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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 = $1,000 + $8.95(125)
Cost of the subscription = $2,118.75
And the savings from having no bad debts will be:
Savings from not selling to bad credit risks = ($750)(125)(.04)
Savings from not selling to bad credit risks = $3,750
So, the company’s net savings will be:
Net savings = $3,750 – 2,118.75
Net savings = $1,631.25
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 = –[($81)(3,280) + ($47)(Q – 3,280)] + [(Q)($84 – 47) – (3,280)($81 – 47)]/.023
0 = –$265,680 – $47Q + $154,160 + $1,608.70Q – $4,848,695.65
$1,561.70Q = $4,960,215.65
Q = 3,176.17
18. We can use the equation for the NPV we constructed in Problem 17. Using the sales figure of 3,310
units and solving for P, we get:
NPV = 0 = –[($81)(3,280) – ($47)(3,310 – 3,280)] + [(P – 47)(3,310) – ($81 – 47)(3,280)]/.023
0 = –$265,680 – 1,410 + $143,913.04P – 6,763,913.04 – 4,848,695.65
$143,913.04P = $11,879,698.70
P = $82.55
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 = –[($131)(1,320) + ($98 – 96)(1,320) + ($98)(1,340 – 1,320)] + [(1,340)(P – 98) –
(1,320)($131 – 96)]/.0085
0 = –[$172,920 + 2,640 + 1,960] + $157,647.06P – 15,449,411.76 – 5,435,294.12
$157,647.06P = $21,062,225.88
P = $133.60
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
Total units sold = 36,400
And, the EOQ is 500 suits, so the number of orders per year is:
Orders per year = 36,400/500
Orders per year = 72.80
To determine the day when the next order is placed, we need to determine when the last order was
placed. Since the suits arrived on Monday and there is a three-day delay from the time the order was
placed until the suits arrive, the last order was placed Friday. Since there are approximately five days
between the orders, the next order will be placed on Wednesday
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
suits must arrive before the store opens on Saturday, they should be ordered three days prior to
account for the delivery time, which again means the suits should be ordered on Wednesday.
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:
NPV = –125($6,900) + (1 – .30)(125)($7,600)/1.019 + .30(125)($7,600 – 6,900)/.019
NPV = $1,171,679.54
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:
NPV = –125($6,900) + (1 – .15)[(1 – .30)(125)($7,600)/1.019 + .30(125)($7,600 – 6,900)/.019]
NPV = $866,552.61
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:
Cash flow from old policy = 25,000($350)
Cash flow from old policy = $8,750,000
The cash flow from the new policy is the quantity sold times the new price, all times one minus the
default rate, so:
Cash flow from new policy = 25,000($368)(1 – .03)
Cash flow from new policy = $8,924,000
The incremental cash flow is the difference in the two cash flows, so:
Incremental cash flow = $8,924,000 – 8,750,000
Incremental cash flow = $174,000
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:
NPV = –$8,750,000 + $174,000/.025
NPV = –$1,790,000
2. a. The old price as a percentage of the new price is:
$99/$100 = .99
So the discount is:
Discount = 1 – .99 = .01, or 1%
The credit terms will be:
Credit terms: 1/20, net 30
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:
Receivables = 2,400($100)
Receivables = $240,000 (at a maximum)
c. Since the quantity sold does not change, the variable cost is the same under either plan.
d. No, because:
d – = .01 – .08
d – = –.07, or –7%
Therefore the NPV will be negative. The NPV is:
NPV = –2,400($99) + (2,400)($100)(.01 – .08)/(.0075)
NPV = –$2,477,600
The break-even credit price is:
P(1 + r)/(1 – ) = $99(1.0075)/(.92)
P = $108.42
This implies that the break-even discount is:
Break-even discount = 1 – ($99/$108.42)
Break-even discount = .0868, or 8.68%
The NPV at this discount rate is:
NPV = –2,400($99) + (2,400)($108.42)(.0868 – .08)/(.0075)
NPV 0
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:
NPV = –15($540) + (1 – .2)(15)($975)/1.02
NPV = $3,370.59
The order should be taken since the NPV is positive.
b. To find the break-even default rate, , we need to set the NPV equal to zero and solve for the
break-even default rate. Doing so, we get:
NPV = 0 = –15($540) + (1 – )(15)($975)/1.02
= .4351, or 43.51%
c. Effectively, the cash discount is:
Cash discount = ($975 – 910)/$975
Cash discount = .0667, or 6.67%
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:
Cash discount = ($69 – 64)/$69
Cash discount = .0725, or 7.25%
The default probability is one minus the probability of payment, or:
Default probability = 1 – .90
Default probability = .10
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:
Additional cost = (5,800)($33 – 32) + (6,400 – 5,800)($33)
Additional cost = $25,600
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)
NPV = –$25,600 – 371,200 + 254,089.56P – 9,316,617.35 – 8,187,330.40
$17,900,747.75 = $254,089.56P
P = $70.45
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 = 5,800($64 – 32) – .90(6,400)$33 – 5,800($64) – 6,400($1.50)
+ {6,400[.90($69 – 33) – 1.50] – 5,800($64 – 32)}/(1.00753 – 1)
NPV = $151,131.30
The reports should be purchased and credit should be granted. Note, in this case, we are
multiplying the new sales per quarter by the percentage of customers who pay. This is an
implicit assumption of buying the credit report. If we buy the credit report, we will correctly
identify the customers who won’t pay. Therefore:
Q = .90(6,400)
Q = 5,760
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:
Incremental cash flow = –(P – v)Q + (P – v)(1 – )Q + Q[(1 – )P – v]
Incremental cash flow = (P – v)(Q – Q) + Q[(1 – )P – P]
Thus:
NPV = (P – v)(Q – Q) – PQ +
[
(P - v)(Q' - Q)+α Q'{(1 - π)P' - P}
R
]
