RSM230 Financial Markets
Old Midterm solutions

David Goldreich
Professor of Finance
Rotman School of Management
University of Toronto

Multiple choice questions

M1. You spent $500 last week fixing the brakes of your car. Now the transmission is not working. You
are trying to decide whether to fix the transmission or sell your car to a dealer. The $500 you spent on
the brakes is an example of a:
a) opportunity cost
b) fixed cost
c) incremental cost
d) sunk cost

M2. When you calculate the NPV of starting a new product line, you realize that instead of buying a
new machine for $1 million, you can use an old machine that you already use that could otherwise be
sold for $150,000. If you decide that it is best to use the old machine, the cash outflow that should be
used for your NPV analysis should be:
a) $1 million
b) $850,000
c) $150,000
d) $0

M3. Suppose you invested $200,000 at 6% per annum compounded semi-annually for 2 years. How
much money would you have at the end of two years?
a) Between $210,000 and $220,000
b) Between $220,001 and $224,000
c) Between $224,001 and $225,000
d) Between $225,001 and $230,000
e) Between $230,001 and $240,000
f) More than $240,000

M4. Suppose you initially invested $50,000 and cashed out with $62,000 after 2 years. What is your
Internal Rate of Return (per annum)?
a) Less than 12%
b) 12%
c) More than 12% but less than 24%
d) 24%
e) More than 24%




M5. You want to start a business that you believe can produce cash flows of $8000, $20,000, and
$50,000 at the end of each of the next three years, respectively. You also think you can sell the
business for $250,000 at the end of three years. At a discount rate of 9 percent, what is this business
worth today (to the nearest $1000)?
a) $240,000
b) $256,000
c) $301,000
d) $328,000

M6. What is the EAR (to the nearest basis point) if a bank charges you an interest rate of 4.56 percent,
compounded quarterly?
a) 1.14 percent
b) 4.48 percent
c) 4.56 percent
d) 4.64 percent
e) 9.12 percent

M7. The credit spread on corporate bonds rated AA by Moody’s is likely to:
a) narrow during a recession
b) be wider for longer-term bonds
c) remain constant as long as the rating doesn’t change



Short answer questions

S1. If there are two bonds available (from the same issuer and with the same maturity) that have two
different coupon rates, why would anyone buy a bond with a lower coupon rate? Explain.

Although the lower coupon bond has smaller cash flows, it will be cheaper by just the right amount to
make it fair.

S2. Consider a corporate bond that was issued recently. What are the two main reasons that the market
price of a bond may go down?

If interest rates go up then for a fixed coupon, the value of the bond will go down. If the company
becomes riskier, the probability that it will pay the promised payments goes down, so the value of the
bond will go down.

S3. When deciding whether to start a new product line, you forecast cash flows. Is it correct to include
overhead as a negative cash flow? Explain.

Overhead is generally not incremental since it has to be paid whether or not you undertake the
project. In such a case, you should not include overhead as a negative cash flow. However, sometimes
undertaking the project increases the company’s overall overhead. That increase should be included
as a negative cash flow.

S4. It has been argued that liquidity in the secondary market for stocks is irrelevant for real economic
activity, such as opening new business and growing existing business. Evaluate this claim.

False. Liquidity in the secondary market makes stocks more valuable in the secondary market. As a
result, someone buying in the primary market would be willing to pay more for a stock since he can
later sell it for a higher price later in the secondary market. In turn, this will encourage businesses to
raise capital since they can sell shares in the primary market at higher prices.

S5. Cash flows to shareholders in the form of dividends is at the discretion of managers. Is it bad for
shareholders if managers choose to pay out low dividends? Explain.

Generally not. If low dividends are paid out, then there is more cash to reinvest in the company to
help the company grow, which ultimately will lead to bigger dividends later. (It depends on the NPV of
the reinvested money, but that is not needed for this question.)

S6. When calculating the NPV of your proposed new product line based on a newer technology, you
realize that it is likely to cannibalize profit from your older existing product line. Should the reduced
profit in the older product line be considered a negative cash flow for the new product? Explain.

In general, yes, since we must consider the incremental cash flow to the entire company. However, if
your competitor is likely to come out with a product based on the newer technology if you don’t start
the new product line, then it is likely that the cannibalized customers would have gone away
regardless and should not be counted as a negative cash flow for your NPV calculation.

S7 Last year at this time, XYZ announced quarterly earnings of 50 cents per share. This year, analysts
were expecting quarterly earnings to rise to 60 cents per share. Today, XYZ announced that earnings
were 54 cents per share for this past quarter. Will the stock price likely go up or go down after the
announcement? Explain. What might the size of the price change depend on? Explain.

It will go down since the earnings were six cents less than the market’s expectation. The price will
likely drop by many times the six cents depending on how much the shortage of six cents indicates
lower profits (or cash flows) in future quarters.

S8. Bond A, issued by the Government of Canada has a face value $1000, 10 years until maturity, and an
annual coupon of 4%. Bond B, also issued by the Government of Canada with a face value $1000, has
only 5 years until maturity, and an annual coupon of 6%. If the general level of interest rates falls, what
will happen to the values of Bonds A & B? Which bond’s value will move more as a percentage of its
original value? Explain.

Both bonds will rise in value. Bond A is longer and has lower coupons. For both of these reasons it is
longer until the investor gets repaid. Therefore, Bond A is more sensitive to interest rate moves and
will rise more in value.





Problem solving

P1. (4 points) When I turn 65, I will receive an annual pension (starting on my 65th birthday) of $80,000
per year. I expect to collect 30 pension payments, the last being on my 94th birthday. The discount rate is
6% per annum.

a) On my 65th birthday, what will be the present value of all my pension payments (as calculated on my
65th birthday)?
b) What is the present value of my future pension, today on my 55th birthday? (But the payments won’t
start until I turn 65.)

a) Since the first cash flow is at age 65, it is easiest to first calculate the value at age 64.
PV(at age 64) = $80,000*(1/.06)*(1/1.06^30) = $1,101,186
Then multiply by 1.06 to get value as of age 65 = $1,167,258
(Alternatively, value 29 year annuity at age 65 plus $80,000)

b) The value at age 55 is
$1,167,258/1.06^10 = $651,791


P2. (5 points) Consider a bond issued by the Government of Canada that has a face value $1000, 10
years until maturity, and an annual coupon of 5%. Suppose the yield is 4% per annum (compounded
annually). What is the value of this bond? Suppose that the bond was callable, allowing the government
to buy back the bond at face value after 5 years, explain in words if the value will be higher or lower?

Coupons of $50 per year for 10 years followed by face value of $1000 at year 10. Discount rate = 4%.
Value of coupons = $50*(1/.04)*(1-1/(1.04)^10) = $405.54
Value of Face = $1000/1.04^10 = $675.56
Total value = $1081.11.

If the bonds were callable, then they would be less valuable, since the government would buy them
back precisely when it is disadvantageous for the bondholder (i.e. when interest rates are lower /
when the bond price would otherwise be higher).



P3. (6 points) Rotman Commerce International (RCI) is a multinational producer of widgets. It expects
free cash flow next year of $150 million, $230 million the following year, $300 million in three years
from now. After that, free cash flow is expecting to grow at 2% per year forever. The appropriate
discount rate is 9%.

a) What is the total company value of RCI?

b) Now that you know the total value of the company, you learn that RCI previously raised capital in
both the equity and debt markets. It has 40 million shares of common stock outstanding. It also has
long-term bonds outstanding that are valued at $700 million. What is the fair price per share of RSC?

a) Present value of first two cash flows = $150M/1.09 + $230M/1.09^2 = $331.20M
Year 2 value of year 3 cash flow onward = $300M/(.09-.02) = $4285.71M
Present value of year 3 cash flow onward = $4285.71M/1.09^2 = $3607.20M
Total value = $331.20M + $3607.20M = $3938.40M

b) Value of Equity = Total firm value - debt = $3938.40M - $700M = $3238.40M
Price per share = $3238.40M/40M = $80.96