Question

Consider an investment that costs $100,000 and has a cash inflow of $25,000 every year for 5 years. The required return is 9%, and the required payback is 4 years.
What is the payback period?
What is the discounted payback period?
What is the NPV?
What is the AAR?
What is the IRR?
What is the MIRR?
What is the PI?
Should we accept the project?
What decision rule should be the primary decision method?
When is the IRR rule unreliable?

Answer 1

Given that Initial Investment is 100000 and cash inflow is 25000 every year for 5 years.

Payback Period:

As, cash inflow is same every year, payback period= Initial Investment/cash inflow each year= 100000/25000= 4. So, Payback Period is 4 Years.

Discounted Payback Period:

Time period	1	2	3	4	5
Dicounted Cash Inflow	22935.77	21042	19304.58	17710.63	16248.28

Cumulative cashinflows till 5th year= 22935.77+21042+19304.58+17710.63+16248.28= 97241.28.

So, using discounted payback, it wont payback the initial investment

NPV:

NPV can be calculated as -10000+25000/1.09+25000/1.09^2+25000/1.09^3+25000/1.09^4+25000/1.09^5= -2758.72.

So, NPV is $-2758.72

AAR:

AAR, Average fate of revenue can be calculated as average cash inflow divided by initial investment. So, ARR= 25000/100000= 25%

IRR:

Let IRR be r, So, -100000+25000/(1+r)+25000/(1+r)^2+25000/(1+r)^3+25000/(1+r)^4+25000/(1+r)^5=0. On solving, we get r= 7.93%

So, IRR is 7.93%

MIRR:

MIRR, called modified internal rate of return is calculated as ((Future value of positive cashflows at cost of capital/Present value of initial investment at financing cost)^(1/n))-1. cost of capital and financing cost is both 9%. So, ((FV(25000) at 9% for 5 year/100000)^(1/5))-1. On calculating, we get MIRR= 8.39%

PI:

PI, profitability index can be calculated as present value of future cashflows/Initial Investment= 97241.28/100000= 0.97

So, PI= 0.97

Though the required payback period of 4 years is satisfied, NPV is less than zero, so, we should not accept the project.

The primary decision rule should be NPV. As it takes into account the time value of money and gives the true value of the investment.

IRR is unreliable, because of its assumption that the cashflows can be reinvested at IRR, which is highly unrealistic. Also, there may be multiple IRRs in some instances.