Question

An investment project provides cash flows of $640 per year for 8 years. a) What is the payback if the initial outlay is $2,700? b) What if the initial outlay is $3,900? c) Will the initial outlay be recovered before the end of the project if it is $6,800?

Answer 1

The formula to calculate the payback period of an investment depends on whether the periodic cash inflows from the project are even or uneven.

If the cash inflows are even (such as for investments in annuities), the formula to calculate payback period is:

Payback Period =	Initial Investment
Net Cash Flow per Period

When cash inflows are uneven, we need to calculate the cumulative net cash flow for each period and then use the following formula:

Payback Period =	A +	B
C

Where,
A is the last period number with a negative cumulative cash flow;
B is the absolute value (i.e. value without negative sign) of cumulative net cash flow at the end of the period A; and
C is the total cash inflow during the period following period A

Cumulative net cash flow is the sum of inflows to date, minus the initial outflow.

a)

Payback if the initial outlay is $2700

Period	Cash Flow	Cumulative
0	-2700	-2700
1	640	-2060
2	640	-1420
3	640	-780
4	640	-140
5	640	500
6	640	1140
7	640	1780
8	640	2420
Payback	4.22	periods

b)

Payback if the initial outlay is $3900

Period	Cash Flow	Cumulative
0	-3900	-3900
1	640	-3260
2	640	-2620
3	640	-1980
4	640	-1340
5	640	-700
6	640	-60
7	640	580
8	640	1220
Payback	6.09	periods

c)

Payback if the initial outlay is $6800

Period	Cash Flow	Cumulative
0	-6800	-6800
1	640	-6160
2	640	-5520
3	640	-4880
4	640	-4240
5	640	-3600
6	640	-2960
7	640	-2320
8	640	-1680
Payback	10.63	periods

No, the initial cannot be outlay be recovered before the end of the project if it is $6,800

Payback period is 10.63 periods to recover the initial outlay $6800.