FIN 470 EXAM 2 - KEY
1. This problem concerns the effect of taxes on the various break-even measures. Consider a project to supply
Detroit with 30,000 tons of machine screws annually for automobile production. You will need an initial
$4,000,000 investment in threading equipment to get the project started; the project will last for three years.
The accounting department estimates that annual fixed costs will be $700,000 and that variable costs should
be $200 per ton; accounting will depreciate the initial fixed asset investment straight-line to zero over the
three-year project life. It also estimates a salvage value of $440,000 after dismantling costs. The marketing
department estimates that the automakers will let the contract at a selling price of $320 per ton. The
engineering department estimates you will need an initial net working capital investment of $400,000. You
require a 11 percent return and face a marginal tax rate of 30 percent on this project. Calculate the
accounting, cash, and financial break-even quantities.
At the cash break-even, the OCF is zero. Setting the tax shield equation equal to zero and solving for the
quantity, we get:
OCF = 0 = [($320 – 200)QC – $700,000](0.70) + 0.30($4,000,000/3)
QC= 1,071
The accounting breakeven is:
QA= [$700,000 + ($4,000,000/3)]/($320 – 200)
QA= 16,944
Using the tax shield approach, the OCF is:
OCF = [($320 – 200)(30,000) – $700,000](0.70) + 0.30($4,000,000/3)
OCF = $2,430,000
And the NPV is:
NPV = –$4,000,000 – 400,000 + $2,430,000(PVIFA11%,3) + [$400,000 + $440,000(1 – .30)]/1.113
NPV = $2,055,910.26
To calculate the sensitivity to changes in quantity sold, we will choose a quantity of 31,000. The OCF at
this level of sales is:
OCF = [($320 – 200)(31,000) – $700,000](0.70) + 0.30($4,000,000/3)
OCF = $2,514,000
The sensitivity of changes in the OCF to quantity sold is:
ΔOCF/ΔQ = ($2,430,000 – 2,514,000)/(30,000 – 31,000)
ΔOCF/ΔQ = +$84.00
The NPV at this level of sales is:
NPV = –$4,000,000 – $400,000 + $2,514,000(PVIFA11%,3) + [$400,000 + $440,000(1 – 0.30)]/1.113
NPV = $2,261,182.29
And the sensitivity of NPV to changes in the quantity sold is:
ΔNPV/ΔQ = ($2,055,910.26 – 2,261,182.29))/(30,000 – 31,000)
ΔNPV/ΔQ = +$205.27
You wouldn’t want the quantity to fall below the point where the NPV is zero. We know the NPV changes
$205.27 for every unit sold, so we can divide the NPV for 30,000 units by the sensitivity to get a change in
quantity. Doing so, we get:
$2,055,910.26 = $205.27(ΔQ)
ΔQ = 10,016
For a zero NPV, we need to decrease sales by 10,016 units, so the minimum quantity is:
QF = 30,000 – 10,016
QF = 19,984
2. The Gecko Company and the Gordon Company are two firms whose business risk is the same but that have
different dividend policies. Gecko pays no dividend, whereas Gordon has an expected dividend yield of 7
percent. Suppose the capital gains tax rate is zero, whereas the income tax rate is 30 percent. Gecko has an
expected earnings growth rate of 16 percent annually, and its stock price is expected to grow at this same
rate. The after-tax expected returns on the two stocks are equal (because they are in the same risk class).
What is the pretax required return on Gordon’s stock?
Assuming no capital gains tax, the after-tax return for the Gordon Company is the capital gains growth rate,
plus the dividend yield (D’) times 1 minus the tax rate. Using the constant growth dividend model, we get:
Aftertax return = g + D’(1 – t) = 0.16
Solving for g, we get:
0.16 = g + 0.07(1 – 0.30)
g = 0.111
The equivalent pretax return for Gordon Company is:
Pretax return = g + D’ = 0.111 + 0.07 = 0.181, or 18.10%
3. You are at your desk at work when a co-worker excitedly comes to your desk and shows you the scenario
analysis that he has just completed for a potential new project. All three scenarios show a positive NPV. He
states, “We have to take this project!” Your initial reaction regarding this new project is skepticism because
you know that in a competitive market all projects “should” have a zero NPV. Why? There are two
possible reasons why the NPVs could all be positive. What are they?
A positive NPV indicates that the project earns a return higher than that required to compensate the investor
for the risk taken. Therefore, even the most likely scenario should be zero. In a competitive market
investors would rush to take advantage of the excess returns. This will result in either an increased initial
cost or decreased future cash flows (due to competition), or both. The NPV will as a result be lowered until
the project’s return is equal to the required return (NPV = 0).
A project NPV may be positive if: There are errors in the estimations of the cash flows or required rate of
return, or if the firm has a competitive advantage over other firms which cannot be easily overcome.
4. Ying Import has several bond issues outstanding, each making semiannual interest payments. The bonds are
listed in the following table. If the corporate tax rate is 30 percent, what is the aftertax cost of Ying’s debt?
Bond
1
2
3
4
Coupon
Rate
5.9%
7.4
7.1
6.7
Price Quote
105.76
114.42
112.97
102.21
Maturity
5 years
8 years
15.5 years
25 years
Face Value
$ 39,000,000
34,000,000
54,000,000
49,000,000
To find the after-tax cost of debt for the company, we need to find the weighted average of the four debt
issues. We will begin by calculating the market value of each debt issue, which is:
MV1 = 1.0576($39,000,000)
MV1 = $41,246,400
MV2 = 1.1442($34,000,000)
MV2 = $38,902,800
MV3 = 1.1297($54,000,000)
MV3 = $61,003,800
MV4 = 1.0221($49,000,000)
MV4 = $50,082,900
So, the total market value of the company’s debt is:
MVD = $41,246,400 + 38,902,800 + 61,003,800 + 50,082,900
MVD = $191,235,900
The weight of each debt issue is:
w1 = $41,246,400/$191,235,900
w1 = 0.2157, or 21.57%
w2 = $38,902,800/$191,235,900
w2 = 0.2034, or 20.34%
w3 = $61,003,800/$191,235,900
w3 = 0.3190, or 31.90%
w4 = $50,082,900/$191,235,900
w4 = 0.2619, or 26.19%
Next, we need to find the YTM for each bond issue. The YTM for each issue is:
P1 = $1,057.60 = $29.50(PVIFAR%,10) + $1,000(PVIFR%,10)
R1 = 2.299%
YTM1 = 2.299% × 2
YTM1 = 4.60%
P2 = $1,144.20 = $37.00(PVIFAR%,16) + $1,000(PVIFR%,16)
R2 = 2.588%
YTM2 = 2.588% × 2
YTM2 = 5.18%
P3 = $1,129.70 = $35.50(PVIFAR%,31) + $1,000(PVIFR%,31)
R3 = 2.909%
YTM3 = 2.909% × 2
YTM3 = 5.82%
P4 = $1,022.10 = $33.50(PVIFAR%,50) + $1,000(PVIFR%,50)
R4 = 3.260%
YTM4 = 3.260% × 2
YTM4 = 6.52%
The weighted average YTM of the company’s debt is thus:
YTM = 0.2157(0.0460) + 0.2034(0.0518) + 0.3190(0.0582) + 0.2619(0.0652)
YTM = 0.0561, or 5.61%
And the aftertax cost of debt is:
RD = 0.0561(1 – 0.30)
RD = 0.0393, or 3.93%
5. Suppose you own Apple Inc. common stock. The most recent financial statements show $13.8B held
domestically in Cash and Cash Equivalents and a dividend yield of only 1.6%. As a stockholder, do you
feel they should use their cash to pay more in dividends? Why or Why not?
If you believe that you could take the money paid in dividends and invest it to earn a higher level of return
with equivalent risk you would favor increased dividends. If you feel that Apple can earn a higher return
than you can at the given risk level you prefer them to keep the money.
6. Loftis Manufacturing, Inc., has recently installed a just-in-time (JIT) inventory system. Describe the effect
this is likely to have on the company’s carrying costs, shortage costs, and operating cycle.
Carrying costs will decrease because they are not holding goods in inventory. Shortage costs will probably
increase depending on how close the suppliers are and how well they can estimate need. The operating cycle
will decrease because the inventory period is decreased.
7. Is it possible for a firm’s cash cycle to be longer than its operating cycle? Explain why or why not.
Since the cash cycle equals the operating cycle minus the accounts payable period, it is not possible for the
cash cycle to be longer than the operating cycle if the accounts payable period is positive. Moreover, it is
unlikely that the accounts payable period would ever be negative since that implies the firm pays its bills
before they are incurred.
8. Why is a preferred stock with a dividend tied to short-term interest rates an attractive short-term investment
for corporations with excess cash?
Such instruments go by a variety of names, but the key feature is that the dividend adjusts, keeping the price
relatively stable. This price stability, along with the dividend tax exemption, makes so-called adjustable rate
preferred stock very attractive relative to interest-bearing instruments.
9. Which would a firm prefer: a net collection float or a net disbursement float? Why?
Net disbursement float is more desirable because the bank thinks the firm has more money than it actually
does, and the firm is, therefore, receiving interest on funds it has already spent.
10. What are the five Cs of credit? Explain why each is important.
1. Character:
2. Capacity:
3. Capital:
flow.
4. Collateral:
5. Conditions:
likely.
determines if a customer is willing to pay his or her debts.
determines if a customer is able to pay debts out of operating cash flow.
determines the customer’s financial reserves in case problems occur with operating cash
assets that can be liquidated to pay off the loan in case of default.
customer’s ability to weather an economic downturn and whether such a downturn is
11. If a company’s inventory carrying costs are $5 million per year and its fixed order costs are $8 million per
year, do you think the firm keeps too much inventory on hand or too little? Why?
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.
12. Suppose the rate of inflation in Mexico will run about 3 percent higher than the U.S. inflation rate over the
next several years. All other things being the same, what will happen to the Mexican peso–U.S. dollar
exchange rate? What relationship are you relying on in answering?
The exchange rate will increase, as it will take progressively more pesos to purchase a dollar. This is the
relative PPP relationship.
13. What is the difference, if any, between a Eurobond and a foreign bond?
Eurobonds are international bonds issued in multiple countries but denominated in a single currency
(usually the issuer’s currency). Foreign bonds are international bonds issued in a single country, usually
denominated in that country’s currency.
14. Using the following financial statement information for the Schwertzec Corporation, Calculate the operating
and cash cycles. Use 365 days a year.
Item
Beginning
Ending
Inventory
Accounts receivable
Accounts payable
Credit sales
Cost of goods sold
$ 10,200
5,200
7,400
$11,200
5,500
7,800
$82,000
62,000
The operating cycle is the inventory period plus the receivables period. The inventory turnover and
inventory period are:
Inventory turnover = COGS/Average inventory
Inventory turnover = $62,000/[($10,200 + 11,200)/2]
Inventory turnover = 5.7944 times
Inventory period = 365 days/Inventory turnover
Inventory period = 365 days/5.7944
Inventory period = 62.99 days
And the receivables turnover and receivables period are:
Receivables turnover = Credit sales/Average receivables
Receivables turnover = $82,000/[($5,200 + 5,500)/2]
Receivables turnover = 15.3271 times
Receivables period = 365 days/Receivables turnover
Receivables period = 365 days/15.3271
Receivables period = 23.81 days
So, the operating cycle is:
Operating cycle = 62.99 days + 23.81 days
Operating cycle = 86.81 days
The cash cycle is the operating cycle minus the payables period. The payables turnover and payables period
are:
Payables turnover = COGS/Average payables
Payables turnover = $62,000/[$7,400 + 7,800)/2]
Payables turnover = 8.1579 times
Payables period = 365 days/Payables turnover
Payables period = 365 days/8.1579
Payables period = 44.74 days
So, the cash cycle is:
Cash cycle = 86.81 days – 44.74 days
Cash cycle = 42.06 days
15. No More Pencils, Inc., disburses checks every two weeks that average $89,000 and take seven days to clear.
How much interest can the company earn annually if it delays transfer of funds from an interest-bearing
account that pays 0.011 percent per day for these seven days? Ignore the effects of compounding interest.
The interest that the company could earn will be the amount of the checks times the number of days it will
delay payment times the number of weeks that checks will be disbursed times the daily interest rate, so:
Interest = $89,000(7)(52/2)(0.00011)
Interest = $1,781.78
16. The Trektronics store begins each week with 580 phasers in stock. This stock is depleted each week and
reordered. The carrying cost per phaser is $53 per year and the fixed order cost is $102. What is the current
total carrying cost? What is the current restocking cost? What is the economic order quantity? How many
orders per year will Tektronics place under the new policy?
The carrying costs are the average inventory times the cost of carrying an individual unit, so:
Carrying costs = (580/2)($53) = $15,370
The order costs are the number of orders times the cost of an order, so:
Restocking costs = 52($102) = $5,304
The economic order quantity is:
EOQ = [(2T × F)/CC]1/2
EOQ = [2(52)(580)($102)/$53]1/2
EOQ = 340.72
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(580)/340.72
Number of orders per year = 88.52
17. The treasurer of a major U.S. firm has $34 million to invest for three months. The interest rate in the United
States is 0.22 percent per month. The interest rate in Great Britain is 0.28 percent per month. The spot
exchange rate is £0.633, and the three-month forward rate is £0.635. What would be the value of the
investment if the money is invested in U.S and Great Britain?
If we invest in the U.S. for the next three months, we will have:
$34,000,000(1.0022)3 = $34,224,894.04
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:
($34,000,000)(£0.633 / $1)(1.0028)3 / (£0.635 / $1) = $34,178,411.76