Question

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Consider the following two mutually exclusive projects: Year Cash Flow (A) ONM $346,000 49,000 69,000 69,000 444,000 Cash Flow (B) $48,000 24,400 22,400 19,900 15,000 Whichever project you choose, if any, you require a return of 16 percent on your investment 0-1 What is the payback period for each project? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) years Project A Project B years a-2 if you apply the payback criterion, which investment will you choose? O Project A O Project B b-1 What is the discounted payback period for each project? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g 32.16.) years Project A Project B I years

Answer 1

a-1]

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

Payback period of A = 3 + (cash flow required in year 4 for cumulative cash flows to equal zero / year 4 cash flow) = 3 + ( $159,000 / $444,000) = 3.36 years.

Payback period of B = 2 + (cash flow required in year 3 for cumulative cash flows to equal zero / year 3 cash flow) = 2 + ( $1,200 / $19,900) = 2.06 years.

A B C D Cumulative Cumulative Cash Flow - Cash Flow - Cash Flow - Cash Flow - 1 Year 0 1 2 3 4 ($346,000) $49,000 $69,000 $69,000 $444,000 ($48,000) $24,400 $22,400 $19,900 $15,000 ($346,000) ($297,000) ($228,000) ($159,000) $285,000 ($48,000) ($23,600) ($1,200) $18,700 $33,700

А в D E 1 Year Cash Flow - A Cash Flow - B Cumulative Cash Flow - A Cumulative Cash Flow - B 20 -346000 -48000 =B2 =C2 3 1 49000 24400 =D2+B3 =E2+C3 4 2 69000 22400 =D3+B4 =E3+C4 5 3 69000 19900 =D4+B5 =E4+C5 64 444000 15000 =D5+B6 =E5+C6

a-2]

Project B will be chosen as it has a shorter payback period.

b-1]

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

Discounted cash flow of each year = cash flow / (1 + required return)^{number of years}

Discounted payback period of A = 3 + (cash flow required in year 4 for discounted cumulative cash flows to equal zero / year 4 discounted cash flow) = 3 + ( $208,275 / $245,217) = 3.85 years.

Discounted payback period of B = 2 + (cash flow required in year 3 for discounted cumulative cash flows to equal zero / year 3 discounted cash flow) = 2 + ( $10,319 / $12,749) = 2.81 years.

ДА В с F G н Discounted Discounted Cumulative Cumulative Cash Flow Cash Cash Flow - Cash Flow - Discounted Discounted 1 Year -A Flow - BA Cash Flow - A Cash Flow - B 2 0 ($346,000) ($48,000) ($346,000) ($48,000) ($346,000) ($48,000) 3 1 $49,000 $24,400 $42,241 $21,034 ($303,759) ($26,966) 2 $69,000 $22,400 $51,278 $16,647 ($252,480) ($10,319) 3 $69,000 $19,900 $44,205 $12,749 ($208,275) $2,430 4 $444,000 $15,000 $245,217 $8,284 $36,942 $10,715 5

A B C D E 1 Year 20 3 1 42 5 3 64 Cash Flow - A -346000 49000 69000 69000 444000 Cash Flow - B - 48000 24400 22400 19900 15000 Cumulative Cash Flow - A =B2 =D2+B3 =D3+B4 =D4+B5 =D5+B6 Cumulative Cash Flow - B =C2 =E2+C3 =E3+C4 =E4+C5 =E5+C6 F — H Cumulative Discounted Discounted Cash Flow - A Discounted Cash Flow - B Cash Flow - A =B2/(1+16%)^A2 =C2/(1+16%)^A2 =F2 =B3/(1+16%)^A3 =C3/(1+16%)^A3 =H2+F3 =B4/(1+16%)^A4 =C4/(1+16%) A4 =H3+F4 =B5/(1+16%)^A5 =C5/(1+16%)^A5 =H4+F5 =B6/(1+16%)^A6 =C6/(1+16%) A6 =H5+F6 Cumulative Discounted Cash Flow - B =G2 =12+G3 =13+G4 =14+G5 =15+G6

c-1]

NPV is calculated using NPV function in Excel.

fox J -NPV(16%,B3:B6)+B2 K L ТА B Cash Flow 1 2 Cash Flow Year A 0 ($346,000) 1 $49,000 2 $69,000 3 $69,000 4 $444,000 NPV 36,942.25 4 ($48,000) $24,400 $22,400 $19,900 $15,000 10,714.79 6 7

c7 fc =NPV(16%,C3:C6)+C2 J K L A B C Cash Flow 2 Cash Flow 1 Year A 0 ($346,000) 3 1 $49,000 2 $69,000 3 $69,000 4 $444,000 7 NPV 36,942.25 ($48,000) $24,400 $22,400 $19,900 $15,000 10,714.79 6

c-2]

Project A will be chosen as it has a higher NPV.

d-1]

IRR is calculated using IRR function in Excel

fax EIRR(B2:B6) ДА В Cash Flow 2 3 Cash Flow 1 Year A ($346,000) 1 $49,000 4 2 $69,000 5 3 $69,000 6 4 $444,000 7 NPV 36,942.25 8 IRR 19.66% ($48,000) $24,400 $22,400 $19,900 $15,000 10,714.79 27.75%

c8 fax IRR(C2:06) K A B C J Cash Flow B Cash Flow 1 Year A 0 ($346,000) 3 1 $49,000 4 2 $69,000 3 $69,000 4 $444,000 7 NPV 36,942.25 8 IRR 19.66% ($48,000) $24,400 $22,400 $19,900 $15,000 10,714.79 27.75%

d-2]

Project B will be chosen as it has a higher IRR.