## 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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