Question

A company is considering a project that has an up-front cost paid today at t = 0. The project will generate positive cash flows of $50,175 a year at the end of each for the next 5 years. The project’s NPV is $87,983 and the company’s return on the project is 8.3 percent. What is the project’s payback?

Answer 1

In order to calculate the payback period we first need to calculate the upfront cost of the project at t = 0 i.e.., Present value of cash outflows

Given :
NPV = $50,175
Project Life = 5 years
Rate of return = 8.3%
NPV = $87,983

Step 1 : Calculate Present Value of Cash Inflows over project life

Year	Cash Inflow	[email protected]%	Present value
1	$50,175.00	0.923361034	$46,329.64
2	$50,175.00	0.852595599	$42,778.98
3	$50,175.00	0.787253554	$39,500.45
4	$50,175.00	0.726919256	$36,473.17
5	$50,175.00	0.671208916	$33,677.91
		Total	$198,760.15

Present Value of cash Inflows = $198,760.15

Step 2 : Calculate Present Value of Cash Outflows

Present Value of Cash Outflows = Present Value of cash Inflows - NPV

Present Value of cash Inflows	$198,760.15
Less: NPV	$87,983.00
Present Value of Cash Outflows	$110,777.15

Step 3 : Calculation of Payback period

Year	Cash flow	Cumulative cash flows
0	$(110,777.15)	$(110,777.15)
1	$50,175.00	$(60,602.15)
2	$50,175.00	$(10,427.15)
3	$50,175.00	$39,747.85
4	$50,175.00	$89,922.85
5	$50,175.00	$140,097.85

Payback Period =Initial Investment / Net Cash Flow per Period

Payback Period = 110,777.15 / 50,175.00 = 2.2078 or 2.21years

Payback Period = 2.21years

Alternatively, Pay back period can be calculated using Cumulative cash flows

Pay back period = A + B/C

Where,
A is the last period number in which we have cumulative cash flow;
B is the cumulative net cash flow (ignoring negative sign) at the end of the period A
C is the total cash inflow during the period following period A

Pay back period = 2 + 10,427.15 / 50,175 = 2 + 0.2078 = 2.2078 or 2.21years

Note :

1. Alternate method for payback period is used when cash flows are uneven

2. PVF = (1/(1+r)^n