Consider the following two mutually exclusive projects Year

Consider the following two mutually exclusive projects: Year Cash Flow (A) Cash Flow (B) 0 –$217,713 –$14,621 1 25,100 4,047 2 57,000 8,150 3 56,000 13,535 4 430,000 8,190 Whichever project you choose, if any, you require a 6 percent return on your investment. Required: (a) What is the payback period for Project A? (b) What is the payback period for Project B? (c) What is the discounted payback period for Project A? (d) What is the discounted payback period for Project B? (e) What is the NPV for Project A? (f) What is the NPV for Project B ? (g) What is the IRR for Project A? (h) What is the IRR for Project B? (i) What is the profitability index for Project A? (j) What is the profitability index for Project B?

Solution

1)

Cumulative cash flow for year 0 = -217,713

Cumulative cash flow for year 1 = -217,713 + 25,100 = -192,613

Cumulative cash flow for year 2 = -192,613 + 57,000 = -135,613

Cumulative cash flow for year 3 = -135,613 + 56,000 = -79,613

Cumulative cash flow for year 4 = -79,613 + 430,000 = 350,387

79,613 / 430,000 = 0.19

Payabck period for project A = 3 + 0.19 = 3.19 years

2)

Cumulative cash flow for year 0 = -14,621

Cumulative cash flow for year 1 = -14,621 + 4,047 = -10,574

Cumulative cash flow for year 2 = -10,574 + 8,150 = -2,424

Cumulative cash flow for year 3 = -2,424 + 13,535 = 11,111

2,424 / 13,535 = 0.18

Payabck period for project B = 2 + 0.18 = 2.18 years

3)

Present value of year 1 cash flow = 25,100 / ( 1 + 0.06)¹ = 23,679.25

Present value of year 2 cash flow = 57,000 / ( 1 + 0.06)² = 50,729.8

Present value of year 3 cash flow = 56,000 / ( 1 + 0.06)³ = 47,018.68

Present value of year 4 cash flow = 430,000 / ( 1 + 0.06)⁴ = 340,600.28

Cumulative cash flow for year 0 = -217,713

Cumulative cash flow for year 1 = -217,713 + 23,679.25 = -194,033.75

Cumulative cash flow for year 2 = -194,033.75 + 50,729.8 = -143,303.95

Cumulative cash flow for year 3 = -143,303.95 + 47,018.68 = -96,285.27

Cumulative cash flow for year 4 = -96,285.27 + 340,600.28 = 244,315.01

96,285.27 / 340,600.28 = 0.28

Discounted Payabck period for project A = 3 + 0.28 = 2.28 years

d)

Present value of year 1 cash flow = 4,047 / ( 1 + 0.06)¹ = 3,817.92

Present value of year 2 cash flow = 8,150 / ( 1 + 0.06)² = 7,253.47

Present value of year 3 cash flow = 13,535 / ( 1 + 0.06)³ = 11,364.25

Present value of year 4 cash flow = 8,190 / ( 1 + 0.06)⁴ = 6,487.25

Cumulative cash flow for year 0 = -14,621

Cumulative cash flow for year 1 = -14,621 + 3,817.92 = -10,803.08

Cumulative cash flow for year 2 = -10,803.08 + 7,253.47 = -3,549.61

Cumulative cash flow for year 3 = -3,549.61 + 11,364.25 = 7,814.64

3,549.61 / 11,364.25 = 0.31

Discounted Payabck period for project B = 2 + 0.31 = 2.31 years

e)

NPV = Present value of cash inflows - present value of cash outflows

NPV of project A =  23,679.25 + 50,729.8 + 47,018.68 + 340,600.28 - 217,713

NPV of project A = $244,315.01

f)

NPV = Present value of cash inflows - present value of cash outflows

NPV of project B =  3,817.92 + 7,253.47 + 11,364.25 + 6,487.25 - 14,621

NPV of project B = $14,301.89

g)

IRR is the rate of return that makes NPV equal to 0

NPV = 25,100 / ( 1 + R)¹ + 57,000 / ( 1 + R)² + 56,000 / ( 1 + R)³ + 430,000 / ( 1 + R)⁴ - 217,713

Using trial and error method, i.e, after trying various values for R, let\'s try 32%

NPV = 25,100 / ( 1 + 0.32)¹ + 57,000 / ( 1 + 0.32)² + 56,000 / ( 1 + 0.32)³ + 430,000 / ( 1 + 0.32)⁴ - 217,713

NPV = 0

Therefore IRR for project A is 32%.

h)

IRR is the rate of return that makes NPV equal to 0

NPV = 4,047 / ( 1 + R)¹ + 8,150 / ( 1 + R)² + 13,535 / ( 1 + R)³ + 8,190 / ( 1 + R)⁴ - 14,621

Using trial and error method, i.e, after trying various values for R, let\'s try 38%

NPV = 4,047 / ( 1 + 0.38)¹ + 8,150 / ( 1 + 0.38)² + 13,535 / ( 1 + 0.38)³ + 8,190 / ( 1 + 0.38)⁴ - 14,621

NPV = 0

Therefore IRR for project B is 38%.

i)

Profitability index = Present value of cash flows / initial investment

Profitability index of project A = (23,679.25 + 50,729.8 + 47,018.68 + 340,600.28) / 217,713

Profitability index of project A = 2.12

j)

Profitability index = Present value of cash flows / initial investment

Profitability index of project B = (3,817.92 + 7,253.47 + 11,364.25 + 6,487.25) / 14,621

Profitability index of project B = 1.98

We choose project A as it has a higher NPV. When two projects are mutually exclusive, we always go by the NPV criteria.