Question

Shannon Industries is considering a project that has the following cash flows :   

Year	CF
0	-6240
1	1980
2	3750
3	?
4	1000

The project has a payback of 2.25 years.
The firm’s cost of capital is 9.3 percent. What is the project’s net present value (NPV)?

Answer 1

Payback period is the ime period in which the initial investment is earned back.

Payback period = 2.25 years

This means that all initial amount is earned in less than 3 years

Initial Investment = 6240

1st year earning = 1980

2nd year earning = 3750

Cumulative (1 + 2) = 1980 + 3750 = 5730

Hence, we know that 5730 amunt is earned till end of 2 years and hence remaining investment amount (6240 - 5730) = 510 amount is earned in (1/4th = 0.25) of the 3 rd year.

Why?

Please see that payback period is 2.25 years. Now remove the the first 2 years eaning (5730) and hence subtract 2 from this payback period. We get (2.25 - 2) = 0.25 years. This is 1/4th of the 3rd year. Hence all remaining amount needs to be eanred in this time.

So in 3 months of 3rd year, the cashflow is 510

hence for the whole 3rd year, the cashflow will be 510 * 4 = 2040

Project
Initial Investment	6,240
year	Cashflow	Cumulative Cashflow
1	1,980	1,980
2	3,750	5,730
3	2,040	7,770
4	1,000	8,770

Now we know all the cashflows.

NPV or the net present value is defined as the difference between the present value fo the cash outfolows and the present value of the cash inflows over the life cycle of the project.

NPV is given by:

Discount rate = 9.3%

Hence,

NPV = [1980 / ( 1 + 9.3%) ^1] + [3750 / ( 1 + 9.3%) ^2] + [2040/ ( 1 + 9.3%) ^1] + [1000/ ( 1 + 9.3%)^1] - Initial Investment

NPV = 1811.53 + 3139 + 1562.32 + 700.68 - 6240

NPV = 973.52