Question

Projects A and? B, of equal? risk, are alternatives for expanding Rosa? Company's capacity. The? firm's cost of capital is 11?%.

The cash flows for each project are shown in the following? table:

Project A		Project B
Initial investment ?(CF 0CF0?)	?$130,000		?$100,000
Year ?(t?)	Cash inflows ?(CF Subscript tCFt?)
1	?$30,000		?$30,000
2	?$35,000		?$30,000
3	?$40,000		?$30,000
4	?$45,000		?$30,000
5	?$50,000		?$30,000

a.??Calculate each? project's payback period.

b.??Calculate the net present value? (NPV) for each project.

c.??Calculate the internal rate of return? (IRR) for each project.

d.??Indicate which project you would recommend.

Answer 1

a) Payback period is basically and undiscounted technique to find out the time by which initial investment is recovered. Lower payback is prefered.

Closing balance = Opening balance + Investment - CF

Opening balance of one period is the closing balance of the previous period.

For project A: We see that at the end of the year 3 the closing balance is of 25000 but at the end of year 3 it is -20000 which implies that some time during the year 4, entire investment is recovered. We assume that entire CF is generated uniformly throughout the year and therefore the payback period is calculated as follows:

For project B: We see that at the end of the year 3 the closing balance is of 10000 but at the end of year 3 it is -20000 which implies that some time during the year 4, entire investment is recovered. We assume that entire CF is generated uniformly throughout the year and therefore the payback period is calculated as follows:

So Project B is preferable.

b) Following Screenshot shows how to calculate the NPV of the two projects, NPV rule is that the project with the highest Positive NPV should be selected which in this case is again Project A:

So NPV equation for Project A:

And NPV equation for Project B:

c) IRR is basically that rate which when used to discount the CF's there sum is equal to the initial cash investment leading to an NPV of 0. Following screenshot gives the IRR for the two projects. As IRR is the cost of the project, lower cost is recommended and therefore according to the IRR rule. project A with lower IRR is better

So IRR equation for Project A:

And IRR equation for Project B:

d) As per rules if there is a conflict between methods, NPV decision rule is the one that is considered therefor as NPV rule suggests project A is better so that is acceptable no matter what the payback period method suggests.