
Practice
Midterm
 Show all your computations and formulae; even if you use a calculator
or a spreadsheet to get the answers, you must show the formula that
you are using. No points will be given if I don't see the formula
and how you got your answer. Make all your assumptions explicit.
If your approach is correct, you will get some credit, even if your
arithmetic answer is wrong. So concentrate on getting your logic
right.
 If you answer a question, I have the discretion to award you some
points, even if you are completely wrong. If you don't attempt
the question at all, I can give you no points! So attempt
every question.
 Any cheating or plagiarism will result in your getting zero credit
for the exam.
 No bonus points  on question 6  will be awarded unless you have
attempted all subsections of all the other questions. So you are better
off concentrating on the nonbonus part of the exam, first!
 One 8.5 x 11 sheet will be allowed, which may contain formulas only!
No worked out examples, nothing else. Violation of this rule will
be considered cheating.
1. Bond A pays 8% coupons, makes annual coupon payments and is priced
at 98% of par. Can you provide bounds on the yieldtomaturity of the
bond? (That is, can you give a maximum or a minimum value for the yield?)
Bond B pays semiannual coupons and sells for 98% of par as well. If the
yieldtomaturity on Bond B is 10.15%, and its maturity is 2 years, what
is its coupon rate?
2. You want to buy a pair of speakers that you have had your eye on,
for a long time. Unfortunately, you don't have the $400 that they cost.
Luckily, through the intercession of a friend of yours, the manager gives
you the following alternative ways of paying for the speakers:
 Pay $200 up front and $20 a month for 14 months.
 Pay $30 a month for 17 months.
Which alternative would you take, if the APR is 14%?
Bonus question: Suppose you do have the $400, but you still want to consider
paying for the speakers at the rate of $30 a month. What is the maximum
number of months that you would be willing to make these $30 monthly payments?
3. It is Jan. 1, 1994. Utopia Power Company has just paid last year's
dividend, and is expected to maintain its 1994 dividend at the same level
as 1993. However, thereafter, it is expected to maintain a constant 5
percent growth rate in its dividends indefinitely. If the company has
a dividend yield of 5.5%, what is the required rate of return on the power
company's stock?
Midterm
 Show all your computations and formulae; even if you use a calculator
or a spreadsheet to get the answers, you must show the formula that
you are using. No points will be given if I don't see the formula
and how you got your answer. Make all your assumptions explicit.
If your approach is correct, you will get some credit, even if your
arithmetic answer is wrong. So concentrate on getting your logic
right.
 If you answer a question, I have the discretion to award you some
points, even if you are completely wrong. If you don't attempt
the question at all, I can give you no points! So attempt
every question.
 Any cheating or plagiarism will result in your getting zero credit
for the exam.
 One 8.5 x 11 sheet will be allowed, which may contain formulas only!
No worked out examples, nothing else. Violation of this rule will
be considered cheating.
1. (10 points) Allona Corporation has issued consol bonds. The coupon
payments on these bonds are $50 per year. If the required rate of return
on these bonds is 10%, at what price would they trade?
2. (15 points) BriteAid Corporation paid a dividend of $2/share yesterday.
They expect to pay dividends of $2/share for the next five years; thereafter,
dividends are expected to increase at the rate of 5% per annum. TruLook
Company is in the same industry as BriteAid, while Shineware company
is in a different industry; however, Shineware common stock has similar
risk to that of BriteAid shares. Investors expect to earn an average
return of 12% per annum on TruLook's shares, while they expect to get
15% if they invest in Shineware. At what price should BriteAid's shares
sell today?
3. You have the following data for the following two companies for 2004
(in millions of dollars):

SinoVac 
Sifco Industries 
Revenue 
120 
140 
Net Income 
35 
10 
Total Assets 
1000 
500 
Total Liabilities (excluding Shareholders Equity) 
200 
200 
 (10 points) What can you say about the different marketing strategies
that the two firms are using?
 (5 points) What is the return on the two firms' equity?
 (10 points) You will note from your answer to the previous question
that Sifco Industries has a lower return to equity. If you were using
the Dupont Model, what might you suggest to Sifco's CEO to improve his
return on equity? Are there any risks in going this route?
4. (20 points) Answer any four the following questions briefly:
 If a firm has cashflow from operations of $2 per share, how much can
it afford to pay out in dividends? Why is your answer not $2? Explain
how you would come up with the right answer.
 If a firm buys a machine for $200,000, it usually has to pay the seller
of the machine right away. Nevertheless, a firm would not subtract the
$200,000 from its revenues in the year that it buys (and pays for) the
machine. Why not?
 What is working capital? Can a firm have negative working capital?
Explain.
 A firm has a current ratio of 1.2. If it's current liabilities equal
$400m., how much is its working capital?
 What is Tobin's Q ratio? What does it measure?
 Trip Co.'s aftertax income in 2003 was $140. It paid $40 in interest
in that year. Assuming that its tax rate is 35%, what is its interest
coverage ratio?
5. (15 points) You wish to buy a house, which costs $200,000. You wish
to finance the entire amount with a bank. The bank's alternative investment
is a project of similar risk where it would get back 15 cents more at
the end of the year for every dollar it invested. What is your monthly
payment if you wish to pay off the entire loan within a year?
6. (30 points) Cenuco Inc. has issued a 10 year bond with a coupon rate
of 10%. The yieldtomaturity on this bond is 12%.
 What is the price of the bond today?
 What will the bond be worth at the end of 1 year if the yieldtomaturity
at that time stays at 12%?
 If you sell the bond at that time, what rate of return would you have
obtained?
Solutions to Midterm
 The
price of the consol bonds would be 50/0.1 or $500
 The
present value of the cashflows for the next 5 years can be treated as
an annuity and would equal
=$6.70. The value of the
subsequent dividends, as of time 5 would be 2(1.05)/(0.150.05) = $21.
The present value of those $21 are 21/(1.15)^{5 }= $10.44.
Hence the price of the stock would be 10.44 + 6.70 or $17.14.
 The
financial ratios of the two companies are as follows:

SinoVac 
Sifco
Industries 
Net Margin = Net Income/Revenue 
35/120 = 29.17% 
10/140 = 7.14% 
Asset Turnover Ratio = Sales/Total Assets 
120/1000 = 0.12 
140/500 = 0.28 
Equity Multiplier = Total Assets/Total Equity 
1000/(1000200) = 1.25 
500/(500200) = 1.67 
Return on Equity = Net Income/Total Equity 
35/(1000200) = 4.375% 
10/(500200) = 3.33% 
a.
SinoVac is working with a high margin, low volume approach, whereas
Sifco has a lower margin, but higher volume approach, as can be seen from
the components of the firm’s ROE numbers.
b.
The return on equity of the two firms are 4.375% and 3.33%.
c.
Sifco could improve performance by increasing leverage; however,
this would increase its risk, as well.
 a.
A firm has to keep back the funds it would need for profitable expansion,
viz. increase in working capital, as well as increase in capital expenditures.
Else, it would decrease its market value.
b. It would not expense the entire $200,000 in that year because of
the accounting principle of revenue matching.
Outlays that would contribute to the generation of future cashflows
would be kept as an asset. Only
outlays that could be matched with current revenues are considered current
expenses, even if they were actually incurred previously, and even if
they have not yet been paid for.
c. Working Capital is the extent of selffinancing of the firm’s shortterm
operations. A negative
working capital means that current assets are lower than current liabilities,
or that the firm’s suppliers are partially financing the firm’s shortterm
operations.
d. Since the current ratio equals current assets/current liabilities,
a current ratio of 1.2 implies that current assets equal $500m.
Hence, its working capital is $500m.  $400m. or $100m.
e. Tobin’s Q ratio is computed as the market value of the firm’s assets
divided by the replacement cost of the firm’s assets.
It measures the extent of the firm’s growth opportunities and
its real options – the extent to which the firm has been able to add
value over and above the simple worth of its assets.
f. The firm’s interest coverage ratio is (NI + Taxes + Interest)/(Interest).
Since NI is $140, and the firm’s tax rate is 35%, the firm’s
taxable income is 140/(1.35) = $215.38.
Hence the interest coverage ratio = (215.38 + 40)/40 = 6.384.
 The
EAR is 15%; hence the effective monthly rate is (1.15)^{(1/12)}
1 = 1.17%. Solving the
following equation:
for C, we get C = 17,962.87.
 a. Assuming annual coupons, the price of the bond is
worth
= $887.
b. At the end of a year, it should be worth 887(1.12) or $993.44, since
12% is still the expected return.
c. Obviously, the return at the end of the year would be 12%.
Final
Exam
 Show all your computations and formulae; even if you use a calculator
or a spreadsheet to get the answers, you must show the formula that
you are using. No points will be given if I don't see the formula
and how you got your answer. Make all your assumptions explicit.
If your approach is correct, you will get some credit, even if your
arithmetic answer is wrong. So concentrate on getting your logic
right.
 If you answer a question, I have the discretion to award you some
points, even if you are completely wrong. If you don't attempt
the question at all, I can give you no points! So attempt
every question.
 Any cheating or plagiarism will result in your getting zero credit
for the exam.
 One 8.5 x 11 sheet will be allowed, which may contain formulas only!
No worked out examples, nothing else. Violation of this rule will
be considered cheating.
1. (20 points) Pfizer Inc. has a beta of 0.433 according to Yahoo.
 If the return on the 10yr Treasury bond is 4.075%, and you estimate
the market risk premium to be 6% per annum, what is the required rate
of return on Pfizer?
 According to Yahoo, the dividend paid last year was 72 cents per share.
According to Yahoo, once again, the growth rate in earnings for next
year is expected to be 8%. If you assume that dividends will increase
at that rate for the next two years, and thereafter at the rate of 3%
forever, what should Pfizer stock sell at?
2. (20 points) Answer the following questions.
 Pfinzer Bros. has issued a bond with a coupon rate of 6% (semiannual
coupons) and a maturity of 10 years. If the yield to maturity of the
bond is 8%, what is the price of the bond?
 Jastrow Inc. has issued a bond with a coupon rate of 7% (semiannual
coupons). Similar bonds can be obtained on the market with a yieldtomaturity
of 8%. Would you buy the bond at par? Explain why or why not?
3. (15 points) You have bought a car for $20,000. Now it's time to pay
for it! And you only have $2000 for a downpayment. Fortunately, the car
dealer is willing to lend you the rest of the money. If the dealer's opportunity
cost is 15% p.a. (i.e. investing $100 today will yield him $115 at the
end of the year), how much would you have to pay every quarter, if the
dealer requires you to make 20 equal quarterly payments?
4. Read the following article, "Lenders Retool LongTerm Mortgages"
from the Wall Street Journal of June 16, 2005 and answer the following
questions:
 (10 points) Suppose you have borrowed $20,000 using an interestonly
mortgage, where you pay only interest for the first 10 years. If the
APR on the loan is 12%, and you elect to make monthly payments for the
next ten years (after the first 10 years of interestonly payments)
to pay off the loan in its entirety, what will be your monthly payments
for the first ten years, and then for the second ten years?
 (10 points) Towards the end of the article, we read "With a $200,000
mortgage with a 5.75% fixed rate, a borrower with a 40year mortgage
will pay roughly $312,000 in interest over the life of the loan, according
to HSH Associates, versus about $220,000 in interest if the same loan
has a 30year term, assuming both loans carry the same interest rate.
If the rate on the 40year mortgage is 6%, the total interest payments
jump to about $328,000." What is the problem with computing the
total interest payments in this manner?
 (10 points) North Fork Bancorp Inc. is traded on the NYSE. It's beta
is provided by Yahoo as 0.191. If the standard deviation of returns
on the market portfolio is 25%, this means that the nondiversifiable
part of the variance of the returns on North Fork would be (0.191)^{2}
x (25)^{2} or 22.8 percentsquared, whereas the total variance
of returns on North Fork is 20^{2} or 400 percentsquared. Your
friend claims that the remaining variance (i.e. 400  22.8 or 377.2
is irrelevant to most investors, since they would hold diversified portfolios.
Is your friend correct, and why?
 (Bonus  10 points) Assuming, once more that the standard deviation
of returns on the market portfolio is 25%, and the standard deviation
of returns on North Fork is 20%, what would be the R^{2} of
the regression of returns on North Fork Bancorp stock on the market
return (keeping in mind that the beta of North Fork stock is 0.191)?
Lenders Retool LongTerm Mortgages
By RUTH SIMON, Staff Reporter of THE WALL STREET JOURNAL, June
16, 2005; Page D1
The mortgage industry is starting to make the move from short to long.
Lenders are rolling out a new crop of 30year fixedrate mortgages that
let homeowners make low, interestonly payments for as long as 10 or 15
years. It is the latest effort to snare borrowers seeking lower monthly
payments. Also getting a new push: mortgages that stretch for as long
as 40 years.
The newest crop of products is largely aimed at borrowers who are looking
for lower payments but are also concerned about interestrate risk. In
recent months, mortgage experts have been surprised by the continued strong
interest in adjustablerate mortgages at a time when borrowers can still
lock in a fixedrate loan at rates well below 6%. With rising shortterm
interest rates reducing the relative attractiveness of adjustable loans,
lenders are seeing greater interest in loans that protect borrowers from
rising interest rates  and are introducing products for that market.
Last month, Wells Fargo & Co. rolled out a 30year fixedrate mortgage
that is interestonly for the first 10 or 15 years. The interest rate
remains the same throughout the life of the loan, but the monthly payment
is recalculated after the interestonly period ends so that the mortgage
balance is paid off over the remaining 15 or 20 years. U.S. Bank Home
Mortgage, a unit of U.S. Bancorp, plans to introduce a 20year fixedrate
mortgage with an interestonly feature for the first 10 years. Bank of
America Corp., IndyMac Bancorp Inc. and LendingTree.com, a unit of IAC/InterActive
Corp., all have fixedrate interestonly mortgages in the works.
Fortyyear mortgages  which keep monthly payments down but cost more
over the long term  also are attracting more notice in the wake of Fannie
Mae's recent decision to expand its purchases of these loans. First offered
in the 1980s, 40year loans account for less than 1% of mortgage originations,
according to the Mortgage Bankers Association. More banks may be willing
to offer them now that they know they can be sold to Fannie Mae, which
has been purchasing 40year mortgages since September 2003 under a pilot
program with 22 credit unions. Fannie will purchase both fixed and adjustablerate
40year mortgages.
Next month, IndyMac Bancorp will reintroduce its 40year mortgage, which
was mothballed last year because of a lack of interest. Fannie Mae's move
"helps by bringing attention to the product and credibility to it,"
says IndyMac Executive Vice President Frank Sillman. "It also brings
a host of investors that will purchase 40year loans." Washtenaw
Mortgage Co. in Ann Arbor, Mich., a unit of Washtenaw Group, began offering
these loans in May. Old National Bancorp. in Evansville, Ind., says it
will add them this summer.
Some lenders have been offering more and more interestonly mortgages
in recent years to eager borrowers, though the vast majority of them have
been adjustablerate loans with interestonly features. These include
both shortterm adjustables, with rates that can adjust as often as once
a month, and socalled hybrid ARMs that can carry a fixed rate for as
long as 10 years, after which the rate can adjust annually.
ARMs and interestonly mortgages have been especially attractive to
borrowers looking to keep their monthly payments down in the face of skyrocketing
home prices. These loans accounted for nearly twothirds of mortgage originations
in the second half of last year, according to the Mortgage Bankers Association.
Among the increasingly popular choices: socalled option ARMs, which are
shortterm ARMs that carry introductory rates of as low as 1% and give
borrowers multiple payment options. Because these loans allow borrowers
to afford more house with a lower payment, some observers worry that they
have helped fuel a heated housing market.
The growing popularity of interestonly and adjustablerate mortgages
has also raised fears that borrowers and lenders are taking on additional
risks that could create problems down the road. "The apparent froth
in housing markets may have spilled over into mortgage markets,"
Federal Reserve Chairman Alan Greenspan told Congress last week. He called
the "dramatic increase in the prevalence of interestonly loans,
as well as the introduction of other relatively exotic forms of adjustablerate
mortgages ... developments of particular concern."
Lenders that now offer fixedrate loans with interestonly features say
they have seen a spurt of interest in these products in recent weeks as
the yield curve has flattened, making ARMs relatively less attractive.
At Greenpoint Mortgage, a unit of North Fork Bancorporation Inc., interestonly
loans now account for about 30% of fixedrate mortgages, up from 15% earlier
this year. Countrywide Financial Corp. says activity in fixedrate interestonly
mortgages has been "brisk" recently.
Because they allow borrowers to lower their monthly payments, the newer
breed of mortgages is aimed at homeowners concerned about affordability
and those who want to free up cash for other purposes. Unlike ARMs, which
allow borrowers to get a lower rate in exchange for accepting the risk
of future rate increases, fixedrate interestonly mortgages carry the
same interest rate over the life of the loan.
But like other interestonly loans, they tend to be more costly than
standard mortgages. At Countrywide, the interest rate on an interestonly
loan is typically oneeighth of a percentage point higher than the rate
on a comparable loan without the interestonly feature. Wells Fargo says
its borrowers typically pay about onequarter point more in upfront costs
 or $500 on a $200,000 mortgage.
Borrowers can face payment shock when the interestonly period ends.
A borrower with a $200,000, 5.50% 30year mortgage that's interestonly
for the first 15 years would see the monthly payment increase to $1,634
from $917 when the loan recasts so that the mortgage can be paid off in
the remaining years, according to HSH Associates in Pompton Plains, N.J.
Some lenders and borrowers are looking to 40year mortgages as an alternative
to interestonly mortgages. The 40year loans are likely to appeal to
borrowers "in the middle of the country, who tend to be more conservative,"
says James Cotton, vice president for singlefamily marketing at Freddie
Mac, which is looking at buying 40year mortgages.
Fortyyear mortgages can be costly over the long haul. Rates on these
loans tend to be about 0.25 to 0.375 percentage point higher than the
rate on a comparable 30year mortgage. Borrowers also pay more interest
over time because the loan is stretched over an additional 10 years. With
a $200,000 mortgage with a 5.75% fixed rate, a borrower with a 40year
mortgage will pay roughly $312,000 in interest over the life of the loan,
according to HSH Associates, versus about $220,000 in interest if the
same loan has a 30year term, assuming both loans carry the same interest
rate. If the rate on the 40year mortgage is 6%, the total interest payments
jump to about $328,000.
Some lenders are tweaking the formula. Hingham Institution for Savings
in Hingham, Mass., last year introduced a 2020 mortgage, a 40year loan
with a single rate adjustment after the first 20 years. Because it is
essentially two 20year loans, the rate on the mortgage is onequarter
to oneeighth of a point below the rate on a standard 30year loan. "It's
been our most popular product," says Hingham vice president Michael
Sinclair.
5. (20 points) You have constructed the following probability distribution
of returns on Countrywide Financial Corp's stock over the next year:
Return 
Probability 
5% 
0.2 
20% 
0.7 
40% 
0.1 
 What is the expected return on Countrywide's stock over the next year?
 What is the standard deviation of returns on Countrywide's stock over
the next year?
Solution to Final
1.a. The expected return on the stock is 4.075 + 0.433(6) = 6.673%
b. The dividend next year is (0.72)(1.08) and the dividend the year after
that is (0.72)(1.08)^{2}. The sum of the present values of these dividends equals $0.729
+ $0.738 = $1.467. The price
of the stock at the end of the second year will be (0.72)(1.08)^{2}(1.03)/(.066730.03)
= $23.55, or in present value terms, $20.692.
Adding this to 1.467, we get $22.16
2 a. The price of the bond is PV(annuity of $30
per period for 20 periods; periodic rate of 4%) + 1000/(1.04)^{20}
= $864.10
b. The bond should be selling at a discount, since the YTM > the coupon
rate; hence you should not buy it at par.
3. The EAR is 15%; hence the quarterly rate is
(1.15)^{0.25} – 1 or 3.5558%.
We can use this and the annuity formula, to compute the periodic
payment to be $1272.90
4. a. Since you are paying interest only for
the first ten years, you will pay, each month, 20000(1.01) or $200. At the end of the period, you will still owe the entire principal
of $20,000. Hence your monthly
payments will simply be the monthly payments on a 10 year loan of $20,000
at an APR of 12%, i.e. $286.94.
b. The problem is that interest paid in different months are simply being
added – this ignores the time value of money.
c. Your friend is correct, since the diversifiable uncertainty will disappear
in a diversified portfolio; it will not add to the total variance of a
diversified portfolio.
d. The R^{2} is equal to 22.8/400 = 0.057
5. The expected returns equal 5(0.2) + 20(.7)
+ 40(0.1) = 19%; the variance of returns, as shown below works out to
81 percentsquared; hence the standard deviation of returns is 9.165%
Prob

Return

sq
dev 
0.2

5

196

0.7

20

1

0.1

40

441


19.0

84.0


