Question

"The initial investment for a project is $116,000. The project will last for 5 years and can be salvaged for $11,600 at the end of 5 years. The annual expenses for the project are $5,700 in year 1 and increase at an annual rate of 3% 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 21.6%? "

Answer 1

Internal rate of return (IRR) is 21.6%, which means that Present value (PV) of all costs must equal PV of revenues. PV of costs, discounted at 21.6%, is computed as follows. In year 5, salvage value is deducted from cost.

PV factor for year N = (1.216)^-N

Year	Cost ($)	PV Factor @21.6%	Discounted Cost ($)
	(A)	(B)	(A) x (B)
0	1,16,000	1.0000	1,16,000
1	5,700	0.8224	4,688
2	5,871	0.6763	3,970
3	6,047	0.5562	3,363
4	6,229	0.4574	2,849
5	-5,185	0.3761	-1,950
		PV of Cost ($) =	1,28,920

If annual revenue be R, then

$128,920 = R x PVIFA(21.6%, 5)

$128,920 = R x 2.8883**

R = $128,920 / 2.8883

R = $44,635

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

PVIFA(21.6%, 5) = [1 - (1.216)^-5] / 0.216 = (1 - 0.3761) / 0.216 = 0.6239 / 0.216 = 2.8883