You have a choice between two mutually exclusive investments. Project A requires

Question

You have a choice between two mutually exclusive investments. Project A requires initial cash outlay of $150,000 and has projected cash flows of $100,000 for year one, $55,000 for year two, and $30,000 for year three. Meanwhile, Project B requires initial cash outlay of $100,000 and has projected cash flows of $40,000 per year for the next three years. The required rate of return is 10%.

(a)(3 points) Calculate the ordinary payback period for both projects and determine which should be accepted. Assume the target payback period is 2 years. Explain why.

(b) (4 points) Calculate the discounted payback period for both projects and determine which should be accepted. Assume the target payback period is 2 years Explain why.

(c) (3 points) Calculate the profitability index (PI) for both projects and determine which should be accepted. Explain why.

(d) (4 points) Assuming the projected cash flow is a future net income, calculate the average accounting return (AAR) for both projects and determine which should be accepted if the target average accounting return is 30%. Explain why.

Explanation / Answer

(a) Non-discounted PBP

The PBP calculations are as follows.

From above calculations, we see that

(1) For A:

Initial cash outflow of $150,000 is recovered (i.e. cumulative cash inflow > 0) between years 1 & 2.

The fractional PBP is computed as

= 1 + (Absolute value of cumulative cash flow at year 1 / Annual cash flow at year 2)

= 1 + (50,000 / 55,000) = 1.91 years

(2) For B:

Initial cash outflow of $100,000 is recovered (i.e. cumulative cash inflow > 0) between years 2 & 3.

The fractional PBP is computed as

= 2 + (Absolute value of cumulative cash flow at year 2 / Annual cash flow at year 3)

= 2 + (20,000 / 40,000) = 2.50 years

Therefore, Project A should be accepted, since its payback period is lower than cut-off payback period of 2 years.

(b) Discounted PBP

The discounted PBP calculations are as follows.

From the calculations, we find:

(1) Project A

Initial cash outflow of $150,000 is recovered (i.e. cumulative cash inflow > 0) between years 2 & 3.

The fractional PBP is computed as

= 2 + (Absolute value of cumulative cash flow at year 2 / Annual cash flow at year 3)

= 2 + (13,636 / 22,539) = 2.61 years

(2) For B:

Initial cash outflow of $100,000 is not recovered (i.e. cumulative cash inflow > 0) within 3 years.

So, based on the cut-off PBP of 2 years, none of the projects is acceptable. Project A should be accepted, because its PBP is higher than the cutoff PBP & B should not be accepted because it never recovers its initial investment within the 3 years project life.

(c) Profitability Index (PI) = Present Value of cash inflows / Initial Investment

(1) Project A

PV of cash inflows = 158,903

So, PI = 158,903 / 150,000 = 1.06

(2) Project B

PV of cash inflows = 99,474

So, PI = 99,474 / 1o0,000 = 0.9945

So, Project A should be accepted because its PI is greater than 1, implying its initial investment is recovered within project life.

(d) ARR = Average Accounting Profit / Initial Investment

(1) Project A

ARR = [(100,000 + 55,000 + 30,000) / 3] / 150,000 = 61,667 / 150,000

= 41.11%

(2) Project B

ARR = [(40,000 + 40,000 + 40,000) / 3] / 100,000 = 40,000 / 100,000

= 40%

If target ARR is 30%, both projects can be accepted since both have a higher ARR. However, since these are mutually exclusive projects, the one with higher ARR should be accepted. So, we should accept project A (whith ARR 41.11%).

Non-Discounted PBP (PROJECT A) Non-Discounted PBP (PROJECT B) Year Cash Flow ($) Cumulative Cash Flow ($) Year Cash Flow ($) Cumulative Cash Flow ($) 0 -1,50,000 -1,50,000 0 -1,00,000 -1,00,000 1 1,00,000 -50,000 1 40,000 -60,000 2 55,000 5,000 2 40,000 -20,000 3 30,000 35,000 3 40,000 20,000

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