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15. The cash flow from the old policy is:
And the cash flow from the new policy will be:
The incremental cash flow, which is a perpetuity, is the difference between the old policy cash flows
and the new policy cash flows, so:
CHAPTER 20 - 2
The cost of switching credit policies is:
In this cost equation, we need to account for the increased variable cost for all units produced. This
includes the units we already sell, plus the increased variable costs for the incremental units. So, the
NPV of switching credit policies is:
16. If the cost of subscribing to the credit agency is less than the savings from collection of the bad
debts, the company should subscribe. The cost of the subscription is:
And the savings from having no bad debts will be:
So, the company’s net savings will be:
The company should subscribe to the credit agency.
Challenge
17. The cost of switching credit policies is:
Cost of new policy = –[PQ + Q(v – v) + v(Q – Q)]
And the cash flow from switching, which is a perpetuity, is:
Cash flow from new policy = [Q(P – v) – Q(P – v)]
To find the break-even quantity sold for switching credit policies, we set the NPV equal to zero and
solve for Q. Doing so, we find:
NPV = 0 = –[($73)(3,280) + ($38)(Q – 3,280)] + [(Q)($75 – 38) – (3,280)($73 – 38)] / .025
CHAPTER 20 - 3
18. We can use the equation for the NPV we constructed in Problem 17. Using the sales figure of 3,420
units and solving for P, we get:
NPV = 0 = [–($73)(3,280) – ($38)(3,420 – 3,280)] + [(P – 38)(3,420) – ($73 – 38)(3,280)] / .025
19. From Problem 15, the incremental cash flow from the new credit policy will be:
Incremental cash flow = Q(P – v) – Q(P – v)
And the cost of the new policy is:
Cost of new policy = –[PQ + Q(v – v) + v(Q – Q)]
Setting the NPV equal to zero and solving for P, we get:
NPV = 0 = –[($125)(1,320) + ($98 – 96)(1,320) + ($98)(1,350 – 1,320)] + [(1,350)(P – 98) –
0 = –[$165,000 + 2,640 + 2,940] + $142,105.26P – 13,926,315.79 – 4,029,473.68
20. Since the company sells 700 suits per week, and there are 52 weeks per year, the total number of
suits sold is:
And, the EOQ is 500 suits, so the number of orders per year is:
To determine the day when the next order is placed, we need to determine when the last order was
Alternatively, we could consider that the store sells 100 suits per day (700 per week / 7 days). This
CHAPTER 20 - 4
21. The cash outlay for the credit decision is the variable cost of the engine. Since the orders can be one-
The company should fill the order.
22. The default rate will affect the value of the one-time sales as well as the perpetual sales. All future
cash flows need to be adjusted by the default rate. So, the NPV now is:
The company should still fill the order.
APPENDIX 20A
1. The cash flow from the old policy is the quantity sold times the price, so:
The cash flow from the new policy is the quantity sold times the new price, all times one minus the
default rate, so:
The incremental cash flow is the difference in the two cash flows, so:
The cash flows from the new policy are a perpetuity. The cost is the old cash flow, so the NPV of the
decision to switch is:
CHAPTER 20 - 5
2. a. The old price as a percentage of the new price is:
$99 / $100 = .99
b. We are unable to determine for certain since no information is given concerning the percentage
of customers who will take the discount. However, the maximum receivables would occur if all
customers took the credit, so:
c. Since the quantity sold does not change, variable cost is the same under either plan.
d. No, because:
Therefore the NPV will be negative. The NPV is:
The break-even credit price is:
This implies that the break-even discount is:
The NPV at this discount rate is:
CHAPTER 20 - 6
3. a. The cost of the credit policy switch is the quantity sold times the variable cost. The cash inflow
The order should be taken since the NPV is positive.
b. To find the break-even default rate, , we just need to set the NPV equal to zero and solve for
the break-even default rate. Doing so, we get:
c. Effectively, the cash discount is:
Since the discount rate is less than the default rate, credit should not be granted. The firm would
be better off taking the $910 up-front than taking an 80% chance of making $975.
4. a. The cash discount is:
The default probability is one minus the probability of payment, or:
Since the default probability is greater than the cash discount, credit should not be granted; the
NPV of doing so is negative.
b. Due to the increase in both quantity sold and credit price when credit is granted, an additional
incremental cost is incurred of:
The break-even price under these assumptions is:
NPV = 0 = –$25,600 – (5,800)($64) + {6,400[(1 – .10)P – $33] – 5,800($64 – 32)} / (1.00753 – 1)
c. The credit report is an additional cost, so we have to include it in our analysis. The NPV when
using the credit reports is:
CHAPTER 20 - 7
The reports should be purchased and credit should be granted. Note, in this case, we are
5. We can express the old cash flow as:
Old cash flow = (P – v)Q
And the new cash flow will be:
New cash flow = (P – v)(1 – )Q + Q [(1 – )P – v]
So, the incremental cash flow is:
