Gomi Waste Disposal is evaluating a project that would last for 4 years. The project’s internal...

Gomi Waste Disposal is evaluating a project that would last for 4 years. The project’s internal rate of return is 8.18 percent; its NPV is 8,920 dollars; and the expected cash flows are -56,800 dollars at time 0, 10,500 dollars in 1 year, 46,300 dollars in 2 years, and X in 4 years. What is X?

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Expert Solution

Computation of NPV at discount rate of 8.18 %.

NPV = PV of future cash inflows – Initial investment

Year	Cash flow (C)	Computation of PV Factor	PV Factor @ 8.18 % (F)	PV (C x F)
0	-$ 56,800	1/ (1+0.0818)⁰	1	-$ 56,800.00
1	$ 10,500	1/ (1+0.0818)¹	0.924385283786282	$ 9706.0454798
2	$ 46,300	1/ (1+0.0818)²	0.854488152880645	$ 39,562.8014784
3	0	1/ (1+0.0818)³	0.789876273692591	0.0000000
4	X	1/ (1+0.0818)⁴	0.730150003413377	0.7301500 X
			NPV	-$ 7,531.153042 + 0.7301500 X

NPV of any project is zero at discount rate equals to IRR.

-$ 7,531.153042 + 0.73015 X = 0

0.73015 X = $ 7,531.153042

X = $ 7,531.153042/0.73015

= $ 10,314.5285790591 or $ 10,315

Cash inflow X in year 4^th is $ 10,315

jeff jeffy answered 1 year ago

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