# Shapiro Chapter 2 Solutions

**Topics:**Net present value, Internal rate of return, Rate of return

**Pages:**18 (5029 words)

**Published:**March 5, 2012

QUESTIONS

1.a.What is the relationship between accounting income and economic profit?

Answer: Accounting income is calculated by taking revenues and subtracting all cash and non-cash expenses (such as depreciation). Accounting income also often recognizes losses for tax purposes as well, even though the economic loss may have taken place at another time. Economic profit is the sum of the present values of all the cash flows net of expenses generated by the firm’s actions. Economic profit measures true increments to value, but is hard to measure. Accounting profit is correlated with economic profit, but not perfectly so. Accounting profit can be measured much more easily.

b.What is the relationship between accounting rate of return and economic rate of return?

Answer: The accounting rate of return is the ratio of after-tax profit to average book investment. Economic rate of return is the ratio of after-tax economic profit to the market value of the investment. Economic profit equals cash accruals to the asset combined with changes in its market value.

2.In 1991, AT&T laid a transatlantic fiber optic cable costing $400 million that can handle 80,000 calls simultaneously. What is the payback on this investment if AT&T uses just half its capacity while netting one cent per minute on calls?

Answer: $210 Million per year assuming the half capacity is for 24 hours a day, 365 days per year. The annual payback is then 53%.

3.The satisfied owner of a new $15,000 car can be expected to buy another ten cars from the same company over the next 30 years (an average of one every three years) at an average price of $15,000 (ignore the effects of inflation). If the net profit margin on these cars is 20 percent, how much should an auto manufacturer be willing to spend to keep its customers satisfied? Assume a 9 percent discount rate.

Answer: At a 20 percent profit margin, the auto company will earn an annuity of about $3,000 every three years for the next 30 years. Discounted at 9 percent, this annuity is worth $9,402, assuming that the first new car is purchased three years from today. Hence, an investment to keep customers satisfied will have a positive NPV as long as the amount spent is less than $9,402. Thus, a car company should be willing to spend up to $9,402 in present value terms to keep its customers satisfied. A trick is available to calculate the present value of this annuity. Recognize that an annuity received every three years for 30 years and discounted at 9 percent is equivalent to a 10-year annuity discounted at 29.5029 percent since each cash flow term is discounted at (1.09)3 = 1.295029. 4.Demonstrate that the following project has internal rates of return of 0 percent, 100 percent, and 200 percent.

|Year |1 |2 |3 |4 | |Cash flow |–$1,200 |+7,200 |–13,200 |+7,200 |

Answer: To demonstrate that an IRR calculation is valid, compute the net present value at the IRR. A valid IRR yields NPV = 0.

|Year |Cash Flow |PV@0% |PV@100% |PV@200% | |1 |-1,200 |-1,200 |-600 |-400.00 | |2 |+7,200 |+7,200 |+1,800 |+800.00 | |3 |-13,200 |-13,200 |-1,650 |-488.89 | |4 |+7,200 |+7,200 |+450 |+88.89 | |Total |0 |0 |0 |0 |

5.During...

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