Question

​(Payback ​period, NPV,​ PI, and IRR calculations​) You are considering a project with an initial cash outlay of ​$85 comma 000 and expected free cash flows of ​$30 comma 000 at the end of each year for 6 years. The required rate of return for this project is 6 percent.

a. What is the​ project's payback​ period?

b. What is the​ project's NPV​?

c. What is the​ project's PI​?

d. What is the​ project's IRR​?

Answer 1

		Payback period	For IRR	For NPV
	Year	Cashflows ($)	Cumulative cashflows	Discounting factor @ 26.804%	PV of cashflows	Discounting factor @ 6%	PV of cashflows
	0	-85000	-85000	1	-85000.00	1	-85000.00
	1	30000	-55000	0.788618656	23658.56	0.943396226	28301.89
	2	30000	-25000	0.621919384	18657.58	0.88999644	26699.89
	3	30000	5000	0.490457228	14713.72	0.839619283	25188.58
	4	30000	35000	0.38678372	11603.51	0.792093663	23762.81
	5	30000	65000	0.305024857	9150.75	0.747258173	22417.75
	6	30000	95000	0.240548293	7216.45	0.70496054	21148.82
			NPV		0		62519.73
a)	Payback period= A+ (B/C)
	where,
	A= last period number with negative cumulative cashflows
	B= absolute value of cumulative net cashflow at the end of period A
	C= total cash inflow during the period following period A
	Payback period = 2+(25000/30000)
			2.83 years
b)	We know NPV of the project is equal to the present value of future cashflows discounted at the required rate of return. NPV of project is $62519.73 - Refer table for details
c)	Profitability index= (Initial investment+NPV)/Initial investment
		(85000+62519.73)/85000
			1.74
d)	We know that IRR is the rate at which NPV of the project is 0. By trial and error method we guessed the IRR of project to be 26.804%. So the IRR is 26.804% as the NPV is zero at that rate (see the table above).