1. a. A sight draft is a commercial draft that is payable immediately.
b. A time draft is a commercial draft that does not require immediate payment.
c. A bankers acceptance is when a bank guarantees the future payment of a commercial draft.
d. A promissory note is an IOU that the customer signs.
e. A trade acceptance is when the buyer accepts the commercial draft and promises to pay it in the future.
2. Trade credit is usually granted on open account. The invoice is the credit instrument.
3. Credit costs: cost of debt, probability of default, and the cash discount
No-credit costs: lost sales
The sum of these are the carrying costs.
4. 1. Character: determines if a customer is willing to pay his or her debts.
2. Capacity: determines if a customer is able to pay debts out of operating cash flow.
3. Capital: determines the customer’s financial reserves in case problems occur with opera-ting cash flow.
4. Collateral: assets that can be liquidated to pay off the loan in case of default.
5. Conditions: customer’s ability to weather an economic downturn and whether such a down-turn is likely.
5. 1. Perishability and collateral value
2. Consumer demand
3. Cost, profitability, and standardization
4. Credit risk
5. The size of the account
6. Competition
7. Customer type
If the credit period exceeds a customer’s operating cycle, then the firm is financing the receivables and other aspects of the customer’s business that go beyond the purchase of the selling firm’s merchandise.
6. a. B: A is likely to sell for cash only, unless the product really works. If it does, then they might grant longer credit periods to entice buyers.
b. A: Landlords have significantly greater collateral, and that collateral is not mobile.
c. A: Since A’s customers turn over inventory less frequently, they have a longer inventory period, and thus, will most likely have a longer credit period as well.
d. B: Since A’s merchandise is perishable and B’s is not, B will probably have a longer credit period.
e. A: Rugs are fairly standardized and they are transportable, while carpets are custom fit and are not particularly transportable.
7. The three main categories of inventory are: raw material (initial inputs to the firm’s production process), work-in-progress (partially completed products), and finished goods (products ready for sale). From the firm’s perspective, the demand for finished goods is independent from the demand for the other types of inventory. The demand for raw material and work-in-progress is derived from, or dependent on, the firm’s needs for these inventory types in order to achieve the desired levels of finished goods.
8. JIT systems reduce inventory amounts. Assuming no adverse effects on sales, inventory turnover will increase. Since assets will decrease, total asset turnover will also increase. Recalling the DuPont equation, an increase in total asset turnover, all else being equal, has a positive effect on ROE.
9. Carrying costs should be equal to order costs. Since the carrying costs are low relative to the order costs, the firm should increase the inventory level.
10. It would be a one-time boost. The drop in liquidity is not as bad as it seems since it came from inventory reduction, and the quick ratio, for example, is unchanged. The firm decreased its leverage as well.
Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem.
Basic
1. a. There are 30 days until account is overdue. If you take the full period, you must remit:
Remittance= 200($95)
Remittance= $19,000
b. There is a 2 percent discount offered, with a 10 day discount period. If you take the discount, you will only have to remit:
Remittance = (1 – .02)($19,000)
Remittance = $18,620
c. The implicit interest is the difference between the two remittance amounts, or:
Implicit interest = $19,000 – 18,620
Implicit interest = $380
The number of days’ credit offered is:
Days’ credit = 30 – 10
Days’ credit = 20 days
2. The receivables turnover is:
Receivables turnover = 365/Average collection period
Receivables turnover = 365/48
Receivables turnover = 7.604 times
And the average receivables are:
Average receivables = Sales/Receivables period
Average receivables = $65 million/7.604
Average receivables = $8,547,945
3. a. The average collection period is the percentage of accounts taking the discount times the discount period, plus the percentage of accounts not taking the discount times the days’ until full payment is required, so:
Average collection period = .65(10 days) + .35(30 days)
Average collection period = 17 days
b. And the average daily balance is:
Average balance = 1,200($2,200)(17)(12/365)
Average balance = $1,475,506.85
4. The daily sales are:
Daily sales = $18,000 / 7
Daily sales = $2,571.43
Since the average collection period is 29 days, the average accounts receivable is:
Average accounts receivable = $2,571.43(29)
Average accounts receivable = $74,571.43
5. The interest rate for the term of the discount is:
Interest rate = .02/.98
Interest rate = .0204 or 2.04%
And the interest is for:
40 – 9 = 31 days
So, using the EAR equation, the effective annual interest rate is:
EAR = (1 + Periodic rate)m – 1
EAR = (1.0204)365/31 – 1
EAR = .2685 or 26.85%
a. The periodic interest rate is:
Interest rate = .03/.97
Interest rate = .0309 or 3.09%
And the EAR is:
EAR = (1.0309)365/31 – 1
EAR = .4314 or 43.14%
b. The EAR is:
EAR = (1.0204)365/51 – 1
EAR = .1556 or = 15.56%
c. The EAR is:
EAR = (1.0204)365/25 – 1
EAR = .3431 or 34.31%
6. The receivables turnover is:
Receivables turnover = 365/Average collection period
Receivables turnover = 365/52
Receivables turnover = 7.02 times
And the annual credit sales are:
Annual credit sales = Receivables turnover × Average daily receivables
Annual credit sales = 7.02($46,000)
Annual credit sales = $322,884.62
7. The total sales of the firm are equal to the total credit sales since all sales are on credit, so:
Total credit sales = 4,000($400)
Total credit sales = $1,600,000
The average collection period is the percentage of accounts taking the discount times the discount period, plus the percentage of accounts not taking the discount times the days’ until full payment is required, so:
Average collection period = .60(15) + .40(40)
Average collection period = 25 days
The receivables turnover is 365 divided by the average collection period, so:
Receivables turnover = 365/25
Receivables turnover = 14.60 times
And the average receivables are the credit sales divided by the receivables turnover so:
Average receivables = $1,600,000/14.60
Average receivables = $109,589.04
If the firm increases the cash discount, more people will pay sooner, thus lowering the average collection period. If the ACP declines, the receivables turnover increases, which will lead to a decrease in the average receivables.
8. The average collection period is the net credit terms plus the days overdue, so:
Average collection period = 25 + 9
Average collection period = 34 days
The receivables turnover is 365 divided by the average collection period, so:
Receivables turnover = 365/34
Receivables turnover = 10.7353 times
And the average receivables are the credit sales divided by the receivables turnover so:
Average receivables = $8M/10.7353
Average receivables = $745,205.48
9. a. The cash outlay for the credit decision is the variable cost of the engine. If this is a one-time order, the cash inflow is the present value of the sales price of the engine times one minus the default probability. So, the NPV per unit is:
NPV = –$1.5M + (1 – .005)($1.8M)/1.025
NPV = $247,317.07 per unit
The company should fill the order.
b. To find the breakeven probability of default, p, we simply use the NPV equation from part a, set it equal to zero, and solve for p. Doing so, we get:
NPV = 0 = –$1.5M + (1 – p)($1.8M)/1.025
p = .1458 or 14.58%
We would not accept the order if the default probability was higher than 14.58 percent.
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 = –$1.5M + (1 – .005)($1.8M – 1.5M)/.025
NPV = $10,440,000.00 per unit
The company should fill the order. The breakeven default probability under these assumptions is:
NPV = 0 = –$1.5M + (1 – p)($1.8M – 1.5M)/.025
p = .8750 or 87.50%
We would not accept the order if the default probability was higher than 87.50 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 the lost sales from the existing policy plus the incremental variable costs under the new policy, so:
Cost of switching = $800(1,130) + $475(1,195 – 1,130)
Cost of switching = $934,875
The benefit of switching is the new sales price minus the variable costs per unit, times the incremental units sold, so:
Benefit of switching = ($800 – 475)(1,195 – 1,130)
Benefit of switching = $21,125
The benefit of switching is a perpetuity, so the NPV of the decision to switch is:
NPV = –$934,875 + $21,125/.015
NPV = $473,458.33
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 = (2,000/2)($20) = $20,000
The order costs are the number of orders times the cost of an order, so:
Order costs = (52)($2,600) = $135,200
The economic order quantity is:
EOQ = [(2T × F)/CC]1/2
EOQ = [2(52)(2,000)($2,600)/$20]1/2
EOQ = 5,200.00
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 = (180/2)($51) = $4,590
The order costs are the number of orders times the cost of an order, so:
Restocking costs = 52($150) = $7,800
The economic order quantity is:
EOQ = [(2T × F)/CC]1/2
EOQ = [2(52)(180)($150)/$51]1/2
EOQ = 234.65
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(180)/234.65
Number of orders per year = 39.89
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
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 = ($75 – 43)(3,200)
Cash flow from old policy = $102,400
And the cash flow from the new policy would be:
Cash flow from new policy = ($80 – 43)(3,500)
Cash flow from new policy = $129,500
So, the incremental cash flow would be:
Incremental cash flow = $129,500 – 102,400
Incremental cash flow = $27,100
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 = –[($75)(3,200) + ($43)(3,500 – 3,200)] + $27,100/.03
NPV = $650,433.33
15. The cash flow from the old policy is:
Cash flow from old policy = ($340 – 260)(1,800)
Cash flow from old policy = $144,000
And the cash flow from the new policy will be:
Cash flow from new policy = ($345 – 265)(1,850)
Cash flow from new policy = $148,000
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 = $148,000 – 144,000
Incremental cash flow = $4,000
The cost of switching credit policies is:
Cost of new policy = –[PQ + Q(v¢ – v) + v¢(Q¢ – Q)]
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:
NPV = –[($340)(1,800) + (1,800)($265 – 260) + ($265)(1,850 – 1,800)] + ($4,000/.02)
NPV = –$434,250
Challenge
16. 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 breakeven quantity sold for switching credit policies, we set the NPV equal to zero and solve for Q¢. Doing so, we find:
NPV = 0 = –[($75)(3,200) + ($43)(Q¢ – 3,200)] + [(Q¢)($80 – 43) – (3,200)($75 – 43)]/.03
0 = –$240,000 – $43Q¢ + $137,600 + $1,233.33Q¢ – $3,413,333.33
$1,190.33Q¢ = $3,515,733.33
Q¢ = 2,953.57
17. We can use the equation for the NPV we constructed in Problem 16. Using the sales figure of 3,300 units and solving for P¢, we get:
NPV = 0 = [–($75)(3,200) – ($43)(3,300 – 3,200)] + [(P¢ – 43)(3,300) – ($75 – 43)(3,200)]/.03
0 = –$240,000 – 4,300 + $110,000P¢ – 8,143,333.33
$110,000P¢ = $8,387,633.33
P¢ = $76.25
18. 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 = –[($340)(1,800) + ($265 – 260)(1,800) + ($265)(1,850 – 1,800)] + [(1,850)(P¢ – 265) –
(1,800)($340 – 260)]/.02
0 = –$612,000 – 9,000 – 13,250 + $92,500P¢ – 31,712,500
$92,500P¢ = $32,346,750
P¢ = $349.69
19. The company places an order every five days. The number of orders per year will be:
Orders per year = 365/5 = 73 times
The next order should be placed after the close of business Saturday.
APPENDIX 21A
1. The cash flow from the old policy is the quantity sold times the price, so:
Cash flow from old policy = 70,000($530)
Cash flow from old policy = $37,100,000
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 = 70,000($552)(1 – .02)
Cash flow from new policy = $37,867,200
The incremental cash flow is the difference in the two cash flows, so:
Incremental cash flow = $37,867,200 – 37,100,000
Incremental cash flow = $767,200
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 = –$37.1M + $767,200/.02
NPV = $1,260,000
2. a. The old price as a percentage of the new price is:
$90/$91.84 = .98
So the discount is:
Discount = 1 – .98 = .02 or 2%
The credit terms will be:
Credit terms: 2/10, 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 = 3,000($90)
Receivables = $270,000 (at a maximum)
c. Since the quantity sold does not change, variable cost is the same under either plan.
d. No, because:
d – p = .02 – .10
d – p = –.08 or –8%
Therefore the NPV will be negative. The NPV is:
NPV = –3,000($90) + (3,000)($91.84)(.02 – .1)/(.01)
NPV = –$2,473,200
The breakeven credit price is:
P(1 + r)/(1 – p) = $90(1.01)/(.9)
P = $101.00
This implies that the breakeven discount is:
Breakeven discount = 1 – ($90/$101)
Breakeven discount = .1089 or 10.89%
The NPV at this discount rate is:
NPV = –3,000($90) + (3,000)($101.00)(.1089 – .1)/(.01)
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 = –12($1,200) + (1 – .2)(12)($1,850)/1.02
NPV = $3,011.76
The order should be taken since the NPV is positive.
b. To find the breakeven default rate, p, we just need to set the NPV equal to zero and solve for the breakeven default rate. Doing so, we get:
NPV = 0 = –12($1,200) + (1 – p)(12)($1,850)/1.02
p = .3384 or 33.84%
c. Effectively, the cash discount is:
Cash discount = ($1,850 – 1,700)/$1,850
Cash discount = .0811 or 8.11%
Since the discount rate is less than the default rate, credit should not be granted. The firm would be better off taking the $1,700 up-front than taking an 80% chance of making $1,850.
4. a. The cash discount is:
Cash discount = ($55 – 51)/$55
Cash discount = .0727 or 7.27%
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 = (3,300)($31 – 29) + (3,500 – 3,300)($31)
Additional cost = $12,800
The breakeven price under these assumptions is:
NPV = 0 = –$12,800 – (3,300)($51) + {3,500[(1 – .10)P¢ – $31] – 3,300($51 – 29)}/(1.00753 – 1)
NPV = –$12,800 – 168,300 + 138,955.23P¢ – 7,988,822.93
$8,169,922.93 = $138,955.23P¢
P¢ = $58.80
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 = 3,300(29) – .90(3,500)31 – 3,300(51) – 7,000 + {3,500[0.90(55 – 31) – 2]
– 3,300(51 – 29)}/(1.00753 – 1)
NPV = $95,700 – 97,650 – 168,300 – 7,000 – 176,451.09
NPV = –$353,701.09
So, credit should not be extended.
5. We can express the old cash flow as:
Old cash flow = (P – v)Q
And the new cash flow will be:
New cash flow = (P – v)(1 – a)Q¢ + aQ¢ [(1 – p)P¢ – v]
So, the incremental cash flow is
Incremental cash flow = –(P – v)Q + (P – v)(1 – a)Q¢ + aQ¢ [(1 – p)P¢ – v]
Incremental cash flow = (P – v)(Q¢ – Q) + aQ¢ [(1 – p)P¢ – P]
Thus:
NPV = (P – v)(Q¢ – Q) – aPQ¢ +
1. a. The dollar is selling at a premium because it is more expensive in the forward market than in the spot market (SFr 1.53 versus SFr 1.50).
b. The franc is expected to depreciate relative to the dollar because it will take more francs to buy one dollar in the future than it does today.
c. Inflation in Switzerland is higher than in the United States, as are interest rates.
2. The exchange rate will increase, as it will take progressively more pesos to purchase a dollar. This is the relative PPP relationship.
3. a. The Australian dollar is expected to weaken relative to the dollar, because it will take more A$ in the future to buy one dollar than it does today.
b. The inflation rate in Australia is higher.
c. Nominal interest rates in Australia are higher; relative real rates in the two countries are the same.
4. A Yankee bond is most accurately described by d.
5. No. For example, if a country’s currency strengthens, imports become cheaper (good), but its exports become more expensive for others to buy (bad). The reverse is true for currency depreciation.
6. Additional advantages include being closer to the final consumer and, thereby, saving on transportation, significantly lower wages, and less exposure to exchange rate risk. Disadvantages include political risk and costs of supervising distant operations.
7. One key thing to remember is that dividend payments are made in the home currency. More generally, it may be that the owners of the multinational are primarily domestic and are ultimately concerned about their wealth denominated in their home currency because, unlike a multinational, they are not internationally diversified.
8. a. False. If prices are rising faster in Great Britain, it will take more pounds to buy the same amount of goods that one dollar can buy; the pound will depreciate relative to the dollar.
b. False. The forward market would already reflect the projected deterioration of the deutsche mark relative to the dollar. Only if you feel that there might be additional, unanticipated weakening of the deutsche mark that isn’t reflected in forward rates today will the forward hedge protect you against additional declines.
c. True. The market would only be correct on average, while you would be correct all the time.
9. a. American exporters: their situation in general improves because a sale of the exported goods for a fixed number of euros will be worth more dollars.
American importers: their situation in general worsens because the purchase of the imported goods for a fixed number of euros will cost more in dollars.
b. American exporters: they would generally be better off if the British government’s intentions result in a strengthened pound.
American importers: they would generally be worse off if the pound strengthens.
c. American exporters: would generally be much worse off, because an extreme case of fiscal expansion like this one will make American goods prohibitively expensive to buy, or else Brazilian sales, if fixed in cruzeiros, would become worth an unacceptably low number of dollars.
American importers: would generally be much better off, because Brazilian goods will become much cheaper to purchase in dollars.
10. IRP is the most likely to hold because it presents the easiest and least costly means to exploit any arbitrage opportunities. Relative PPP is least likely to hold since it depends on the absence of market imperfections and frictions in order to hold strictly.
Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem.
Basic
1. Using the quotes from the table, we get:
a. $100(€0.8206/$1) = €82.06
b. $1.2186
c. €5M($1.2186/€) = $6,093,103
d. Singapore dollar
e. Mexican peso
f. (P11.4850/$1)($1.2186/€1) = P13.9959/€
This is a cross rate.
g. Most valuable: Bahrain dinar = $3.3920
Least valuable: Turkish lira = $0.00000067
2. a. You would prefer £100, since:
(£100)($1.8301/£1) = $54.642
b. You would still prefer £100. Using the $/£ exchange rate and the SF/£ exchange rate to find the amount of Swiss francs £100 will buy, we get:
(£100)($1.8301/£1)(SF .8008/$1) = SF 43.7572
c. Using the quotes in the book to find the SF/£ cross rate, we find:
(SF .8008/$1)($1.8301/£1) = SF 0.4376/£1
The £/SF exchange rate is the inverse of the SF/£ exchange rate, so:
£1/SF0.4376 = £2.2853/SF 1
3. a. F180 = ¥106.86 (per $). The yen is selling at a premium because it is more expensive in the forward market than in the spot market ($0.009268 versus $0.009358).
b. F90 = $0.7409/C$1. The dollar is selling at a discount because it is less expensive in the forward market than in the spot market ($0.7425 versus $0.7409).
c. The value of the dollar will fall relative to the yen, since it takes more dollars to buy one yen in the future than it does today. The value of the dollar will rise relative to the Canadian dollar, because it will take fewer dollars to buy one Canadian dollar in the future than it does today.
4. a. The U.S. dollar, since one Canadian dollar will buy:
(Can$1)/(Can$1.26/$1) = $0.7937
b. The cost in U.S. dollars is:
(Can$2.19)/(Can$1.26/$1) = $1.74
Among the reasons that absolute PPP doesn’t hold are tariffs and other barriers to trade, transactions costs, taxes, and different tastes.
c. The U.S. dollar is selling at a discount, because it is less expensive in the forward market than in the spot market (Can$1.22 versus Can$1.26).
d. The Canadian dollar is expected to appreciate in value relative to the dollar, because it takes fewer Canadian dollars to buy one U.S. dollar in the future than it does today.
e. Interest rates in the United States are probably higher than they are in Canada.
5. a. The cross rate in ¥/£ terms is:
(¥115/$1)($1.70/£1) = ¥195.5/£1
b. The yen is quoted too low relative to the pound. Take out a loan for $1 and buy ¥115. Use the ¥115 to purchase pounds at the cross-rate, which will give you:
¥115(£1/¥185) = £0.6216
Use the pounds to buy back dollars and repay the loan. The cost to repay the loan will be:
£0.6216($1.70/£1) = $1.0568
You arbitrage profit is $0.0568 per dollar used.
6. We can rearrange the interest rate parity condition to answer this question. The equation we will use is:
RFC = (Ft – S0)/S0 + RUS
Using this relationship, we find:
Great Britain: RFC = (£0.5549 – £0.5464)/£0.5464 + .025 = 4.06%
Japan: RFC = (¥106.86 – ¥107.90)/¥107.90 + .025 = 1.54%
Switzerland: RFC = (SFr 1.2413 – SFr 1.2488)/SFr 1.2488 + .025 = 1.90%
7. If we invest in the U.S. for the next three months, we will have:
$30M(1.0045)3 = $30,406,825.23
If we invest in Great Britain, we must exchange the dollars today for pounds, and exchange the pounds for dollars in three months. After making these transactions, the dollar amount we would have in three months would be:
($30M)(£0.56/$1)(1.0060)3/(£0.59/$1) = $28,990,200.05
We should invest in U.S.
8. Using the relative purchasing power parity equation:
Ft = S0 × [1 + (hFC – hUS)]t
We find:
Z3.92 = Z3.84[1 + (hFC – hUS)]3
hFC – hUS = (Z3.92/Z3.84)1/3 – 1
hFC – hUS = .0069
Inflation in Poland is expected to exceed that in the U.S. by 0.69% over this period.
9. The profit will be the quantity sold, times the sales price minus the cost of production. The production cost is in Singapore dollars, so we must convert this to U.S. dollars. Doing so, we find that if the exchange rates stay the same, the profit will be:
Profit = 30,000[$145 – {(S$168.50)/(S$1.7117/$1)}]
Profit = $1,396,795.58
If the exchange rate rises, we must adjust the cost by the increased exchange rate, so:
Profit = 30,000[$145 – {(S$168.50)/1.1(S$1.7117/$1)}]
Profit = $1,665,268.71
If the exchange rate falls, we must adjust the cost by the decreased exchange rate, so:
Profit = 30,000[$145 – {(S$168.50)/0.9(S$1.7117/$1)}]
Profit = $1,068,661.76
To calculate the breakeven change in the exchange rate, we need to find the exchange rate that make the cost in Singapore dollars equal to the selling price in U.S. dollars, so:
$145 = S$168.50/ST
ST = S$1.1621/$1
ST = –.3211 or –32.11% decline
10. a. If IRP holds, then:
F180 = (Kr 6.43)[1 + (.08 – .05)]1/2
F180 = Kr 6.5257
Since given F180 is Kr6.56, an arbitrage opportunity exists; the forward premium is too high. Borrow Kr1 today at 8% interest. Agree to a 180-day forward contract at Kr 6.56. Convert the loan proceeds into dollars:
Kr 1 ($1/Kr 6.43) = $0.15552
Invest these dollars at 5%, ending up with $0.15931. Convert the dollars back into krone as
$0.15931(Kr 6.56/$1) = Kr 1.04506
Repay the Kr 1 loan, ending with a profit of:
Kr1.04506 – Kr1.03868 = Kr 0.00638
b. To find the forward rate that eliminates arbitrage, we use the interest rate parity condition, so:
F180 = (Kr 6.43)[1 + (.08 – .05)]1/2
F180 = Kr 6.5257
11. The international Fisher effect states that the real interest rate across countries is equal. We can rearrange the international Fisher effect as follows to answer this question:
RUS – hUS = RFC – hFC
hFC = RFC + hUS – RUS
a. hAUS = .05 + .035 – .039
hAUS = .046 or 4.6%
b. hCAN = .07 + .035 – .039
hCAN = .066 or 6.6%
c. hTAI = .10 + .035 – .039
hTAI = .096 or 9.6%
12. a. The yen is expected to get stronger, since it will take fewer yen to buy one dollar in the future than it does today.
b. hUS – hJAP » (¥129.76 – ¥131.30)/¥131.30
hUS – hJAP = – .0117 or –1.17%
(1 – .0117)4 – 1 = –.0461 or –4.61%
The approximate inflation differential between the U.S. and Japan is – 4.61% annually.
13. We need to find the change in the exchange rate over time so we need to use the relative purchasing power parity relationship:
Ft = S0 × [1 + (hFC – hUS)]t
Using this relationship, we find the exchange rate in one year should be:
F1 = 215[1 + (.086 – .035)]1
F1 = HUF 225.97
The exchange rate in two years should be:
F2 = 215[1 + (.086 – .035)]2
F2 = HUF 237.49
And the exchange rate in five years should be:
F5 = 215[1 + (.086 – .035)]5
F5 = HUF 275.71
Intermediate
14. a. Implicitly, it is assumed that interest rates won’t change over the life of the project, but the exchange rate is projected to decline because the Euroswiss rate is lower than the Eurodollar rate.
b. We can use relative purchasing power parity to calculate the dollar cash flows at each time. The equation is:
E[St] = (SFr 1.72)[1 + (.07 – .08)]t
E[St] = 1.72(.99)t
So, the cash flows each year in U.S. dollar terms will be:
t SFr E[St] US$
0 –27.0M 1.7200 –$15,697,674.42
1 +7.5M 1.7028 $4,404,510.22
2 +7.5M 1.6858 $4,449,000.22
3 +7.5M 1.6689 $4,493,939.62
4 +7.5M 1.6522 $4,539,332.95
5 +7.5M 1.6357 $4,585,184.79
And the NPV is:
NPV = –$15,697,674.42 + $4,404,510.22/1.13 + $4,449,000.22/1.132 + $4,493,939.62/1.133 +
$4,539,332.95/1.134 + $4,585,184.79/1.135
NPV = $71,580.10
c. Rearranging the relative purchasing power parity equation to find the required return in Swiss francs, we get:
RSFr = 1.13[1 + (.07 – .08)] – 1
RSFr = 11.87%
So the NPV in Swiss francs is:
NPV = –SFr 27.0M + SFr 7.5M(PVIFA11.87%,5)
NPV = SFr 123,117.76
Converting the NPV to dollars at the spot rate, we get the NPV in U.S. dollars as:
NPV = (SFr 123,117.76)($1/SFr 1.72)
NPV = $71,580.10
Challenge
15. a. The domestic Fisher effect is:
1 + RUS = (1 + rUS)(1 + hUS)
1 + rUS = (1 + RUS)/(1 + hUS)
This relationship must hold for any country, that is:
1 + rFC = (1 + RFC)/(1 + hFC)
The international Fisher effect states that real rates are equal across countries, so:
1 + rUS = (1 + RUS)/(1 + hUS) = (1 + RFC)/(1 + hFC) = 1 + rFC
b. The exact form of unbiased interest rate parity is:
E[St] = Ft = S0 [(1 + RFC)/(1 + RUS)]t
c. The exact form for relative PPP is:
E[St] = S0 [(1 + hFC)/(1 + hUS)]t
d. For the home currency approach, we calculate the expected currency spot rate at time t as:
E[St] = (€0.5)[1.07/1.05]t = (€0.5)(1.019)t
We then convert the euro cash flows using this equation at every time, and find the present value. Doing so, we find:
NPV = – [€2M/(€0.5)] + {€0.9M/[1.019(€0.5)]}/1.1 + {€0.9M/[1.0192(€0.5)]}/1.12 +
{€0.9M/[1.0193(€0.5/$1)]}/1.13
NPV = $316,230.72
For the foreign currency approach we first find the return in the euros as:
RFC = 1.10(1.07/1.05) – 1 = 0.121
Next, we find the NPV in euros as:
NPV = – €2M + (€0.9M)/1.121 + (€0.9M)/1.1212 + (€0.9M)/1.1213 = €158,115.36
And finally, we convert the euros to dollars at the current exchange rate, which is:
NPV ($) = €158,115.36 /(€0.5/$1) = $316,230.72
1. Since the firm is selling futures, it wants to be able to deliver the lumber; therefore, it is a supplier. Since a decline in lumber prices would reduce the income of a lumber supplier, it has hedged its price risk by selling lumber futures. Losses in the spot market due to a fall in lumber prices are offset by gains on the short position in lumber futures.
2. Buying call options gives the firm the right to purchase pork bellies; therefore, it must be a consumer of pork bellies. While a rise in pork belly prices is bad for the consumer, this risk is offset by the gain on the call options; if pork belly prices actually decline, the consumer enjoys lower costs, while the call option expires worthless.
3. Forward contracts are usually designed by the parties involved for their specific needs and are rarely sold in the secondary market; forwards are somewhat customized financial contracts. All gains and losses on the forward position are settled at the maturity date. Futures contracts are standardized to facilitate their liquidity and to allow them to be effectively traded on organized futures exchanges. Gains and losses on futures are marked-to-market daily. The default risk is greatly reduced with futures, since the exchange acts as an intermediary between the two parties, guaranteeing performance; default risk is also reduced because the daily settlement procedure keeps large loss positions from accumulating. You might prefer to use forwards instead of futures if your hedging needs were different from the standard contract size and maturity dates offered by the futures contract.
4. The firm is hurt by declining oil prices, so it should sell oil futures contracts. The firm may not be able to create a perfect hedge because the quantity of oil it needs to hedge doesn’t match the standard contract size on crude oil futures, or perhaps the exact settlement date the company requires isn’t available on these futures (exposing the firm to basis risk), or maybe the firm produces a different grade of crude oil than that specified for delivery in the futures contract.
5. The firm is directly exposed to fluctuations in the price of natural gas, since it is a natural gas user. In addition, the firm is indirectly exposed to fluctuations in the price of oil. If oil becomes less expensive relative to natural gas, its competitors will enjoy a cost advantage relative to the firm.
6. Buying the call options is a form of insurance policy for the firm. If cotton prices rise, the firm is protected by the call, while if prices actually decline, they can just allow the call to expire worthless. However, options hedges are costly because of the initial premium that must be paid. The futures contract can be entered into at no initial cost, with the disadvantage that the firm is locking in one price for cotton; it can’t profit from cotton price declines.
7. The put option on the bond gives the owner the right to sell the bond at the option’s strike price. If bond prices decline, the owner of the put option profits. However, since bond prices and interest rates move in opposite directions, if the put owner profits from a decline in bond prices, he would also profit from a rise in interest rates. Hence, a call option on interest rates is conceptually the same thing as a put option on bond prices.
8. The company would like to lock in the current low rates, or at least be protected from a rise in rates, allowing for the possibility of benefit if rates actually fall. The former hedge could be implemented by selling bond futures; the latter could be implemented by buying put options on bond prices or buying call options on interest rates.
9. A swap contract is an agreement between parties to exchange assets over several time intervals in the future. The swap contract is usually an exchange of cash flows, but not necessarily so. Since a forward contract is also an agreement between parties to exchange assets in the future, but at a single point in time, a swap can be viewed as a series of forward contracts with different settlement dates. The firm participating in the swap agreement is exposed to the default risk of the dealer, in that the dealer may not make the cash flow payments called for in the contract. The dealer faces the same risk from the contracting party, but can more easily hedge its default risk by entering into an offsetting swap agreement with another party.
10. The firm will borrow at a fixed rate of interest, receive fixed rate payments from the dealer as part of the swap agreement, and make floating rate payments back to the dealer; the net position of the firm is that it has effectively borrowed at floating rates.
11. Transactions exposure is the short-term exposure due to uncertain prices in the near future. Economic exposure is the long-term exposure due to changes in overall economic conditions. There are a variety of instruments available to hedge transaction exposure, but very few long-term hedging instruments exist. It is much more difficult to hedge against economic exposure, since fundamental changes in the business generally must be made to offset long-run changes in the economic environment.
12. The risk is that the dollar will strengthen relative to the yen, since the fixed yen payments in the future will be worth fewer dollars. Since this implies a decline in the $/¥ exchange rate, the firm should sell yen futures.
13. a. Buy oil and natural gas futures contracts, since these are probably your primary resource costs. If it is a coal-fired plant, a cross-hedge might be implemented by selling natural gas futures, since coal and natural gas prices are somewhat negatively related in the market; coal and natural gas are somewhat substitutable.
b. Buy sugar and cocoa futures, since these are probably your primary commodity inputs.
c. Sell corn futures, since a record harvest implies low corn prices.
d. Buy silver and platinum futures, since these are primary commodity inputs required in the manufacture of photographic equipment.
e. Sell natural gas futures, since excess supply in the market implies low prices.
f. Assuming the bank doesn’t resell its mortgage portfolio in the secondary market, buy bond futures.
g. Sell stock index futures, using an index most closely associated with the stocks in your fund, such as the S&P 100 or the Major Market Index for large blue-chip stocks.
h. Buy Swiss franc futures, since the risk is that the dollar will weaken relative to the franc over the next six month, which implies a rise in the $/SFr exchange rate.
i. Sell Euro futures, since the risk is that the dollar will strengthen relative to the Euro over the next three months, which implies a decline in the $/€ exchange rate.
14. Sysco must have felt that the combination of fixed plus swap would result in an overall better rate. In other words, variable rate available via a swap may have been more attractive than the rate available from issuing a floating-rate bond.
Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem.
Basic
1. The initial price is $1,451 per metric ton and each contract is for 10 metric tons, so the initial contract value is:
Initial contract value = ($1,451 per ton)(10 tons per contract) = $14,510
And the final contract value is:
Final contract value = ($1,402 per ton)(10 tons per contract) = $14,020
You will have a loss on this futures position of:
Loss on futures contract = $14,510 – 14,020 = $490
2. The price quote is $6.187 per ounce and each contract is for 5,000 ounces, so the initial contract value is:
Initial contract value = ($6.187 per oz.)(5,000 oz. per contract) = $30,935
At a final price of $6.45 per ounce, the value of the position is:
Final contract value = ($6.45 per oz.)(5,000 oz. per contract) = $32,250
Since this is a short position, there is a net loss of:
$32,250 – 30,935 = $1,315
At a final price of $5.86 per ounce, the value of the position is:
Final contract value = ($5.86 per oz.)(5,000 oz. per contract) = $29,300
Since this is a short position, there is a net gain of $30,935 – 29,300 = $1,635
With a short position, you make a profit when the price falls, and incur a loss when the price rises.
3. The price quote is $2.07 per barrel and each contract is for 1,000 barrels, so the cost per contract is:
Cost = ($2.07 per barrel)(1,000 barrels per contract) = $2,070
If the price of oil at expiration is $35.45 per barrel, the call is out of the money since the strike price is above the oil price. The contracts will expire worthless, so your loss will be the initial investment of $2,070.
If oil prices at contract expiration are $43.24 per barrel, the call is in the money since the price per barrel is above the strike price. The payoff on your position is the current price minus the strike price, times the 1,000 barrels per contract, or:
Payoff = ($43.24 – 39.50)(1,000) = $3,740
And the profit is the payoff minus the initial cost of the contract, or:
Profit = $3,740 – 2,070 = $1,670
4. The call options give the manager the right to purchase oil futures contracts at a futures price of $35 per barrel. The manager will exercise the option if the price rises above $35. Selling put options obligates the manager to buy oil futures contracts at a futures price of $35 per barrel. The put holder will exercise the option if the price falls below $35. The payoffs per barrel are:
Oil futures price: $30 $32 $35 $38 $40
Value of call option position: 0 0 0 3 5
Value of put option position: –5 –3 0 0 0
Total value: –$5 –$3 $0 $3 $5
The payoff profile is identical to that of a forward contract with a $35 strike price.
Intermediate
5. a. You’re concerned about a rise in corn prices, so you would buy December contracts. Since each contract is for 5,000 bushels, the number of contracts you would need to buy is:
Number of contracts to buy = 75,000/5,000 = 15
By doing so, you’re effectively locking in the settle price in December, 2004 of $2.585 per bushel of corn, or:
Total price for 75,000 bushels = 15($2.585)(5,000) = $193,875.
b. If the price of corn at expiration is $2.64 per bushel, the value of you futures position is:
Value of future position = ($2.64 per bu.)(5,000 bu. per contract)(15 contracts) = $198,000
Ignoring any transaction costs, your gain on the futures position will be:
Gain = $198,000 – 193,875 = $4,125
While the price of the corn your firm needs has become $4,125 more expensive since July, your profit from the futures position has netted out this higher cost.
6. a. XYZ has a comparative advantage relative to ABC in borrowing at fixed interest rates, while ABC has a comparative advantage relative to XYZ in borrowing at floating interest rates. Since the spread between ABC and XYZ’s fixed rate costs is only 1%, while their differential is 2% in floating rate markets, there is an opportunity for a 3% total gain by entering into a fixed for floating rate swap agreement.
b. If the swap dealer must capture 2% of the available gain, there is 1% left for ABC and XYZ. Any division of that gain is feasible; in an actual swap deal, the divisions would probably be negotiated by the dealer. One possible combination is ½% for ABC and ½% for XYZ:
Challenge
7. The financial engineer can replicate the payoffs of owning a put option by selling a forward contract and buying a call. For example, suppose the forward contract has a settle price of $50 and the exercise price of the call is also $50. The payoffs below show that the position is the same as owning a put with an exercise price of $50:
Price of coal: $40 $45 $50 $55 $60
Value of call option position: 0 0 0 5 10
Value of forward position: 10 5 0 –5 –10
Total value: $10 $5 $0 $0 $0
Value of put position: $10 $5 $0 $0 $0
The payoffs for the combined position are exactly the same as those of owning a put. This means that, in general, the relationship between puts, calls, and forwards must be such that the cost of the two strategies will be the same, or an arbitrage opportunity exists. In general, given any two of the instruments, the third can be synthesized.
