Question

Consider the following two mutually exclusive projects: Cash Flow Year 0 Cash Flow (B) - $ 50,000 24,000 22,000 19,500 14, 600 - $ 350,000 45,000 65,000 65,000 440,000 AM + Whichever project you choose, if any, you require a 15% return on your investment. a-1. What is the payback period for each project? (Round the final answers to 2 decimal places.) Payback Period Project A Project B years years a-2. If you apply the payback criterion, which investment will you choose? Project A Project B

Answer 1

a-1]

Payback period is the time taken for the cumulative cash flows to equal zero

Payback period of Project A = 3 + (cash flow required in year 4 for cumulative cash flows to equal zero / year 4 cash flow) = 3 + ( $175,000 / $440,000) = 2.40 years

Payback period of Project B = 2 + (cash flow required in year 3 for cumulative cash flows to equal zero / year 3 cash flow) = 2 + ( $4,000 / $19,500) = 2.21 years

B Cumulative Cumulative Cash Flow Cash Cash Flow - Cash Flow - 1 Year A Flow - BA 0 $(350,000) $(50,000) $ (350,000) $ (50,000) 3 1 $ 45,000 $ 24,000 $ (305,000) $ (26,000) 2 $ 65,000 $ 22,000 $ (240,000) $ (4,000) 3 $ 65,000 $ 19,500 $ (175,000) $ 15,500 4 $ 440,000 $ 14,600 $ 265,000 $ 30,100

A B C D E 1 Year A 20 3 1 Cash Flow Cash Flow - Cumulative B Cash Flow - A -350000 -50000 =B2 45000 24000 =D2+B3 65000 22000 =D3+B4 65000 19500 =D4+B5 440000 14600 =D5+B6 cumulative Cash Flow - B =C2 =E2+C3 =E3+04 =E4+C5 =E5+C6 4 2 53 64

a-2]

Investment B will be chosen as it has a shorter payback period

b-1]

discounted cash flow of each year = cash flow / (1 + required return)ⁿ

where n = number of years after which the cash flow occurs

Discounted Payback period is the time taken for the cumulative discounted cash flows to equal zero

Discounted Payback period of A = 3 + (discounted cash flow required in year 4 for cumulative discounted cash flows to equal zero / year 4 discounted cash flow) = 3 + ($218,982 / $251,571) = 3.87 years

Discounted Payback period of B = 2 + (discounted cash flow required in year 3 for cumulative discounted cash flows to equal zero / year 3 discounted cash flow) = 2 + ($12,495 / $12,822) = 2.97 years

A B C D Cumulative Cumulative Discounted Discounted Cash Flow-Cash Discounted Discounted Cash Flow - Cash Flow - 11 Year A Flow-B Cash Flow - A Cash Flow-BA 12 0 $(350,000) $(50,000) $ (350,000) $ (50,000) $ (350,000) $ (50,000) 13 1 $ 45,000 $ 24,000 $ 39,130 $ 20,870 $ (310,870) $ (29,130) 14 2 $ 65,000 $ 22,000 $ 49,149 $ 16,635 $ (261,720) $ (12,495) 15 3 $ 65,000 $ 19,500 $ 42,739 $ 12,822 $ (218,982) $ 326 4 $ 440,000 $ 14,600 $ 251,571 $ 8,348 $ 32,590 $ 8,674

А В 11 Year 120 13 1 14 2 15 3 16 4 Cash Flow - A -350000 45000 65000 65000 440000 Cash Flow - B -50000 24000 22000 19500 14600 Discounted Cash Flow - A =B12/(1+15%)^A12 =B13/(1+15%)^A13 =B14/(1+15%)^A14 =B15/(1+15%)^A15 =B16/(1+15%) A16 Cumulative Cumulative Discounted Cash Flow Discounted Cash Discounted Cash Flow - A Flow - B =C12/(1+15%)^A12 =D12 =E12 =C13/(1+15%)^A13 =F12+D13 =G12+E13 =C14/(1+15%)^A14 =F13+D14 =G13+E14 =C15/(1+15%)^A15 =F14+D15 =G14+E15 =C16/(1+15%)"A16 =F15+D16 =G15+E16

b-2]

Investment B will be chosen as it has a shorter discounted payback period