Ross5eChap07sm - Chapter 7 Net Present Value and Other...

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Answers to End–of–Chapter Problems B–57 Chapter 7: Net Present Value and Other Investment Rules 7.2 To calculate the payback period, we need to find the time that the project has recovered its initial investment. The cash flows in this problem are an annuity, so the calculation is simpler. If the initial cost is $3,000, the payback period is: Payback = 3 + ($480 / $840) = 3.57 years There is a shortcut to calculate the payback period if the future cash flows are an annuity. Just divide the initial cost by the annual cash flow. For the $3,000 cost, the payback period is: Payback = $3,000 / $840 = 3.57 years For an initial cost of $5,000, the payback period is: Payback = 5 + ($800 / $840) = 5.95 years The payback period for an initial cost of $7,000 is a little trickier. Notice that the total cash inflows after eight years will be: Total cash inflows = 8($840) = $6,720 If the initial cost is $7,000, the project never pays back. Notice that if you use the shortcut for annuity cash flows, you get: Payback = $7,000 / $840 = 8.33 years. This answer does not make sense since the cash flows stop after eight years, so there is no payback period. 7.4. To calculate the discounted payback, discount all future cash flows back to the present, and use these discounted cash flows to calculate the payback period. Doing so, we find: r = 0%: 4 + ($1,600 / $2,100) = 4.76 years Discounted payback = Regular payback = 4.76 years r = 5%: $2,100/1.05 + $2,100/1.05 2 + $2,100/1.05 3 + $2,100/1.05 4 + $2,100/1.05 5 = $9,091.90 $2,100/1.05 6 = $1,567.05 Discounted payback = 5 + ($10,000 – 9,091.90) / $1,567.05 = 5.58 years r = 15%: $2,100/1.15 + $2,100/1.15 2 + $2,100/1.15 3 + $2,100/1.15 4 + $2,100/1.15 5 + $2,100/1.15 6 = $7,947.41; The project never pays back. 7.6 a. The average accounting return is the average project earnings after taxes, divided by the average book value, or average net investment, of the machine during its life. The book value of the machine is the gross investment minus the accumulated depreciation.
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Answers to End–of–Chapter Problems B–58 Average book value = (Book value 0 + Book value1 + Book value 2 + Book value 3 + Book value 4 + Book value 5) / (Economic life) Average book value = ($20,000 + 12,000 + 11,000 + 10,000 + 0) / (5 years) Average book value = $10,600 Average project earnings = $4,500 To find the average accounting return, we divide the average project earnings by the average book value of the machine to calculate the average accounting return. Doing so, we find: Average accounting return = Average project earnings / Average book value Average accounting return = $4,500 / $10,600 Average accounting return = 0.4245 or 42.45% b. 1. The average accounting return uses accounting data rather than net cash flows. 2. The average accounting return uses an arbitrary firm standard as the decision rule. The firm standard is arbitrary because it does not necessarily relate to a market rate of return. 3. The average accounting return does not consider the timing of cash flows. Hence, it does not consider the time value of money. 7.8 Determine the average book value of the investment. The book value is the gross investment minus accumulated depreciation.
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