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Unformatted text preview: imply use the NPV equation from part a, set it equal to zero, and solve for π . Doing so, we get: NPV = 0 = –$1,600,000 + (1 – π )($1,870,000)/1.029 π = .1196 or 11.96% We would not accept the order if the default probability was higher than 11.96 percent. 529 c. If the customer will become a repeat customer, the cash inflow changes. The cash inflow is now one minus the default probability, times the sales price minus the variable cost. We need to use the sales price minus the variable cost since we will have to build another engine for the customer in one period. Additionally, this cash inflow is now a perpetuity, so the NPV under these assumptions is: NPV = –$1,600,000 + (1 – .005)($1,870,000 – 1,600,000)/.029 NPV = $7,663,793.10 per unit The company should fill the order. The breakeven default probability under these assumptions is: NPV = 0 = –$1,600,000 + (1 – π )($1,870,000 – 1,600,000)/.029 π = .8281 or 82.81% We would not accept the order if the default probability was higher than 82.81 percent. This default probability is much higher than in part b because the customer may become a repeat customer. d. It is assumed that if a person has paid his or her bills in the past, they will pay their bills in the future. This implies that if someone doesn’t default when credit is first granted, then they will be a good customer far into the future, and the possible gains from the future business outweigh the possible losses from granting credit the first time. 10. The cost of switching is any lost sales from the existing policy plus the incremental variable costs under the new policy, so: Cost of switching = $720(1,305) + $495(1,380 – 1,305) Cost of switching = $976,725 The benefit of switching is any increase in the sales price minus the variable costs per unit, times the incremental units sold, so: Benefit of switching = ($720 – 495)(1,380 – 1,305) Benefit of switching = $16,875 The benefit of switching is a perpetuity, so the NPV of the decision to switch is: NPV = –$976,275 + $16,875/.015 NPV = $148,275.00 The firm will have to bear the cost of sales for one month before they receive any revenue from credit sales, which is why the initial cost is for one month. Receivables will grow over the one month credit period and will then remain stable with payments and new sales offsetting one another. 11. The carrying costs are the average inventory times the cost of carrying an individual unit, so: Carrying costs = (2,500/2)($9) = $11,250 530 The order costs are the number of orders times the cost of an order, so: Order costs = (52)($1,700) = $88,400 The economic order quantity is: EOQ = [(2T × F)/CC]1/2 EOQ = [2(52)(2,500)($1,700)/$9]1/2 EOQ = 7,007.93 The firm’s policy is not optimal, since the carrying costs and the order costs are not equal. The company should increase the order size and decrease the number of orders. 12. The carrying costs are the average inventory times the cost of carrying an individual unit, so: Carrying costs = (300/2)($41) = $6,150 The order costs are the number of orders times the cost of an order, so: Restocking costs = 52($95) = $4,940 The economic order quantity is: EOQ = [(2T × F)/CC]1/2 EOQ = [2(52)(300)($95)/$41]1/2 EOQ = 268.87 The number of orders per year will be the total units sold per year divided by the EOQ, so: Number of orders per year = 52(300)/268.87 Number of orders per year = 58.02 The firm’s policy is not optimal, since the carrying costs and the order costs are not equal. The company should decrease the order size and increase the number of orders. Intermediate 13. The total carrying costs are: Carrying costs = (Q/2) × CC where CC is the carrying cost per unit. The restocking costs are: Restocking costs = F × (T/Q) Setting these equations equal to each other and solving for Q, we find: CC × (Q/2) = F × (T/Q) Q2 = 2 × F × T /CC Q = [2F × T /CC]1/2 = EOQ 531 14. The cash flow from either policy is: Cash flow = (P – v)Q So, the cash flows from the old policy are: Cash flow from old policy = ($91 – 47)(3,850) Cash flow from old policy = $169,400 And the cash flow from the new policy would be: Cash flow from new policy = ($94 – 47)(3,940) Cash flow from new policy = $185,180 So, the incremental cash flow would be: Incremental cash flow = $185,180 – 169,400 Incremental cash flow = $15,780 The incremental cash flow is a perpetuity. The cost of initiating the new policy is: Cost of new policy = –[PQ + v(Q′ – Q)] So, the NPV of the decision to change credit policies is: NPV = –[($91)(3,850) + ($47)(3,940 – 3,850)] + $15,780/.025 NPV = $276,620 15. The cash flow from the old policy is: Cash flow from old policy = ($290 – 230)(1,105) Cash flow from old policy = $66,300 And the cash flow from the new policy will be: Cash flow from new policy = ($295 – 234)(1,125) Cash flow from new policy = $68,625 The incremental cash flow, which is a perpetuity, is the difference between the old policy cash flows and the new policy cash flows, so: Incremental cash flow = $68,62...
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This note was uploaded on 07/10/2010 for the course FIN 6301 taught by Professor Eshmalwi during the Spring '10 term at University of TexasTyler.
 Spring '10
 eshmalwi
 Finance, Corporate Finance

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