exam solution 7 fundamentals of corporate finance, 4th edition brealey

SOLUTIONS – TYPE A Summer 2007 – 3530 Midterm Exam
1. (Q6 in Type B) How much will be in an account after 3 years if the initial deposit was
$10, and which earned 10% interest compounded quarterly for the 3 years?
A)
$10.77
B)
$13.31
C)
$13.45
D)
$31.38
Solution C. $10 x (1+.10/4)12 = $13.45
2. (Q7 in Type B) If I promise to pay you $1,800 nine years from now in return for a loan
of $1,000 today, what is the effective annual interest rate for this agreement?
A)
5.26%
B)
6.75%
C)
9.00%
D)
10.00%
Solution B.
r = (FV/PV)1/t – 1 = (1800/1000)1/9 – 1 = 6.75%
or use your financial calculator PV=1,000; FV=1,800; t=9, solve for r
3. (Q8 in Type B) In June 2007, the posted mortgage rate at CIBC was 6% for a 6-year
term. What is the monthly interest rate? Use 6 decimal places in your calculations.
(Remember that mortgages are compounded semi-annually)
A)
0.4939%
B)

0.5000%
C)
0.5061%
D)
6.0900%
Solution A.
The 6% posted rate is an APR from 3% per 6 months. The EAR is 1.032 – 1 = 0.0609.
The monthly rate is (1.0609)1/12 – 1 = 0.004939.
4. (Q9 in Type B) How much can be accumulated for retirement if $2,000 is deposited
annually, beginning today, and the account earns 9% interest compounded annually for
40 years?
A)
$ 17,558.
B)
$506,824.
C)
$552,438.
D)
$802,876
Solution C.
Use you calculator PMT = 1,500 r = 9% , t = 40, find FV = 506,824 But payment starts
immediately -> annuity DUE = 506,824 x 1.09 = $552,438.


5. (Q10 in Type B)What is the effective annual rate on a deposit of $5,000 made ten
years ago if the deposit is worth $9,948.94 today? The deposit pays interest semiannually.
A)
3.50%
B)
6.76%

C)
7.00%
D)
7.12%
Solution D.
From the formula for PV, FV, r, and t, we have r = (FV/PV)1/t – 1. Using t=20 because of
semi-annual interest, we get r = 0.035 as the 6-month rate. Then (1+0.035)2 -1 = 0.0712.
6. (Q11 in Type B)Assume your uncle recorded his salary history during a 40-year career
and found that it had increased ten-fold (i.e., his salary at the end of his career was 10
times his salary at the beginning). If inflation averaged 5% annually during the period,
how would you describe his purchasing power, on average?
A)
His purchasing power remained on par with inflation.
B)
He “beat” inflation by nearly 1% annually.
C)
He “beat” inflation by slightly over 2% annually.
D)
He “beat” inflation by 5% annually.
Solution B.
For the annual increase in his nominal salary, r = (FV/PV)1/t – 1 = (10)1/40 – 1 = 5.93%.
By either the exact formula or the approximation, this is a real increase of nearly 1
percentage point.
7. (Q12 in Type B) How much interest will be earned in the third year if $1,000 is
deposited that earns 8% interest compounded annually?
A)
$ 70.00
B)
$ 93.31
C)

$105.62
D)
$140.00
Solution B.
The deposit grows to $1000 x 1.07 = $1080 at the end of the first year, $1166.40 at the
end of the second year, and $1259.71 at the end of the third year. The difference between
$1259.71 - $1166.40 = $93.31
8. (Q13 in Type B) A credit card account that charges interest at the rate of 1.25% per
month would have an annually compounded rate of _______ and an APR of _______.
A)
16.08%; 15.00%
B)
14.55%; 16.08%
C)
12.68%; 15.00%
D)
15.00%; 14.55%
Solution A.


(1+.0125)12 – 1 = 16.08%; 1.25%x12 = 15%
9. (Q14 in Type B)You decide to sell your car and someone has offered you four equal
annual payments of $3,100, beginning two years from today. Your alternative is to sell
your car today for $9,000 cash. Assuming everything else is equal, should you accept the
offer of the four equal payments (the prevailing rate of interest is 10%)?
A)
Yes; present value is $9,510.
B)
Yes; present value is $11,372.
C)

No; present value is $8,933.
D)
No; present value is $7,461.
Solution C.
The PV of the four payments PV= 3,100 / (1+0.1)^2 +3,100 / (1+0.1)^3 +3,100 /
(1+0.1)^4 +3,100 / (1+0.1)^5 = $8,933 or use the annuity formula. This is less than the
$9,000 you would get today. Therefore you would not accept the offer.
10. (Q15 in Type B)How much more is a annual perpetuity of $1,000 worth than an
annual annuity of the same amount for 20 years? Assume a 9% interest rate and cash
flows are at end of each year.
A)
$297.29
B)
$1,486.44
C)
$1,982.57
D)
$2,000.00
Solution C.
The perpetuity is worth $1000/.09 = $11,111.11 The PV of the twenty-year annuity = C *
[1/r – 1/r(1+r)^t ] = $9128.55; or use your financial calculator. The difference between
the perpetuity and annuity is $1982.57.
11. (Q1 in Type B) Two years ago bonds were issued with 10 years until maturity,
selling at par, and a 7% coupon. Interest is paid semi-annually. If market interest rates
for that grade of bond are currently 8.25%, what will be the price of these bonds?
A)
$700.00
B)
$916.00
C)

$927.84
D)
$987.50
Solution: C
Using your calculator: PMT = $35, i= 8.25/2 = 4.125, n = 8 yrs remaining x 2=16,
FV=$1000, COMP PV Æ PV = $927.84
12. (Q2 in TYPE B)What is the yield to maturity of a bond with the following
characteristics? Coupon rate is 8% with semi-annual payments, current price is $960,
three years until maturity.
A)
2.39%
B)
4.78%


C)
D)

9.57%
12.17%

Solution: C
Using your calculator: PMT = $40, PV = - 960, 4.125, n = 3 x 2 = 6, FV=$1000,
COMP i Æ i = 4.7826 x 2= 9.567
13. (Q3 in Type B) What is the current yield of the following bond: it has 10 years until
maturity, sells for $1033, has a face value of $1000 and a 6% coupon rate (paid semiannually).
A)
2.39%
B)
4.78%

C)
5.81%
D)
11.62%
Solution: B
Current Yield = Annual coupon / Current price
= $60/$1033 = 5.81%
14. (Q4 in Type B) BCE was recently been bought out by a U.S. private equity firm who
levered the company and now BCE is having cash flow problems. Its existing bonds have
the following terms: 6% coupon, $1000 face value and they mature in 10 years. Bonds of
equivalent risk yield 12%. BCE is asking the bondholders to swap their existing bonds
into 5 year zero-coupon bonds with a face value of $1000. Assuming BCE will not be in
default during the next 10 years, should existing bondholders accept the deal?
A) No, because the existing bonds are worth more.
B) Yes, because, the zero coupon bonds are worth more.
C) Yes, because the zero coupon bonds have a shorter 5 year maturity.
D) No, because zero coupon bonds do not pay interest.
Solution: A
Current Price of existing bonds:
PMT = $30, n = 10 x 2 = 20, FV = $1000, I = 12/2 = 6,
COMP PV -> PV = $655.90
Current value of Zero-coupon bonds:
PV = $1000/ (1.12)5 = $567.43
As long as BCE will not be in default of its bond payments, the bondholders should keep
their existing bonds as they have a higher PV.
15. (Q5 in Type B)You bought a bond with a 7% annual coupon rate four years ago
when market interest rates for similar bonds was 6%. The bond had an original maturity
of 10 years and a par value of $1000. Today, the yield to maturity of the bond has
increased to 8% annually. If you sell the bond today, what would be your annual rate of

return over the past 4 years? The bond pays coupons semi-annually. Assume coupons are
not reinvested.
A) 3.50%
B) 3.69%
C) 7.33%
D) 14.77%
Solution: A
Step 1, Find purchase price of bond 4 years ago, using your calculator:
PMT = $35, n = 10 x 2 = 20, I = 6/2 = 3, FV = $1000
COMP PV -> PV = $1074.39
Step 2, find price of bond today, using your calculator:
PMT = $35, n = 6 x2 = 12, I = 8/2 = 4, FV = $1000
COMP PV -> PV = $953.07
Step 3: Find Rate of Return over the 4 year holding period
= (Coupon Interest + or - Cap gain/loss)
Original price paid
= (70 x 4) + ($953.07 – 1074.39)
$1074.39

=

280 – 121.32
$1074.39

= 0.1477 or 14.77% over 4 years
Step 4: Annual rate of return = (1 + .1477) ¼ -1 = 3.50%
16. (Q16 in Type B) How much of a stock’s $25 price is reflected in the PVGO if it
expects to earn $3 of earnings per share next year, and has a required rate of return of
14%?

A)
$3.57.
B)
$5.00.
C)
$21.43
D)
$22.00
Solution: A
If all earnings are paid out as dividends to shareholders, the stock price will be $3.00/0.14
= $21.43. This is the stock price when there is “no growth.”
Therefore, the PVGO = $25.00 - $21.43 = $3.57.
17. (Q17 in Type B) TD Bank’s earnings and dividends are expected to grow at a rate of
10% during the next 2 years, at 8% in the third year, and at a constant rate of 6%
thereafter. If last dividend paid was $1 and the required rate of return on its common
stock is 12%. How much should you pay today for one share of TD Bank?
A)
$19.31


B)
C)
D)

$24.66
$25.97
$28.02

Solution: A
g1, g2 = 10%

g3 = 8%
g4 and onwards = 6%
r = 12%
DIV0 = 1.00
Constant Growth DDM

P0 = DIV1
r–g

and

P3 =

DIV4
r–g

= DIV3 (1 +g)
r-g

First, Find DIV3
DIV1 = DIV0 (1 +g) = 1.00 (1.10) = 1.10
DIV2 = DIV1 (1 +g) = 1.10 (1.10) = 1.21
DIV3 = DIV2 (1 +g) = 1.21 (1.08) = 1.3068
DIV4 = DIV3 (1 +g) = 1.3068 (1.06) = 1.3852
P3 = 1.3852 / (.12-.06) =$23.09
P0 = DIV1/(1 +r)1 + DIV2 /(1 +r)2 + DIV3/(1 +r)3 + P3/(1 +r )3
= 1.10/(1.12) + 1.21/(1.12)2 + 1.3068/(1.12)3 + 23.09/(1.12)3
= 0.9821 + 0.9646 + .9302 + 16.4350
= $19.31
18. (Q18 in Type B) How much should you pay today for a stock per share that offers a

constant growth rate of 9% for dividends, requires a 12% rate of return, and is expected
to sell for $40 one year from now?
A)
$35.71.
B)
$38.83.
C)
$41.20.
D)
$44.80.
Solution: B
The easiest way to solve this problem is to realize that:
Cap Gain return + Div Yield = 12%
Cap Gain return = 12% - 9% = 3%
P0 = P1 / (1.03)
P0 = $40/(1.03)
= $38.83
19. (Q19 in Type B)What should be the annual dividend yield for Year 3 of a stock if a
$4 dividend per share was just paid, the stock has an annual required rate of return of
18%, and a constant dividend growth rate of 6%?


A) 6.35%
B) 7.57%
C) 12.00%
D) 13.48%
Solution: C
DIV3 = DIV0 x (1 + g)3 = 4 x (1.06)3 = $4.7641
P2 = DIV3/ (r-g) = $4.7641 / (.18 - .06) = $39.70
Î annual dividend yield for Year 3 = DIV3/P2 = $4.7641/$39.70

= 12.00%
20. (Q20 in Type B) What is the implied constant growth rate of dividends for a stock
currently priced at $25, that just paid a dividend $2 per share, and has a yearly expected
rate of return of 18%?
A) 3.41%
B) 9.26%
C) 10.0%
D) 13.5%
Solution: B

21. (Q24 in Type B) A stream of equal cash payments lasting forever is termed:
A)
an annuity.
B)
an annuity due.
C)
an installment plan.
D)
a perpetuity.
Solution D. definition of a perpetuity
22. (Q25 in Type B)Given a set future value (greater than zero), which of the following
will contribute to a lower present value?
A)
Higher discount rate.
B)
Fewer time periods.
C)
Less frequent discounting.
D)
Lower discount factor.

Solution A. The higher discount rate lowers the PV; the other three will raise the PV.


23. (Q26 in Type B) If we assume that in the market place the nominal rate of interest is
greater than that real rate of interest we can normally assume that
A) there is deflation in the economy
B) the CPI is increasing
C) Price of the average home is going down
D) No one wants to borrow money as the rates are too high
Solution B. It implies that we are in an inflationary environment and that the CPI
(consumer price index) is going up.
24. (Q27 in Type B) Which of the following theories is generally supported by the
principles of compound interest, assuming we invest in interest bearing securities?
A)
B)
C)
D)

the longer you invest the more likely your investment will grow
Whether you invest for your retirement early or late in life are irrelevant.
The rate at which your retirement investment grows is irrelevant
The later in life you invest the better off you will be.

Solution A. Assuming a positive rate of interest the longer you invest the more your
investment will grow over time.
25. (Q21 in Type B) Which of the following is correct for a CCC-rated bond, compared
to a BBB-rated bond?
A)
The CCC bond must have protective covenants.
B)

The CCC bond must have a sinking fund provision.
C)
The CCC bond must offer a higher coupon rate.
D)
The CCC bond must offer a higher yield to maturity.
Solution: D
See text p.150
26. (Q22 in Type B) Which of the following bond features would be attractive to the
bond investor and allow him/her to lend funds at a lower rate?
A)
A call provision.
B)
A sinking fund provision.
C)
A subordination provision.
D)
A zero coupon feature.
Solution: B See text p.150
27. (Q23 in Type B) Which of the following is correct for a bond currently selling at a
premium?
A) Its current yield is higher than its coupon rate.
B) Its current yield is lower than its coupon rate.
C) Its yield to maturity is higher than its coupon rate.
D) Its default risk is extremely low.


Solution: B
28. (Q28 in Type B)The maximum number of shares that a company is permitted to
issue, as specified in the firm’s articles of incorporation is called:
A)

authorized share capital
B)
issued share capital
C)
issued and outstanding share capital
D)
additional paid-in capital
Solution: A
29. (Q29 in Type B)Bank of Montreal had fallen upon hard times due to a rogue trader
and dividends on their non-cumulative, preferred stock were not paid for three years.
They are now able to resume the dividend payments. Which of the following is true?
A)
Common shareholders must now receive three years' worth of dividends.
B)
Preferred shareholders must now receive three years' worth of dividends.
C)
The corporation must close if preferred shareholders are not paid.
D)
Common shareholders have not received dividends for three years.
Solution: D.
If a company omits the dividend on preferred stock, it must also omit the dividend on
common stock. Because the preferred shares are non-cumulative, the company does not
need to pay out the last three years of dividends.
30. (Q30 in Type B) The form of market efficiency that best describes the inability of
professional portfolio managers to outperform the market is:
A)
strong-form efficiency
B)
semi-strong form efficiency
C)

weak-form efficiency
D)
None of the above. All professional portfolio managers outperform the
market.
Solution: B (see text p.187-188)