## Answers to Appendix Review and Self Test Problems

21A.1 As we saw earlier, if the switch is made, an extra 100 units per period will be sold at a gross profit of \$175 — 130 = \$45 each. The total benefit is thus \$45 X 100 = \$4,500 per period. At 2.0 percent per period forever, the PV is \$4,500/.02 = \$225,000.

The cost of the switch is equal to this period's revenue of \$175 X 1,000 units = \$175,000 plus the cost of producing the extra 100 units, 100 X \$130 = \$13,000. The total cost is thus \$188,000, and the NPV is \$225,000 — 188,000 = \$37,000. The switch should be made.

For the accounts receivable approach, we interpret the \$188,000 cost as the investment in receivables. At 2.0 percent per period, the carrying cost is \$188,000 X .02 = \$3,760 per period. The benefit per period we calculated as \$4,500; so the net gain per period is \$4,500 — 3,760 = \$740. At 2.0 percent per period, the PV of this is \$740/.02 = \$37,000.

Finally, for the one-shot approach, if credit is not granted, the firm will generate (\$175 — 130) X 1,000 = \$45,000 this period. If credit is extended, the firm will invest \$130 X 1,100 = \$143,000 today and receive \$175 X 1,100 = \$192,500 in one period. The NPV of this second option is \$192,500/1.02 — 143,000 = \$45,725.49. The firm is \$45,725.49 — 45,000 = \$725.49 better off today and in each future period because of granting credit. The PV of this stream is \$725.49 + 725.49/.02 = \$37,000 (allowing for a rounding error).

21A.2 The costs per period are the same whether or not credit is offered; so we can ignore the production costs. The firm currently has sales of, and collects, \$110 X 2,000 = \$220,000 per period. If credit is offered, sales will rise to \$120 X 2,000 = \$240,000.

Defaults will be 4 percent of sales, so the cash inflow under the new policy will be .96 X \$240,000 = \$230,400. This amounts to an extra \$10,400 every period. At 2 percent per period, the PV is \$10,400/.02 = \$520,000. If the switch is

Ross et al.: Fundamentals of Corporate Finance, Sixth Edition, Alternate Edition

VII. Short-Term Financial Planning and Management

21. Credit and Inventory Management

© The McGraw-Hill Companies, 2002

PART SEVEN Short-Term Financial Planning and Management made, De Long will give up this month's revenues of \$220,000; so the NPV of the switch is \$300,000. If only half of the customers take the credit, then the NPV is half as large: \$150,000. So, regardless of what percentage of customers take the credit, the NPV is positive. Thus, the change is a good idea.

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