# 1 should dons expand or raise its price hint compute

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(1) Should Don’s expand or raise its price? [Hint: Compute Don’s NPV from raising the price.] (2) What if Don’s could only increase its annual net CFA by \$26,000 instead of \$30,000? (3) For every \$0.05 increase in price, what is the increase in after-tax revenues? (4) What is the PVA of the amount in (3)? (5) Given your answer in (4), what does this tell you about the needed price increase if you are to equal the NPV of \$130,000 from expanding? Show this is true by computing the NPV with the increase in annual net CFA caused by this price increase. ANSWER (1): The formula is: NPV = PMT(PVAF r,n ) – costs = PMT([(1 + r) n 1] / [r(1 + r) n ]) – costs = \$30,000([(1.12) 8 – 1] / [0.12(1.12) 8 ]) – 0 = \$149,029.19 . This is \$19,029.19 greater than the \$130,000 from the expansion plan. Therefore, although the expansion plan is better than the status quo, the alternative of increasing the price is even better than expansion. Thus, raise price . ANSWER (2): The formula is: NPV = PMT(PVAF r,n ) – costs = PMT([(1 + r) n 1] / [r(1 + r) n ]) – costs = \$26,000([(1.12) 8 – 1] / [0.12(1.12) 8 ]) – 0 = \$129,158.63 . This is \$841.37 less than the \$130,000 from the expansion plan. Therefore, the expansion plan is better but not by that much.] ANSWER (3): An increase of \$0.05 generates an increase of \$30,000. Since \$0.05 divided by 5 equals \$0.01 this implies that \$0.01 will generate an increase of \$30,000 / 5 = \$6,000 in after-tax revenues. ANSWER (4): The formula is: PVA n = PMT(PVAF r,n ) = PMT([(1 + r) n 1] / [r(1 + r) n ]) = \$6,000([(1.12) 8 – 1] / [0.12(1.12) 8 ]) = \$29,805.84 . ANSWER (5): With an increase of \$29,805.84 (in today’s dollars) for every \$0.01 increase in price, this tells us that (\$130,000 / \$29,805.84)(0.01) = \$0.043615616 or about \$0.0436 increase will achieve a NPV of \$130,000. To prove this we take \$0.043615616 times \$1 million and get \$43,615.62. After-taxes, we have: \$43,615.62(1 – 0.04) = \$26,169.37.Taking the present value of these cash flows, we have: PVA n = PMT(PVAF r,n ) = PMT([(1 + r) n 1] / [r(1 + r) n ]) =

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\$26,169.37 ([(1.12) 10 – 1] / [0.12(1.12) 10 ]) = \$ 130,000.00 which is the same as the NPV of the expansion . It is also the NPV from the price increase since costs are zero. 71. RMC can currently produce up to ten million bars with its given capacity. Based on RMC’s sales projections, demand at its current wholesale price of \$0.629 is expected to exceed ten million bars per year for the next ten years. With an increase of \$0.017 over the current price, RMC could still sell ten million bars a year for ten years. This increase would create additional before-tax revenues of \$0.017(10 million) = \$170,000 per year. This translates into an increase in after-tax revenues of \$170,000(1 – 0.4) = \$102,000 per year. As an alternative to the expansion plan, then, RMC could increase its wholesale price and obtain an increase of \$102,000 in its annual net CFAT–– with no other changes whatsoever in its after-tax cash flows . The net present value from the expansion plan is \$342,266. Answer the below questions assuming a required rate of return of 16%. (1) Should RMC expand or raise its price? (2) What if RMC could only increase its annual net CFA by \$70,800 instead of \$102,000? (3) For every \$0.001 increase in price, what is the increase in after-tax revenues?
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