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15. The cash flow from the old policy is:
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 = $75,375 – 69,615
Incremental cash flow = $5,760
The cost 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:
Cost of the subscription = $950 + $15(700)
Cost of the subscription = $11,450
And the savings from having no bad debts will be:
Challenge
17. The cost of switching credit policies is:
Cost of new policy = –[PQ + Q(v – v) + v(Q – Q)]
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And the cash flow from switching, which is a perpetuity, is:
To find the breakeven quantity sold for switching credit policies, we set the NPV equal to zero and
solve for Q. Doing so, we find:
18. We can use the equation for the NPV we constructed in Problem 17. Using the sales figure of 3,150
units and solving for P, we get:
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:
20. Since the company sells 700 suits per week, and there are 52 weeks per year, the total number of
suits sold is:
Total suits sold = 700 × 52 = 36,400
And, the EOQ is 500 suits, so the number of orders per year is:
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Alternatively, we could consider that the store sells 100 suits per day (700 per week / 7 days). This
implies that the store will be at the safety stock of 100 suits on Saturday when it opens. Since the
21. The cash outlay for the credit decision is the variable cost of the engine. Since the orders can be one-
time or perpetual, the NPV of the decision is the weighted average of the two potential sales streams.
The initial cost is the cost for all of the engines. So, the NPV is:
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:
APPENDIX 28A
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:
2. a. The old price as a percentage of the new price is:
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So the discount is:
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 breakeven credit price is:
This implies that the breakeven discount is:
3. a. The cost of the credit policy switch is the quantity sold times the variable cost. The cash inflow
is the price times the quantity sold, times one minus the default rate. This is a one-time lump
sum, so we need to discount this value one period. Doing so, we find the NPV is:
The order should be taken since the NPV is positive.
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b. To find the breakeven default rate, , we just need to set the NPV equal to zero and solve for
the breakeven default rate. Doing so, we get:
c. Effectively, the cash discount is:
4. a. The cash discount is:
Cash discount = ($75 – 71)/$75
The default probability is one minus the probability of payment, or:
b. Due to the increase in both quantity sold and credit price when credit is granted, an additional
incremental cost is incurred of:
The breakeven price under these assumptions is:
NPV = 0 = –$29,300 – (6,200)($71) + {6,900[(1 – .10)P – $33] – 6,200($71 – 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:
NPV = 6,200(32) – .90(6,900)33 – 6,200(71) – 6,900($1.50) + {6,900[.90(75 – 33) – 1.50]
The reports should not be purchased and credit should not be granted.
5. We can express the old cash flow as:
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Old cash flow = (P – v)Q
And the new cash flow will be:
Thus:
[
(P – v)(Q‘ – Q)+α Q‘{(1 – π)P‘ – P}
R
]
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