	(A) x (B)
0	91,000	1.0000	91,000
1	5,500	0.8013	4,407
2	5,775	0.6421	3,708
3	6,064	0.5145	3,120
4	6,367	0.4122	2,625
5	-595	0.3303	-196
		PV of Cost ($) =	1,04,663

If annual revenue be R, then

$104,663 = R x PVIFA(24.8%, 5)

$104,663 = R x 2.7003**

R = $104,663 / 2.7003

R = $38,759.77 ~ $38,760

**PVIFA(r%, N) = [1 - (1 + r)^-N] / r

PVIFA(24.8%, 5) = [1 - (1.248)^-5] / 0.216 = (1 - 0.3303) / 0.248 = 0.6697 / 0.248 = 2.7003