Question

Calculate the payback period, net present value, profitability index, and internal rate of return for Project A. Assume a discount rate of 20%. Should the firm accept or reject Project A? Explain. If the firm must choose between Project A and Project B, which is the better choice? Explain. Under what circumstances should the modified internal rate of return be used instead of the standard internal rate of return?

Project A			Project B
Year	Cash Flow		Year	Cash Flow
0	-$100,000		0	-$1
1	$40,000		1	$0
2	$50,000		2	$0
3	$60,000		3	$10

Answer 1

For Project A,

For first two years, cash inflows are 40000+50000=90000. An inflow of 10000 is further required to get back the initial investment. It can be obtained in further 0.167 years, as third year cash flow is 60000. So, payback period is 2+0.167= 2.167 years.

Net present value is calcualted as follows: -100000+40000/1.2+50000/1.2^2+60000/1.2^3= 2777.77. So, Net present value is $2777.77

Profitability index is calculated by Present value of cash inflows/Initial investment= (40000/1.2+50000/1.2^2+60000/1.2^3)/100000= 1.0277

Let IRR be r, where -100000+40000/r+50000/r^2+60000/r^3=0. On solving, we get 21.65%.

As NPV is positive, the firm should accept project A.

If the firm must choose between Project A and Project B, the decision should be taken based on NPV, as it is a better evaluating option among others. NPV of project B is -1+10/1.2^3= $4.78. As NPV of project A is greater than project B, Project A should be chosen.

Modified internal rate of return is used to address few problems with standard internal rate of return. IRR assumes that positive cashflows can be reinvested at the same rate as they are generated which is not always possible. There is one more circumstance where Multiple IRRs are obtained for a given set of cashflows. To overcome these type of drawbacks, MIRR is preferred.