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6. Chapter Interest Rates
1. If 0R1=5%, E(1R2)=4%, what is 0R2 according to the Expectations Hypothesis?
(1+0R2)^2 = (1+0R1)*(1+E(1R2)) => (1+0R2)^2 = (1.05)*(1.04) => (1+(0R2))^2 = 1.092 => 0R2 = 4.4988%
Approximately, 0R2 = (0R1+E(1R2))/2 = 4.5%
2. If the current one year CD rate is 5% and the best estimate of one year CD which will be available one year from
today is 7%, what is the current two year CD rate with 1% liquidity premium?
0R1 + E(1R2) = 2 * (0R2  LP) => 5% + 7% = 2 * (0R2  1%) => 0R2 = 7%
3. David Cone is concerned about the interest rate changes for his fixed income investment. He looked at the treasury
yield curve on Wall Street Journal and observed a normal yield curve. Based on this observation, which of the
following statements is correct?
a. Companies must have more investment opportunities now than they expected to have in the future
b. Future shortterm interest rates are expected to be higher than current shortterm interest rates assuming the pure
expectation theory holds.
c. Maturity risk premium is positive
d. Inflation must be expected to increase in the future
e. Expectation theory must be correct
b. Assuming that the expectations theory holds, the overall expected returns from shortterm rollover and longterm
investments are the same. This implies that the longterm rate is an average of current shortterm and expected future
shortterm rates. A normal (rising) yield curve with a long term rate being higher than the current shortterm rate is
indicative of the fact that future shortterm rates are expected to be higher than current shortterm rates.
4. The current interest rate on a 2year Treasury security is 5.5% while the 1year US Treasury security yields 5%.
Assuming that the pure expectations theory holds, what is the markets estimated interest rate on 1year Treasury
security one year from now?
0R2 = [0R1 + E(1R2)]/2, 5.5% = [5% + E(1R2)]/2, E(1R2) = 6%
5. Assume that interest rates on 20year Treasury and corporate bonds are as follows:
Tbond = 7.72%
AAA = 8.72%
A = 9.64%
BBB = 10.18%
The differences in these rates were probably caused primarily by:
a. Tax effects b. Default risk differences c. Maturity risk differences
d. Inflation differences e. Real riskfree rate differences
b
6. A bond trader observes the following information:
The Treasury yield curve is downward sloping.
Empirical data indicate that a positive maturity risk premium applies to both Treasury and corporate bonds.
Empirical data also indicate that there is no liquidity premium for Treasury securities but that a positive
liquidity premium is built into corporate bond yields.
On the basis of this information, which of the following statements is most CORRECT?
a. A 10year corporate bond must have a higher yield than a 5year Treasury bond.
b. A 10year Treasury bond must have a higher yield than a 10year corporate bond.
c. A 5year corporate bond must have a higher yield than a 10year Treasury bond.
d. The corporate yield curve must be flat.
e. Since the Treasury yield curve is downward sloping, the corporate yield curve must also be downward sloping.
c
7. If 10year Tbonds have a yield of 6.2%, 10year corporate bonds yield 8.5%, the maturity risk premium on all 10year bonds is 1.3%, and corporate bonds have a 0.4% liquidity premium versus a zero liquidity premium for Tbonds, what is the default risk premium on the corporate bond?
Liquidity risk premium = LP is included in corporate only = 0.40%
Corporate bond yield = r = r* + IP + MRP + DRP + LP = 8.50%
Tbond yield = rRF = r* + IP + MRP + 0 + 0 = 6.20%
Difference = DRP + LP = DRP + 0.40% = 2.30%
DRP = Difference LP = 1.90%
8. Suppose the interest rate on a 1year Tbond is 5.0% and that on a 2year Tbond is 7.0%. Assuming the pure
expectations theory is correct, what is the market's forecast for 1year rates 1 year from now?
0R2 = [0R1 + E(1R2)]/2 => 7% = [5% + E(1R2)]/2, E(1R2) = 9%
Chapter 5. Time Value of Money
1. Given an interest rate and the number of periods being greater than zero, which statements are correct? (Hint: use
I/Y=5%, N=3 to check out as an example)
I. Present value interest factors are greater than 1.0
II. Future value interest factors are less than 1.0
III. Present value interest factors are less than future value interest factors
IV. Future value interest factors grow as t grows, provided r is held constant
a. I only
b. I and III
c. I and IV
d. II and III
e. III and IV
e. PVIF <1, FVIF>1, PVIF<FVIF, FVIF grows at t increases
2. If you save $100 today and $100 two years from now, how much can you have three years from now if the savings
rate is 10%? (Note that you save nothing next year)
100*(1.1)^3 + 100(1.1)=133.10+110=243.10
3. FVIF(10%, 1)?
1+.1 = 1.1
4. You received a $1 savings account earning 5% from you father today. How much will you have in the account 40
years from today if you don't withdraw any money before then?
$1 * FVIF(5%, 40) = 1*(1.05)^40=$7.04
5. What is the relationship between FVIF(r%, N) and PVIF(r%, N)?
a. PVIF is greater than FVIF b. FVIF is a sum of PVIF from n=1 to n=N c. PVIF is an inverse of FVIF
d. PVIF is used for an annuity e. FVIF*PVIF=2.0
c. FVIFA(r%, n) = sum of FVIF from t=1 to t=n,
PVIFA(r%, n) = sum of all PVIF from t=1 to t=n,
PVIF and FVIF have an inverse relationship. PVIF*FVIF=1.0
6. You want to buy a $15,000 car. If you borrow money from the dealer, they are willing to give you a 1 year loan and
you need to make a single payment one year from today at zero interest. If you borrow money from a bank for the
same one year period and make a cash payment to the dealer right now (using the money you borrow from the
bank), you can enjoy a $1,000 discount from a dealer. The bank interest rate is 12% and you need to make a single
payment one year from today to pay off the debt. Which alternative do you like better. Basically, you need to
borrow money, either from the dealer or from the bank. What is the difference between the future payments of these
two choices?
a. Loan from the dealer, more than $2,000
b. Bank, more than $2,000
c. Loan from the dealer, less than $2,000
d. Bank, less than $2,000
e. Equivalent
c. In terms of FV, $15,000 vs $14,000*(1.12)^1=$15,680.
You can save $680 in terms of FV by getting a zero rate loan the dealer.
7. You want to buy a trailer house worth $25,000 today 3 years later. It is expected that the price of this house will go
up at 5% each year for the next 3 years. How much do you need to save today in your investment account, which is
expected to grow at 10% rate each year for the next 3 years?
Projected price of the trailer house 3 years later = 25,000*(1.05)^3=$28,940.60,
PV of this amount of money with r=10%, t=3 => 28,940.60*(1/1.1^3) = 21,743.45
8. How long approximately does it take to double your investment at 12% per period?
The rule of 72, 72/interest rate per period=# of periods to double your money, example: 72/12% = 6 periods. I can
switch interest rates and # of periods to obtain the interest rate which allows me to double money investment in 6
periods.
9. Susie Orman argues that you can have more money by saving $100 each month (starting at the end of this month for
12 deposits) instead of saving $1,200 at the end of each year. To check whether that is true, you are going to
compare saving $600 every six months for a year (starting from 6 months from today for 2 deposits) visvis
$1,200 at the end of the year. What is the future value of $600 saved every six months for a year at the end of the
first year at 10% APR?
Susies argument: better to save less and more frequently than to save more and less frequently.
600*(1.05)+600=$1,230, FV of $1,200 saved at the end of the year=$1,200, FV of $1,200 you save today=
1,200*(1.05)^2=1,323 (Aside: 10% with no 6 month compounding = 1,200*1.1=1,320
10. If your two year CD rate is 3%, how much do you approximately earn over the two year investment period from the
CD?
3%*2 for 2 years, approximately. However, the exact (taking into consideration the compounding effect) total return
should be (1.03)^2 1 = 6.09%
11. How much do you have to save one year from today to have $100 three years from today at 10%, semiannual
compounding?
100*PVIF(5%,4)
12. This is not covered in class. You are not responsible for this problem
For x/15, net 30, what is x if the discount on an annual basis is 36%? If the cost of borrowing money is 15%, would
you take the discount by paying early or not?
x * 360/(3015) = x * 24 = 36% => x=1.5%. Since 36% of savings from the discount > 15% interest cost of buying
money (both discount rates and interest rates are compared based on annual percentage rates), you would like to take
the discount by paying early.
13. If you save $788 each month starting next month, how much can you have at the end of the year (12 months later)
at a 12% rate?
N=12, I/Y=1, PMT=788 => FV=9,993.81
14. If you save $100 today and $100 two years from now, how much can you have three years from now if the savings
rate is 10%? (note that you save nothing next year)
100*(1.1)^3 + 100*(1.1)^1, or 100*FVIF(10%,3) + 100*FVIF(10%,1) = $243
15. What is the relationship between PVIFA(r%, N) and PVIF(r%, N)?
a. PVIF is greater than PVIFA b. PVIFA is a sum of PVIF from n=1 to n=N
c. PVIFA is an inverse of FVIFA d. PVIF is used for an annuity e. None of the above
b. For example, PVIFA(r%, 2) = PVIF (r%, 1) + PVIF(r%, 2), FVIFA of an annuity is sum of future values of
payments. Therefore, FVIFA is greater than or equal to FVIF (they are the same only when the period = 1)
16. You want to buy a $15,000 car. If you borrow money from the dealer, they are willing to give you a 3 year loan (36
payments) at zero interest. If you borrow money from a bank for the same period and make a cash payment to the
dealer right now, you can get a loan for 6% APR and enjoy a $1,000 discount from the dealer. Which alternative do
you like better. How much savings do you have in terms of PV by choosing one over the other?
a. Loan from the dealer, more than $2,000
b. Bank, more than $2,000
c. Loan from the dealer, less than $2,000
d. Bank, less than $2,000 e. All are equivalent
c. Lets compare the monthly payments. Dealer: n=36, i/Y=0%, PV=15,000 => 416.67, Bank: n=36, i/Y=0.5%,
PV=14,000 => 425.91. If we determine the PV of the loan from the dealer at the market interest rate 6% APR or
0.5% per period, then n=36, PMT=416.67, i/Y=0.5% => PV=13,696.37. Therefore, the difference between the
PVs of these two loans ($14,000.00 vs $13,696.37) is $303.63
17. What is the value of the trailer house you can buy 4 years from today, if you save $25,000 today at 10% rate?
25,000*FVIF(10%,4)
18. What is the rate of return on the investment to triple your money every 9 years?
N=9, PV=1, FV=3 => CPT I/Y = 12.98%
19. How long will it take for you to pay off $1,200 charged on your credit card, if you plan to make the minimum
payment of $10 per month and the credit card charges 24% per annum?
PV=1200, PMT=10, i/Y=2%, n=infinite, there is no way you can pay of the debt in this case. $10 is not enough to
catch up the increase in the interest
20. How much do you have to save one year from today to have $100 three years from today at 10%, semiannual
compounding?
N=4, I/Y=5, PMT=0, FV=100 => PV?
21. You received $100 each year for the past 10 years. How much do you have now in your 5% savings account if you
don't withdraw any money before?
N=10, I/Y=5, PV=0, PMT=100 => FV?
22. There are two alternatives to buy your dream car valued at $10k. The #1 alterative is making a cash purchase with a
5% cash discount. The #2 alternative is to finance its purchase at a rate of 12% for 2 years. Which alternative is more
attractive (cost saving) at the 12% discount rate? And how much?
In terms of PV today, alternative #1 is 10,000*(10.05) = 9,500. It is 10,000 for alternative #2 because you are
borrowing 10,000 today.
23. What is the monthly payment to pay off $1,000 charged on your credit card, if you plan to have a zero debt in 4
years and the credit card charges 24% per annum?
N=48, I/Y=2, PV=1,000 => PMT?
24. How much do you need to save each year from two years from today so that you can have $1,000 six years from
today at 10% interest rate?
N=5, I/Y=10, FV=1,000 => PMT?
25. You have a choice of receiving $90 one year from today (#1) or $100 two years from today (#2) from the same
amount of money invested today. Which one do you prefer if the market interest rate is 10%. If you need to make a
payment to pay off your debt since you owe money to someone (instead of receiving the money from your
investment), which one do you like better?
a. #1, #1
b. #1, #2
c. #2, #1
d. #2,#2
e. They are all equivalent
b.
26. Which of the following 10year annuities has the largest PV assuming the interest rate is the same for all of them?
a. An annuity due that pays $500 semiannually
b. An ordinary annuity that pays $500 semiannually
c. An annuity due that pays $1,000 annually
d. An ordinary annuity that pays $1,000 annually
e. All of the above has the same PV
c. PV of an ordinary annuity is less than the annuity due. Also, if you are supposed to receive same amount of
payments, semiannual PV will be less than the annual PV because you receive the second half payment of the year
later.
27. You have 2 options to buy a membership. One is to pay $5,000 upfront today and the other one is to pay $500 each
year starting today. If the prevailing discount rate is 8%, how many years do you remain as a member before the $500
annual payment becomes more expensive than the onetime membership?
Set it BGN, then I=8, PV=5000, PMT=500 => N=17.54, 18 after rounding. Alternatively, you can take a difference
between the two payment ($4,500), then I=8%, PV=4500, PMT=500 => N=16.54. Since your membership last for one
more year after the current membership fee is paid, your membership ends in 17.54 years.
28. Jennifer can make a 100,000 down payment to buy a house. The house is $380,000 and she was offered 30year
mortgage and 15year mortgage at a market rate of 12%. How much more interest would Jennifer pay if she took out a
30year mortgage instead 15year mortgage?
For 30 years: N=30*12=360, I=1%, PV= (380,000100,000) => PMT=2,880.12
INT = (2,880.12*360) 280,000 = 756,843.20
For 15 years: N=15*12=180, I=1%, PV= (380,000100,000) => PMT=3,360.47
INT = (3,360.47*180) 280,000 = 324,884.60
Therefore, the difference in the interests is 756,843.20  324,884.60 = 431,958.60
29. Given an interest rate and the number of periods being greater than zero, which statements are correct?
I. Present value interest factors are less than 1.0
II. Future value interest factors are less than 1.0
III. Present value interest factors are greater than future value interest factors
IV. Future value interest factors grow as t grows, provided r is held constant
a. I only
b. I and III
c. I and IV
d. II and III
e. III and IV
c. PV is a discounting process, so PVIF is less than 1. If r is constant, FVIF increases as t goes up. FVIF is greater than
1. Therefore PVIF is less than FVIF
30. PVIFA(10%, 1)?
1/(1.1)= 0.909
31. You want to buy a $15,000 car. If you borrow money from the dealer, they are willing to give you a 1 year loan and
you need to make a single payment one year from today at zero interest. If you borrow money from a bank for the same
one year period and make a cash payment to the dealer right now (using the money you borrow from the bank), you can
enjoy a $1,000 discount from a dealer. The bank interest rate is 6% and you need to make a single payment one year
from today to pay off the debt. Which alternative do you like better. What is the difference between the future
payments of these two choices?
You only need to borrow $14,000 from the bank. 14,000 * (1.06) = $14,840. It is better off to borrow from the bank.
32. How long does it take to triple your investment at 6% per period?
I/y=6, PV=1, FV=3 => N=18.85, 18.9 years
33. Vince won the lottery and agreed to receive the equal Jackpot amount for 20 years semiannually starting six months
from today. The jackpot is $20 million and annual interest rate is 2%. Vince thought that the present value would show
how much he receives actually. How much did Vince actually win?
N=20*2=40, I=2/2=1%, PMT=20,000,000/40 => PV=$16,581.52
34. Jennifer plans to buy a dream home at $300,000. Right now, she only has enough to make a 20% down payment.
She was offered a 30year mortgage at 6% interest rate. What is Jennifers monthly mortgage payment?
N=30*12=360, I=6/12=0.5%, PV= (300,000*0.8) => PMT=1,438.92
35. You are offered to be paid $3,000 at the end of each month forever. How much this would be worth at an interest
rate of 18%?
PV of perpetuity = PMT/i = $3,000/(0.18/12) = $200,000
36. What is the relationship between PVIFA(r%, N) and PVIF(r%, N)?
a. PVIFA is greater than or equal to PVIF
b. PVIF is a sum of PVIFA from n=1 to n=N
c. PVIF is an inverse of PVIFA
d. PVIF is used for an annuity
e. None of the above
a. PVIFA is a sum of present values of payments.
37. You want to buy a trailer house worth $25,000 today, 3 years later. It is expected that the price of this house will go
up at 5% each year for the next 3 years. How much do you need to save each month for the next 3 years, starting 30
days from today to be able to buy this dream home 3 years later if you earn 12% APR on your savings?
Projected price of the trailer house 3 years later = 25,000*(1.05)^3=$28,940.63 (also N=3, I=5, PV=25,000 =>
FV=28,940.63), N=3*12, I=12/12, FV=28,840.63 => PMT = 671.84, Therefore $672
38. How long approximately does it take to double your investment at 6% APR, if you earn interest every six months?
The rule of 72, 72/interest rate per period=# of periods to double your money: 72/12% = 6 periods. I can switch interest
rates and # of periods. So, 72/3 = 24 months => 12 years
39. Susie Orman argues that you can have more money by saving $100 each month (starting at the end of this month
for 12 deposits) instead of saving $1,200 at the end of each year. To check whether that is true, you are going to
compare saving $100 every month for a year visvis $1,200 at the end of the year. How much extra will you have by
saving less, but more frequently? Use 6% interest rate.
N=12, I/y=0.5, PMT=100, FV=1233.56. Therefore, 1233.561200=$33.56
40. You plan to analyze the value of a potential investment by calculating the sum of the present values of its expected
cash flows. Which of the following would lower the calculated value of the investment?
a. The cash flows are in the form of a deferred annuity, and they total to $100,000. You learn that the annuity lasts for
only 5 rather than 10 years, hence that each payment is for $20,000 rather than for $10,000.
b. The discount rate increases.
c. The riskiness of the investments cash flows decreases.
d. The total amount of cash flows remains the same, but more of the cash flows are received in the earlier years and less
are received in the later years.
e. The discount rate decreases.
b
41. Which of the following statements is CORRECT?
a. The cash flows for an ordinary (or deferred) annuity all occur at the beginning of the periods.
b. If a series of unequal cash flows occurs at regular intervals, such as once a year, then the series is by definition an
annuity.
c. The cash flows for an annuity due must all occur at the beginning of the periods.
d. The cash flows for an annuity may vary from period to period, but they must occur at regular intervals, such as once
a year or once a month.
e. If some cash flows occur at the beginning of the periods while others occur at the ends, then we have what the
textbook defines as a variable annuity.
c
42. Your uncle is about to retire, and he wants to buy an annuity that will provide him with $75,000 of income a year
for 20 years, with the first payment coming immediately. The going rate on such annuities is 5.25%. How much
would it cost him to buy the annuity today?
BEGIN Mode, N 20, I/YR 5.25%, PMT $75,000, FV
$0.00 => PV $963,213
44. Suppose you inherited $275,000 and invested it at 8.25% per year. How much could you withdraw at the end of
each of the next 20 years?
N 20, I/Y 8.25%, PV $275,000, => PMT $28,532
45. Your bank offers to lend you $100,000 at an 8.5% annual interest rate to start your new business. The terms require
you to amortize the loan with 10 equal endofyear payments. How much interest would you be paying in Year 2?
PMT $15,241 Found with a calculator or Excel.
Amortization schedule (first 2 years)
Year
Beg. Balance
Payment
Interest
Principal
End. Balance
1
100,000
15,241
8,500
6,741
93,259
2
93,259
15,241
7,927
7,314
85,945
Chapter 7. Bonds and Their Valuation
1. Consider a 10 year semiannual coupon paying bond with a face value=$1,000 and a coupon rate=8%. What is the
PV of the bond at 8% discount rate? If the market price of the bond is $1,050, would you buy the bond?
You can use a financial calculator with input values, 40 PMT, 20 N, 4 i/y, 1000 FV, CPT PV=1000. Since coupon
rate = discount rate, you already know that PV=Face Value=1000. Since the price > PV, you do not want to buy
(=invest).
2. A taxfree muni yields 7.5% and the beforetax equivalent yield of a corporate bond is 10%, what is your tax
bracket?
10% * (1t) = 7.5%. Solve the equation for x or try all different choices
3. Which indenture provision may affect the price of the bond differently?
a. convertibility b. sinking fund c. call d. restrictions on dividends e. collateral
c. Investors do not like a call provision => they want to pay less or expect a higher return. What about other
indenture provisions?
4. A 10 year discount bond with a face value $1,000 is now sold for $800. What is the PV of the bond at the discount
rate of 6%? Do you want to buy the bond?
What is a discount bond? Using a financial calculator, 1000 FV, 6 i/y, 10 N, (0 PMT), CPT PV=558.36. The closest
one is $560. Since PV<the price, you do not want to buy this bond.
5. Which stakeholder has the lowest priority?
a. suppliers b. secured bonds c. junior bonds d. senior debenture e. unsecured bonds
c. If you look at an income statement, you have an idea who may have a higher priority. CGS=> supplier, Operating
expenses => employees, contractors, etc, interest expenses => creditors like debt security holders, taxes =>
government, etc. Among creditors or debt security holders, those who have secured debt or have a collateral
backing may feel secure. Those bonds with no collateral backing is called debenture and there are two types, one
is senior and the other is a junior bond. The junior bond holders have the lowest priority other than common stock
share holders as they are residual claimants.
6. Consider a 10 year semiannual coupon paying bond with a face value=$1,000 and a coupon rate=8%. What is the
PV of the bond at 8% discount rate? If the market price of the bond is $950, would you buy the bond?
Because coupon rate = YTM, the value of the bond today is same as the face value. If PV of the bond is $1,000 and
the current market price is $950, it is undervalued in the market. Therefore, buy. Or check PV with: N=20, I/Y=4,
PMT=40, FV=1,000 => PV=?
7. A taxfree municipal bond (muni) yields 7%. What is the beforetax equivalent yield of a corporate bond when you
are in a 30% tax bracket?
7%/(10.3) = 10%
8. You are considering two investment opportunities with $900. One is to invest in a two year CD at 10% per annum.
The other is to invest in a two year annual coupon paying bond with a coupon rate=8% and FV=$1,000. What is the
YTM of the bond? Are you going to invest in the CD or not?
N=2, PV=900, PMT=80, FV=1000 => I/Y=14.08%. YTM is higher than CD yield, so do not invest in the CD
9. What is the PV of a bond with the following information: FV=$1000, Annual coupon rate 8%, Semiannual coupon
payments, 3 year maturity, discount rate = 10%, the price of the bond = $1000. Based on the PV, do you want to
invest in the bond or not?
N=6, I/Y=5, PMT=40, FV=1000 => PV=949.24. Intrinsic value is less than the market price, which means it is
overpriced. Therefore No.
10. You purchased a 10 year zero coupon bond with a face value $1,000 for $600 about 3 years ago. It sells for $800
now with 7 years remaining until its maturity (3 years later since the original purchase of the bond). What is the
current YTM for the bond? (Hint, you need to have a timeline from now on). You now consider selling the bond and
having the proceeds invested in a CD from Bank of America, offering 5%. Do you want to keep the bond or switch
to the CD?
N=7, PV=800, PMT=0, FV=1,000 => I/Y=3.24%. It is less than 5%, therefore switch
11. What are the YTM of a bond with the following information: FV=$1000, Annual coupon rate 10%, semiannual
coupon payments, 5 year maturity, required rate of return = 8%, the price of the bond = $1000. Based on the YTM,
do you want to invest in the bond or not?
Face value = price, so YTM = coupon rate = 10%. Or N=10, PV=1000 PMT=50, FV=1000 => I/Y=10. Required
return < expected return, therefore invest.
12. AT&T has two $1,000 face value bonds with an 8% (APR) semiannual coupon. One issue matures in 5 years and
the other matures in 10 years. Both bonds have the same PV at $1,000 at an 8% discount rate as the PV=Face Value
when the coupon rate=discount rate. We also know that the PVs of both bonds would be negatively related to the
discount rate. The PV of a 5 year bond (shortterm bond), however, would be {greater, less} than that of a 10 year
(longerterm) bond when the discount rate decreases as its (5 year bond s) PV does change {more, less} than that of
10 year bond. The conclusion: A longerterm bond is more sensitive to changes in discount interest rate. (Hint: you
dont need to do any calculation. However, if you want, you can do the calculation with a new hypothetical
discount rate).
a. Greater, More b. Greater, Less c. More, Less d. Less, Less e. Indifferent
d. Because long term bond is more sensitive to the yield change, decrease in the yield will have greater PV for the
longterm bond, which means longterm bonds value changes more than shortterm bond.
13. You have a 7 year time to maturity semiannual coupon paying bond with an 8% coupon, FV=$1,000. Calculate the
bonds YTM if its current market price is $875. Instead of keeping it until it matures, you are holding it for 3 years
(after receiving 6 coupon payments), and then sell it for $975 (instead of $1,000 FV). What is the first 3 year
holding period yield (Hint: draw a timeline, especially for the second part)?
N=14, PV=875 PMT=40, FV=1,000 => I/Y=10.58%,
N=6, PV=875, PMT=40, FV=975 => I/Y=12.40%
14. What is the PV of a bond with the following information: FV=$1000, Annual coupon rate 8%, Semiannual coupon
payments, 2 year maturity, discount rate = 10%, the price of the bond = $1000.
N=4, I/Y=5, PMT=40, FV=1000 => PV=964.54
15. If beforetax YTM of a bond is 10%, what would be the aftertax cost of debt if the company is in a 35% tax
bracket?
10% * (10.35) = 6.5%
16. If an issuer can retire the bond prior to its maturity, what kind of indenture provision does the bond have? Does the
return on this bond tend to be higher or lower than a bond without such a provision?
a. convertibility higher b. convertibility lower c. call higher
d. sinking fund lower e. sinking fund higher
c. Callable bond refers to the bonds which an issuer can purchase the bond back when interest rates fall. Because
the buyer of the callable bond cant enjoy the price appreciation when interest rates rise, the issuer should
provide incentives for the buyer. Therefore callable bonds usually have higher yield than noncallable bonds
17. A 10 year discount bond with a face value $1,000 is now sold for $800. What is the PV of the bond at the discount
rate of 5%?
A zero coupon bond is also called a deepdiscount bond. N=10, I/Y=5, PMT=0, FV=1000 => PV=613.91
18. What is the debenture?
a. FRN b. Euro$ c. secured bonds
e.
d. junk bonds
e. unsecured bond
19. A muni is offering 8% interest. What should the return on a corporate bond be so that both the muni and the
corporate bond are equally competitive when you are in a 30% tax bracket?
Tax equivalent yield = taxfree yield / (1tax bracket rate) = 8%/(10.3) = 11.43%
20. What is the YTM (=return on the bond) of a bond with the following information: FV=$1000, Annual coupon rate
10%, Semiannual coupon payments, 1 year maturity, required rate of return = 8%, the price of the bond = $1000.
Because price = face value, annual coupon rate = YTM = 10%. Or can check by N=2, PV=1000, PMT=50,
FV=1000
21. White & Decker Co. has 7% semiannual coupon paying bonds outstanding maturing in 20 years. The bonds par
value is $1,000 and expected to earn 5.89%. What is the expected capital gains yield for White & Decker Co.s bonds?
a. Between 6% and 7% b. Greater than 7% c. Between 0% and 5% d. Between 5% and 6% e. Less than 0%
e. Since the coupon rate is greater than YTM, White & Decker, Co.s bonds sell at a premium (the current price is
greater than the face value). So, expected capital gains yield will be negative (capital gains between your current price
and the price you are selling it for (this time, it is the Face Value)).
22. Limitless Energy, Inc. is considering to issue 8.8% semiannual coupon bonds with 15 years to maturity. The bonds
are selling at $965.75 with a par value of $1,000. What rate of return are investors expected to earn?
YTM calculation. N=15*2=30, PV= 965.75, PMT=(0.088*1000)/2, FV=1000 => I=4.62, 4.62*2=9.24%
23. Queens of Leon Corp. has 9.8% semiannual coupon bonds outstanding with a face value of $1,000. It will mature
in 20 years and current YTM is 10.24%. However, Queens of Leon Corp.s bonds have a call provision in 5 years at a
call price of $1,020. The Federal Reserve is likely to lower the benchmark rate. What is the rate of return investors are
likely to earn on Queens of Leon Corp.s bond?
N=20*2=40, I=10.24/2=5.12%, PMT=(0.098*1000)/2, FV=1,000=> PV= 962.86
N=5*2, PV= 962.86, PMT=(0.098*1000)/2, FV=1,020=> I=5.55%, 5.55*2=11.10%
24. Consider a 10 year semiannual coupon paying bond with a face value=$1,000 and a coupon rate=8%. What is the
PV of the bond at 8% discount rate? If the market price of the bond is $1,050, would you buy the bond?
Because coupon rate = YTM, the PV or the current price is $1,000. Comparing to the market price of $1,050, the
market price is overvalued. Therefore, dont buy.
25. York, Inc. issued 6%, semiannual coupon bonds outstanding with 10 years to maturity. The bonds par value is
$1,000 and expected to earn 8.42%. What is the current yield for York, Inc?
N=10*2=20, I=8.42/2=4.21%, PMT=(0.06*1000)/2, FV=1000 => PV=838.57, Current yield = Annual coupon
payment/current price = 60/838.57 = 7.16%
26. Birdland, Inc. has 8.8% semiannual coupon bonds with 15 years to maturity. The bonds are selling at $965.75 with
a face value of $1,000 and a call price of $1,020. The call provision specifies the bonds may be called in 5 years. What
is the rate of return investors expected to earn if the Federal Reserve is expected to lower the benchmark rate?
YTC calculation. N=5*2, PV= 965.75, PMT=(0.088*1000)/2, FV=1,020=> I=5.00, 5.00*2=10.01%
27. A 15year bond with a face value of $1,000 currently sells for $850. Which of the following statements is
CORRECT?
a. The bonds coupon rate exceeds its current yield.
b. The bonds current yield exceeds its yield to maturity.
c. The bonds yield to maturity is greater than its coupon rate.
d. The bonds current yield is equal to its coupon rate.
e. If the yield to maturity stays constant until the bond matures, the bonds price will remain at $850.
c
28. A 10year Treasury bond has an 8% coupon, and an 8year Treasury bond has a 10% coupon. Neither is callable,
and both have the same yield to maturity. If the yield to maturity of both bonds increases by the same amount, which
of the following statements would be CORRECT?
a. The prices of both bonds will decrease by the same amount.
b. Both bonds would decline in price, but the 10year bond would have the greater percentage decline in price.
c. The prices of both bonds would increase by the same amount.
d. One bond's price would increase, while the other bonds price would decrease.
e. The prices of the two bonds would remain constant.
b W e can tell by inspection that c, d, and e are all incorrect. A is also incorrect because the 10year bond will
fall more due to its longer maturity and lower coupon. That leaves Answer b as the only possibly correct
statement. Recognize that longerterm bonds, and ones where payments come late (like low coupon bonds) are
m ost sensitive to changes in interest rates. Thus, the 10year, 8% coupon bond should be more sensitive to a
decline in rates. You could also do some calculations to confirm that b is correct.
29. If its yield to maturity declined by 1%, which of the following bonds would have the largest percentage increase in
value?
a. A 1year zero coupon bond
b. A 1year bond with an 8% coupon
c. A 10year bond with an 8% coupon
d. A 10year bond with a 12% coupon
e. A 10year zero coupon bond.
e A bond with longer maturity and lower coupon rate is more sensitive to changes in the interest rate (here, YTM)
30. Towson Inc.'s bonds currently sell for $1,250. They pay a $90 annual coupon, have a 25year maturity, and a
$1,000 par value, but they can be called in 5 years at $1,050. Assume that no costs other than the call premium
would be incurred to call and refund the bonds, and also assume that the yield curve is horizontal, with rates
expected to remain at current levels on into the future. What is the difference between this bond's YTM and its
YTC? (Subtract the YTC from the YTM; it is possible to get a negative answer.)
If held to maturity:
If called in 5 years:
N = Maturity
25
N = Call
5
Price = PV
PMT
FV = Par
I/YR = YTM
Difference: YTM YTC = 2.62%
$1,250
$90
$1,000
6.88%
PV
PMT
FV = Call Price
I/YR = YTC
$1,250
$90
$1,050
4.26%
31. A 25year, $1,000 par value bond has an 8.5% annual payment coupon. The bond currently sells for $925. If the
yield to maturity remains at its current rate, what will the price be 5 years from now?
First find the YTM at this time, then use the YTM with the other data to find the bond's price 5 years hence.
PMT $85, FV $1,000, I/YR 9.28% => PV$930.11
32. Towson Co's bonds have a 15year maturity, a 7.25% semiannual coupon, and a par value of $1,000. The going
interest rate (rd) is 6.20%, based on semiannual compounding. What is the bonds price?
FV $1,000, N 30, I/YR 3.10%, PMT $36.25 => PV $1,101.58
33. (extra) WSJ quotation of a Treasury security (semiannual coupon paying) is as follows:
Rate 8 7/8 Maturity Nov 18 Bid 124:04 Asked 124:10 Chg 14 Ask Yld 6.52. Provide your explanation.
(Explanations: coupon rate, maturity date Nov 2018 (10 years from today), you get paid if you sell at 124+4/32% or
124.125% of the FV, you need to pay if you buy at 124+10/32%. Ignore the rest).
What is the PV of the bond at 10% discount rate? What is the YTM of the bond evaluated at the asked price? Are
you going to buy the bond? Why or why not? This is not a multiple choice question.
a. PV: N=20, I/Y=5, PMT=44.375, FV=1000 => PV=929.90 (Coupon rate: 8 7/8 = 8.875%)
b. YTM: N=20, PV=1243.125, PMT=44.375, FV=1000 => I/Y=5.66% price (Asked quote: 124:10 = (124+10/32)%
of par value => 124.3125% * 1000 = 1234.125)
c. Yes, comparing the calculated YTM (5.66%) to the Yield (6.52%), specified yield is better than the required
return. Therefore, it is good to invest.
Chapter 8. Risk and Rates of Return
1. What is the Expected Return and Standard Deviation of the probability distribution given below?
Goo
State
Avg Bad
d
Possible Return 10%
10% 10%
Probability
30%
50% 20%
You need to know how to calculate expeceted return and standard deviation. In this particular question, the
expected return should be 10% as you get 10% for all states. There is no risk as it is certain that you will get 10%
for not matter what.
2. If you expect (=demand=require) 10% return on security A and 12% return on security B, what causes such a
disparity?
a. real risk free rate b. expected inflation rate c. risk premium d. A & B e. B& C
c.
3. What is the Expected Return and Standard Deviation of the probability distribution given below?
State Poss Return Probablity
Good
10%
50%
Avg
10%
30%
Bad
10%
20%
Expected return is the weighted average of the possible return based on the probability. Therefore, the expected
return = (0.1*0.5) + (0.1*0.3) (0.1*0.2) = 6%
Standard deviation {(6%10%)^2*0.5)+(6%10%)^2*0.3)+(6%(10%)^2*0.2)}^(1/2) = 8%
4. Determine the expected rates of return for Security ABC, given the following probability distribution.
Possible Return 10%
15%
Probability
40%
60%
Expected return is the weighted average of the possible return based on the probability. Therefore, the expected
return = (0.1 * 0.4) + (0.15 * 0.6) = 13%
5. Given that a (nominal) risk free rate is 2% and the market average return is expected to be 5%, what is the market
risk premium (=slope of the SML)? Determine the required rate of return for a security with a beta of 1.5.
R or K = Rrf + beta*(Rm Rrf) = 2% + 1.5*(5% 2%) = 6.5%. (Rm Rrf) is market risk premium
6. Given that a (nominal) risk free rate is 2% and the market average return is expected to be 5%, determine the
required rate of return for a security with a beta of 1.5.
R or K = Rrf + beta*(Rm Rrf) = 2% + 1.5*(5%  2%) = 6.5%
7. If US T Bill has 4% return, what is the risk premium of an investment which has 7% required rate of return?
Risk premium on a security other than US Treasury securities is called spread. Spread reflects risk premiums that a
security bears. Therefore 7%  4% = 3%
8. If a security has a beta greater than 1.0, we call it an aggressive security. To show that an aggressive security tends to
have required return greater than the market average return, I use the CAPM equation with the risk free rate 3%,
market average return 5%, the securitys required return 6%. Note that 6% > 5%. What is the securitys beta?
From CAPM, R or K = Rrf + beta*(Rm Rrf) => 6% = 3% + beta*(5%  3%) => 3% = 2%*beta => beta =1.5
9 10
Boom
Average
Recession
Probability
35%
40%
25%
Ra(State=?)
0.30
0.08
0.15
Rb(S=?)
0.06
0.06
0.05
9. What is the expected return on Security a?
E(Ra) = (0.35 * 30%) + (0.40 * 8%)  (0.25 * 15%) = 9.95%
10. What is the standard deviation of Security b, if its expected return is 3.25%?
((6 3.25)^2*0.35 + (6 3.25)^2*0.40 + (5 3.25)^2*0.25)^0.5 = 4.76% Therefore, 4.8%
11. What is the correlation coefficient of two security returns if the expected returns of two securities are 4% and 5%
respectively and the standard deviations of the two securities are 2% and 3% respectively, while the covariance is 5
(%2)?
CORR(Ra, Rb) = Cov(Ra, Rb)/{SD(Ra)*SD(Rb)} = 5/(2*3) = 0.83. Note that the correlation coefficient has a value
between 1 and +1.
1213
Boom
Average
Recession
Probability
0.35
0.40
0.25
Ra(State=?)
0.30
0.10
0.15
Rb(S=?)
0.05
0.05
0.05
12. What is the expected return on Security a?
E(Ra) = (0.35 * 30%) + (0.40 * 10%)  (0.25 * 15%) = 10.75%
13. What is the correlation coefficient of two security returns if the expected returns of two securities are 2% and 3%
respectively and the standard deviations of the two securities are 4% and 5% respectively, while the covariance is 10
(%2)?
a. CORR(Ra, Rb) = Cov(Ra, Rb)/{SD(Ra)*SD(Rb)} = 10/(4*5) = 0.5
14. Which of the following statements best describes what you should expect if you randomly select stocks and add
them to your portfolio?
a. Adding more such stocks will reduce the portfolio's unsystematic, or diversifiable, risk.
b. Adding more such stocks will increase the portfolio's expected rate of return.
c. Adding more such stocks will reduce the portfolio's beta coefficient and thus its systematic risk.
d. Adding more such stocks will have no effect on the portfolio's risk.
e. Adding more such stocks will reduce the portfolio's market risk but not its unsystematic risk.
a
15. Which of the following statements is CORRECT? (Assume that the riskfree rate is a constant.)
a. If the market risk premium increases by 1%, then the required return will increase for stocks that have a beta greater
than 1.0, but it will decrease for stocks that have a beta less than 1.0.
b. The effect of a change in the market risk premium depends on the slope of the yield curve.
c. If the market risk premium increases by 1%, then the required return on all stocks will rise by 1%.
d. If the market risk premium increases by 1%, then the required return will increase by 1% for a stock that has a beta
of 1.0.
e. The effect of a change in the market risk premium depends on the level of the riskfree rate.
d
16. During the coming year, the market risk premium (rM rRF), is expected to fall, while the riskfree rate, r RF, is
expected to remain the same. Given this forecast, which of the following statements is CORRECT?
a. The required return will increase for stocks with a beta less than 1.0 and will decrease for stocks with a beta greater
than 1.0.
b. The required return on all stocks will remain unchanged.
c. The required return will fall for all stocks, but it will fall more for stocks with higher betas.
d. The required return for all stocks will fall by the same amount.
e. The required return will fall for all stocks, but it will fall less for stocks with higher betas.
c
17. Roenfeld Corp believes the following probability distribution exists for its stock. What is the coefficient of
variation on the company's stock?
Probability
State of
of State
the Economy
Return
Boom
0.45
Normal
0.50
Recession
0.05
Expected return =19.00%, = 5.83%
Coefficient of variation = /Expected return = 0.3069
Stock's
Possible Return
25%
15%
5%
18. Jill Angel holds a $200,000 portfolio consisting of the following stocks. The portfolio's beta is 0.875.
Stock
Investment
Beta
A
$ 50,000
0.50
B
50,000
0.80
C
50,000
1.00
D
50,000
1.20
Total
$200,000
If Jill replaces Stock A with another stock, E, which has a beta of 1.50, what will the portfolio's new beta be?
Original Portfolio
New Portfolio
StockInvestment Percentage
Beta
Product
Percentage
Beta
Product
A
$50,000
25.00%
0.50
0.125
B
$50,000
25.00%
0.80
0.200
25.00%
0.80
0.200
C
$50,000
25.00%
1.00
0.250
25.00%
1.00
0.250
D
$50,000
25.00%
1.20
0.300
25.00%
1.20
0.300
E
25.00%
1.50
0.375
Total $200,000 100.00%
0.875
New Portfolio Beta =
1.125
19. Towson Co's stock had a required return of 11.75% last year, when the riskfree rate was 5.50% and the market risk
premium was 4.75%. Then an increase in investor risk aversion caused the market risk premium to rise by 2%. The
riskfree rate and the firm's beta remain unchanged. What is the company's new required rate of return?
Old risk premium 4.75%, Old required return 11.75%
=> b = based on the information above and CAPM equation, you can backfigure the beta b=1.32
Now, the new market risk premium 6.75%
New required return based on the CAPM= rRF + b(RPM) =14.38%
20. ABC has a beta of 1.3, while DEF has a beta of .70. What is the beta of a portfolio which is comprised of the two
securities with the wealth invested evenly between them (Hint: portfolios beta is a portfolio weighted average of
individual stock betas). If the nominal risk free rate is 3% and the market average return is expected to be 5%, what
is the corresponding required return for the portfolio?
Portfolio beta = (1.3*0.5) + (0.7 * 0.5) = 1. Required Return = 3% + 1* (5%  3%) = 5%
21. If you are allowed to form a welldiversified portfolio, some part of total risk measured by standard deviation for
each security does really cause us no concern in the sense that the kind of individual security return volatility may
not produce any volatility in the portfolio return. What is the name of such an irrelevant risk (hardly a risk at all)?
a. systematic risk
b. total risk
c. nondiversifiable risk
d. beta risk e. idiosyncratic risk
e.
22. You are considering to invest in two securities, A and B. Note that the Prob(Good)=60%, Prob(Bad)=40%. You
have $40,000 out of $100,000, total amount of money available, invested in security A and the rest invested in B.
Possible A Possible B Possible
Ret
Ret
Port Ret
Good
10.0%
15.0%
?%
Bad
5.0%
10.0%
?%
E(R)
4.0%
5.0%
What is the possible portfolio return in each state (Good and Bad)?
Expected return is an Average return of (say, two) possible returns with probability being used as weight. Portfolio
return is an Average return of (say, two) security returns with portfolio weight being used. What is the expected return
of a portfolio? It is an Average of Averages. There are two ways you can compute that. You can get the possible
portfolio return for each state. Then you can get the expected return of the portfolio. Alternatively, you can get the
expected return of each security first and get the portfolios expected return using the information provided below
employing each approach. Note that the Prob(Good)=60%, Prob(Bad)=40%, W a=40%, Wb=60%.
Good = (0.1*0.4) + (0.15*0.6) = 13%, Bad = (0.05*0.4) + (0.1*0.6) = 8%
23. If a security is overvalued, it implies that either the PV is (greater, less) than the market price. If a security is
undervalued, you are expecting (=> since the future is uncertain, we can just expect on average) to receive ROI
(higher, less) than what you are seeking (=requiring= demanding=asking for) at minimum. Eventually, the price
would change as the demand changes and the price and ROI will get respectively close to the PV and the required
rate of return.
a. Greater, Greater b. Greater, Less c. Less, Greater d. Less, Less e. Indifferent
c.
Chapter 9. Stocks and Their Valuation
1. Given D1 = $1.00 and K=10%, what is the value of the stock at 8% growth rate? If the current price of the stock is
$50, would you buy it?
PV=D1/(kg)=1.00/(0.10  0.08) = $50. Since the price=PV, you are indifferent.
2. What is the major problem with DJIA compared to S&P 500 index, other than the smaller number of stocks
included?
a. average stock prices b. firm sizes c. annual sales d. funding needs e. none
a. See lecture notes and the textbook.
3. Given Do = $1.00 and K=10%, what is the value of the stock at 8% growth rate? If the current price of the stock is
$50, would you buy it?
Constant growth model. V0=D1/(kg)=(1*1.08)/(0.10.08)=$54. It is undervalued in the market, so buy!
4. Sorenson Corp.s expected yearend dividend is D1 = $1.60, its required return is rs = 11.00%, its dividend yield is
6.00%, and its growth rate is expected to be constant in the future. What is Sorenson's expected stock price in 7
years, i.e., what is P7 ?
Dividend yield = D1/P0 = 6.0% =>Find the growth rate: g = rs yield = 5.0% => P0 = D1/(rs g) = $26.67
P7 = P0*(1+g)7= $37.52
5. Given D1 = $1.08 and the dividends are expected to growth at 8%, what is the ROI(=yield) for this stock if the
current price is $60? If the required rate of return is 10%, would you buy it?
k = D1/P0 + g = 1.08/60 + 0.08 = 9.8%. Expected return (ROI) is less than the required return. Therefore, dont.
6. For a preferred stock with the dividend amount of $2.00 each quarter, what is the PV of it with an annual discount
rate of 8%? If the price of the preferred stock is $80, what is the yield (ROI, APR) of this security?
PV = D/k = 8/0.08 = $100. ROI = (80+8)/80 = 10%
7. What is ROI (yield)?
a. discount rate which is given, b. opportunity cost, c. required rate of return,
d. the (discount) rate which makes the PV of the future benefits equal to the market price,
d.
e. interest rate
8. Other than the increased number of companies included, what else is taken into consideration for S&P 500 instead of
DJIA?
a. stock prices b. firm sizes c. annual sales d. funding needs e. none
b.
9. Differentiate between SEC registration and the exchange listing requirements.
a. stock vs. bonds b. longterm vs shortterm c. formality
d. minimal government requirements vs additional e. secondary market
d.
10. Which one is not an advantage of a preferred stock from the issuers perspective?
a. no collaterals required b. better debt management c. no ownership dilution d. smaller risk
d.
e. none
11. Goode Inc.'s stock has a required rate of return of 11.50%, and it sells for $25.00 per share. Goode's dividend is
expected to grow at a constant rate of 7.00%. What was the last dividend, D0?
P0 = D1/(rs g), so D1 = P0(rs g) = $1.1250 => Last dividend = D0 = D1/(1 + g) = $1.05
12. For a preferred stock with the dividend amount of $2.00 every quarter, if the price of the preferred stock is $200,
what is the yield (ROI, APR) of this security?
8/200 = 4%
13. For a common stock with the current dividend amount of = $.70 (Do = .70), what is the (P)V of it with an annual
discount rate of 12% and the dividend is expected to grow at the rate of 10% per annum forever?
V0 = D1 / (kg) = (0.70* 1.1)/(0.120.10) = 38.5
14. How is IPO (initial public offering) different from seasoned public offering?
a. New shares issued
b. Previously privately held company
d. Block trading
e. Cost of capital
b.
c. Large corporations
15. Stock X has the following data. Assuming the stock market is efficient and the stock is in equilibrium, which of the
following statements is CORRECT?
Expected dividend, D1 =$3.00
Current Price, P0 =$50
Expected constant growth rate=6.0%
a. The stocks required return is 10%.
b. The stocks expected dividend yield and growth rate are equal.
c. The stocks expected dividend yield is 5%.
d. The stocks expected capital gains yield is 5%.
e. The stocks expected price 10 years from now is $100.00.
b D1=$3.00, D1/P0=6.0%, P0=$50.00, rX=12.0% =>g=6.0%
16. Which of the following statements is NOT CORRECT?
a. The corporate valuation model can be used both for companies that pay dividends and those that do not pay
dividends.
b. The corporate valuation model discounts free cash flows by the required return on equity.
c. The corporate valuation model can be used to find the value of a division.
d. An important step in applying the corporate valuation model is forecasting the firm's pro forma financial statements.
e. Free cash flows are assumed to grow at a constant rate beyond a specified date in order to find the horizon, or
terminal, value.
b
17. Which of the following statements is CORRECT?
a. Preferred stockholders have a priority over bondholders in the event of bankruptcy to the income, but not to the
proceeds in a liquidation.
b. The preferred stock of a given firm is generally less risky to investors than the same firms common stock.
c. Corporations cannot buy the preferred stocks of other corporations.
d. Preferred dividends are not generally cumulative.
e. A big advantage of preferred stock is that dividends on preferred stocks are tax deductible by the issuing corporation.
b
18. Molen Inc. has an outstanding issue of perpetual preferred stock with an annual dividend of $7.50 per share. If the
required return on this preferred stock is 6.5%, at what price should the stock sell?
Preferred price = DP/rP = $115.38
19. The Isberg Company just paid a dividend of $0.75 per share, and that dividend is expected to grow at a constant
rate of 5.50% per year in the future. The company's beta is 1.15, the market risk premium is 5.00%, and the riskfree
rate is 4.00%. What is the company's current stock price, P 0?
D0=$0.75, b=1.15, rRF=4.0%, RPM=5.0%, g=5.5% =>D1 = D0(1 + g) = $0.7913
rs = rRF + b(RPM) = 9.75% => P0 = D1/(rs g)=$18.62
Chapter 10. The Cost of Capital (Funding, Financing)
1. Capital structure refers to
a. the types of projects a firm invests in.
b. the mixture of shortterm and longterm debt.
c. the amount of debt and equity a firm has d. shortterm assets and shortterm liabilities.
e. the size, timing, and risk
c.
2. What is the % of total financing by equity if the total $12m funding includes $7.5m from debt?
Component of capital: (LT)debt, PFD stocks, and Common Equity. Therefore (127.5)/12 = 37.5%
3. The amount of retained earnings limit the size of internal equity financing. If the amount of retained earnings is
$25m, where do you have a switch from the internal to external equity financing in terms of the size of the total
funding when the equity financing accounts for 25% of the total funding and the remaining is from debt?
25m/.25=$100m
4. Longterm debt of Topstone Industries is currently selling for $1,045. Its face value is $1,000. The issue matures in
10 years and pays an annual coupon of 8% of face. What is the beforetax cost of debt for Topstone if the company is
in 30% tax bracket?
Find YTM. N=10, PV=1045, PMT=80, FV=1000 => I/Y= 7.35%
5. Longterm debt of Topstone Industries is currently selling for $1,045 of its face value. The issue matures in 10 years
and pays an semiannual coupon of 8% of face. What is the aftertax cost of debt for Topstone if the company is in
30% tax bracket?
N=20, PV=1045, PMT=40, FV=1000 => I/Y=3.68*2=7.36%. Therefore aftertax cost of debt = 7.36%(10.3)=5.15%
6. The costs of financing from different sources are as follows:
IEF = 5%, EEF=6%, cost of debt before tax = 5%, tax rate=20%, the size of retained earnings=$30m. The capital
structure is: We=40% and Wd=60%. Determine the WAMCC before and after the break point.
5%*0.4 + 5%*(1.02)*0.6 = 4,4%, 6%*0.4 + 5%*(10.2)*0.6=4.8%
7. Which of the following statements is CORRECT?
a. When calculating the cost of debt, a company needs to adjust for taxes, because interest payments are deductible by
the paying corporation.
b. When calculating the cost of preferred stock, companies must adjust for taxes, because dividends paid on preferred
stock are deductible by the paying corporation.
c. Because of tax effects, an increase in the riskfree rate will have a greater effect on the aftertax cost of debt than on
the cost of common stock as measured by the CAPM.
d. If a companys beta increases, this will increase the cost of equity used to calculate the WACC, but only if the
company does not have enough retained earnings to take care of its equity financing and hence must issue new stock.
e. Higher flotation costs reduce investors' expected returns, and that leads to a reduction in a companys WACC.
a Statement a is true, because interest payments on debt are tax deductible. The other statements are false.
8. Which of the following statements is CORRECT?
a. A change in a companys target capital structure cannot affect its WACC.
b. WACC calculations should be based on the beforetax costs of all the individual capital components.
c. Flotation costs associated with issuing new common stock normally reduce the WACC.
d. If a companys tax rate increases, then, all else equal, its weighted average cost of capital will decline.
e. An increase in the riskfree rate will normally lower the marginal costs of both debt and equity financing.
d The cost of debt for WACC purposes = rd(1 T), so if T increases, then rd(1 T) declines.
9. For a company whose target capital structure calls for 50% debt and 50% common equity, which of the following
statements is CORRECT?
a. The interest rate used to calculate the WACC is the average aftertax cost of all the company's outstanding debt as
shown on its balance sheet.
b. The WACC is calculated on a beforetax basis.
c. The WACC exceeds the cost of equity.
d. The cost of equity is always equal to or greater than the cost of debt.
e. The cost of retained earnings typically exceeds the cost of new common stock.
d Equity is more risky than debt and hence investors require a higher return on equity. Also, interest on debt is
deductible, and this further reduces the cost of debt. The other statements are false.
10. Several years ago the Jakob Company sold a $1,000 par value, noncallable bond that now has 20 years to maturity
and a 7.00% annual coupon that is paid semiannually. The bond currently sells for $925, and the companys tax rate
is 40%. What is the component cost of debt for use in the WACC calculation?
N 40, PV $925.00, PMT $35, FV $1,000, I/Y 3.87% => beforetax cost of debt = 7.74%
=> Aftertax cost of debt (AT rd) for use in WACC = 4.65%
11. Assume that Kish Inc. hired you as a consultant to help estimate its cost of capital. You have obtained the
following data: D0 = $0.90; P0 = $27.50; and g = 7.00% (constant). Based on the DCF approach, what is the cost of
equity from retained earnings?
D1 = D0 (1 + g) = $0.963 => rs = D1/P0 + g = 10.50%
12. Weaver Chocolate Co. expects to earn $3.50 per share during the current year, its expected dividend payout ratio is
65%, its expected constant dividend growth rate is 6.0%, and its common stock currently sells for $32.50 per share.
New stock can be sold to the public at the current price, but a flotation cost of 5% would be incurred. What would
be the cost of equity from new common stock?
D1 = EPS Payout ratio = $2.275, re = D1/(P0 (1 F)) + g = 13.37%
13. Sorensen Systems Inc. is expected to pay a $2.50 dividend at year end (D 1 = $2.50), the dividend is expected to
grow at a constant rate of 5.50% a year, and the common stock currently sells for $52.50 a share. The beforetax
cost of debt is 7.50%, and the tax rate is 40%. The target capital structure consists of 45% debt and 55% common
equity. What is the companys WACC if all the equity used is from retained earnings?
rd(1 T) = 4.50%, rs = D1/P0 + g = 10.26%
= > WACC = wd(rd)(1 T) + wc(rs) = 7.67%
14. You were hired as a consultant to Quigley Company, whose target capital structure is 35% debt, 10% preferred, and
55% common equity. The interest rate on new debt is 6.50%, the yield on the preferred is 6.00%, the cost of retained
earnings is 11.25%, and the tax rate is 40%. The firm will not be issuing any new stock. What is Quigley's WACC?
Weights
rd
AT Costs
Debt
35%
6.50%
3.90%
Preferred
10%
6.00%
Common
55%
11.25%
WACC = 8.15%
15. Which one(s) is(are) an external financing and has the flotation cost?
a. Retained earnings
b. Bonds
c. Preferred stock
d. A&B e. B&C
e. Retained earnings is internal source of fund. Issuing bonds, preferred stocks, and common stocks are external
source of fund, which have the floatation cost.
Chapter 11.The Basics of Capital Budgeting
1. What would you do for capital budgeting if you have limited resources?
a. focus on the projects the firm has already invested in. b. reduce shortterm and longterm debt.
c. rank good looking projects and choose from the most profitable ones d. evaluate to determine good projects
e. determine the size, timing, and risk of a firm's future cash flows.
c.
2. Towson Inc. is considering a project that has the following cash flow and WACC data. What is the project's
MIRR? .
WACC: 12.25%
Year
Cash flows
Year
Cash flows
Compounded values
0
$850
1
$300
2
$320
3
$340
4
$360
0
$850
1
$300
$424.31
2
$320
$403.20
3
$340
$381.65
4
$360
$360.00
TV = FV Sum of all cash inflows at the terminal period: $1,569.16
MIRR can be found as a discount rate that equates PV of TV to the cost ($850), discounted back 4 years =>
MIRR = 16.56%
3. You have only three investment opportunities as follows: Project A with 5% return, B with 9% return, C with 8%
return. What should be the required rate of return when you consider Project C. Are you going to take C?
No, to accept C, required return (=opportunity cost, 9%) should be less than the expected return of C
4. Which of the following statements is CORRECT?
a. For a project to have more than one IRR, then both IRRs must be greater than the WACC.
b. If two projects are mutually exclusive, then they are likely to have multiple IRRs.
c. If a project is independent, then it cannot have multiple IRRs.
d. Multiple IRRs can only occur if the signs of the cash flows change more than once.
e. If a project has two IRRs, then the smaller one is the one that is most relevant, and it should be accepted and relied
upon.
d
4. What is the decision rule for IRR?
a. Accept a project when IRR > 0
b. Accept a project if at the IRR the NPV is positive
c. Reject any project if the IRR is below 10%
d. Accept a project if the IRR exceeds the firm's bank borrowing rate
e. Accept a project if the IRR exceeds the firm's required rate of return
e. IRR decision rule: accept when IRR > WAMCC
5. Which of the following statements is CORRECT?
a. The NPV method was once the favorite of academics and business executives, but today most authorities regard the
MIRR as being the best indicator of a projects profitability.
b. If the cost of capital declines, this lowers a projects NPV.
c. The NPV method is regarded by most academics as being the best indicator of a projects profitability, hence most
academics recommend that firms use only this one method.
d. A projects NPV depends on the total amount of cash flows the project produces, but because the cash flows are
discounted at the WACC, it does not matter if the cash flows occur early or late in the projects life.
e. The NPV and IRR methods may give different recommendations regarding which of two mutually exclusive projects
should be accepted, but they always give the same recommendation regarding the acceptability of a normal,
independent project.
e If you draw an NPV profile for one project, you will see that if the WACC is less than the IRR, the NPV will be
positive.
6. Projects A and B have identical expected lives and identical initial cash outflows (costs). However, most of one
projects cash flows come in the early years, while most of the other projects cash flows occur in the later years.
The two NPV profiles are given below:
NPV
($)
A
B
r (%)
Which of the following statements is CORRECT?
a. More of Project As cash flows occur in the later years.
b. More of Project Bs cash flows occur in the later years.
c. We must have information on the cost of capital in order to determine which project has the larger early cash flows.
d. The NPV profile graph is inconsistent with the statement made in the problem.
e. The crossover rate, i.e., the rate at which Projects A and B have the same NPV, is greater than either projects IRR.
a. Distant cash flows are more severely penalized by high discount rates, so if the NPV profile line has a steep slope,
this indicates that cash flows occur relatively late.
7. Lasik Vision Inc. recently analyzed the project whose cash flows are shown below. However, before Lasik decided
to accept or reject the project, the Federal Reserve took actions that changed interest rates and therefore the firm's
WACC. The Fed's action did not affect the forecasted cash flows. By how much did the change in the WACC affect
the project's forecasted NPV? Note that a project's projected NPV can be negative, in which case it should be
rejected.
Old WACC: 8.00%
New WACC: 11.25%
Year
0
1
2
3
Cash flows
$1,000
$410
$410
$410
Old NPV = $56.61, New NPV = $2.42 => Change = $59.03
8. Towson Associates is considering a project that has the following cash flow data. What is the project's payback?
Year
0
1
2
3
4
5
Cash flows
$1,100
$300
$310
$320
$330
$340
Year
Cumulative CF
Payback = 3.52
0
$1,100

1
$800

2
$490

3
$170

4
$160
3.52
5
$500

9. What is the NPV of investing in T Bills when you use the T Bill yield as a discount rate?
It is 0 (Zero). When investing T Bills, discount rate on T Bill is T Bill yield, which make PV of face value = price of T
Bill (Note that T Bill does not pay coupon payments). NPV=PV Po = Po Po = 0. Investing in a T Bill is just a
breakeven situation. Any riskfree security with a return higher than T Bill would have a positive NPV. Any security
less than that would have a negative NPV.
10. Explain why you do not want to keep your money under the rug as its NPV is negative.
If you keep $100 under the rug for a year and the opportunity cost (the highest interest rate you can earn from having
$100 invested elsewhere is say 10%), then the NPV=PV of $100  $100 = 100/1.1  100=90.90.91 100 = 9.09.
11. How are the capital budgeting criteria for mutually exclusive projects different for independent projects?
For independent projects, you take all good projects. For mutually exclusive projects, you need to choose only the
best one among the good ones. If none of the projects you consider looks good, you reject them all whether they are
independent or mutually exclusive.
Chapter 12. Cash Flow Estimation and Risk Analysis
1. A company is considering a new project. The CFO plans to calculate the projects NPV by estimating the relevant
cash flows for each year of the projects life (i.e., the initial investment cost, the annual operating cash flows, and the
terminal cash flow), then discounting those cash flows at the companys overall WACC. Which one of the following
factors should the CFO be sure to INCLUDE in the cash flows when estimating the relevant cash flows?
a. All sunk costs that have been incurred relating to the project.
b. All interest expenses on debt used to help finance the project.
c. The investment in working capital required to operate the project, even if that investment will be recovered at the end
of the projects life.
d. Sunk costs that have been incurred relating to the project, but only if those costs were incurred prior to the current
year.
e. Effects of the project on other divisions of the firm, but only if those effects lower the projects own direct cash
flows.
c
2. Which one of the following would NOT result in incremental cash flows and thus should NOT be included in the
capital budgeting analysis for a new product?
a. Using some of the firm's highquality factory floor space that is currently unused to produce the proposed new
product. This space could be used for other products if it is not used for the project under consideration.
b. Revenues from an existing product would be lost as a result of customers switching to the new product.
c. Shipping and installation costs associated with a machine that would be used to produce the new product.
d. The cost of a study relating to the market for the new product that was completed last year. The results of this
research were positive, and they led to the tentative decision to go ahead with the new product. The cost of the
research was incurred and expensed for tax purposes last year.
e. It is learned that land the company owns and would use for the new project, if it is accepted, could be sold to another
firm.
d
3. A company is considering a proposed new plant that would increase productive capacity. Which of the following
statements is CORRECT?
a. In calculating the project's operating cash flows, the firm should not deduct financing costs such as interest expense,
because financing costs are accounted for by discounting at the WACC. If interest were deducted when estimating
cash flows, this would, in effect, double count it.
b. Since depreciation is a noncash expense, the firm does not need to deal with depreciation when calculating the
operating cash flows.
c. When estimating the projects operating cash flows, it is important to include both opportunity costs and sunk costs,
but the firm should ignore the cash flow effects of externalities since they are accounted for in the discounting
process.
d. Capital budgeting decisions should be based on beforetax cash flows.
e. The WACC used to discount cash flows in a capital budgeting analysis should be calculated on a beforetax basis.
a
4. Towson Inc., is considering a new project whose data are shown below. The required equipment has a 3year tax
life, and the accelerated rates for such property are 33%, 45%, 15%, and 7% for Years 1 through 4. Revenues and
other operating costs are expected to be constant over the project's 10year expected operating life. What is the
project's Year 4 cash flow?
Equipment cost (depreciable basis)
Sales revenues, each year
Operating costs (excl. deprec.)
Tax rate
Depreciation rate, Year 4
Sales revenues
Operating costs (excl. deprec.)
Depreciation
Operating income (EBIT)
Taxes
Rate = 35%
Aftertax EBIT
+ Depreciation
Cash flow, Year 4
$70,000
$42,500
$25,000
35.0%
7.0%
$42,500
25,000
4,900
$12,600
4,410
$ 8,190
4,900
$13,090
5. Temple Corp. is considering a new project whose data are shown below. The equipment that would be used has a 3year tax life, would be depreciated by the straightline method over its 3year life, and would have a zero salvage
value. No new working capital would be required. Revenues and other operating costs are expected to be constant
over the project's 3year life. What is the project's NPV?
Riskadjusted WACC
Net investment cost (depreciable basis)
Straightline deprec. rate
Sales revenues, each year
Operating costs (excl. deprec.), each year
Tax rate
WACC
10.0%
10.0%
$65,000
33.3333%
$65,500
$25,000
35.0%
Years
0
2
$65,500
$65,500
25,000
25,000
21,667
21,667
$18,833
$18,833
6,592
6,592
$12,242
$12,242
21,667
Investment cost
Sales revenues
1
3
21,667
$33,908
$33,908
$65,000
$65,500
Operating costs (excl. deprec.)
25,000
Depreciation rate = 33.333%
21,667
Operating income (EBIT)
$18,833
Taxes
6,592
Aftertax EBIT
Rate = 35%
$12,242
+ Depreciation
21,667
Cash flow
$65,000
$33,908
NPV
$19,325
6. Liberty Services is now at the end of the final year of a project. The equipment originally cost $22,500, of which
75% has been depreciated. The firm can sell the used equipment today for $6,000, and its tax rate is 40%. What is
the equipments aftertax salvage value for use in a capital budgeting analysis? Note that if the equipment's final
market value is less than its book value, the firm will receive a tax credit as a result of the sale.
% depreciated on equip.
75%
Tax rate
40%
Equipment cost
$22,500
Accumulated deprec.
16,875
Current book value of equipment
$ 5,625
Market value of equipment
6,000
Gain (or loss): Market value Book value
$ 375
Taxes paid on gain () or credited (+) on loss
150
AT salvage value = market value +/ taxes
$ 5,850
7. MarshallMiller & Company is considering the purchase of a new machine for $50,000, installed. The machine has
a tax life of 5 years, and it can be depreciated according to the following rates. The firm expects to operate the
machine for 4 years and then to sell it for $12,500. If the marginal tax rate is 40%, what will the aftertax salvage
value be when the machine is sold at the end of Year 4?
Year
1
2
3
4
5
6
e
Depreciation Rate
0.20
0.32
0.19
0.12
0.11
0.06
Year
1
2
3
4
5
6
Deprec.
Rate
0.20
0.32
0.19
0.12
0.11
0.06
1.00
Gross sales proceeds
Book value, end of Year 4
Profit
Tax on profit
Rate = 40%
AT salvage value = market value +/ taxes
Basis
$50,000
50,000
50,000
50,000
50,000
50,000
$10,900
Annual
Deprec.
$10,000
16,000
9,500
6,000
5,500
3,000
$50,000
$12,500
8,500
$ 4,000
1,600
Yearend
Book Value
$40,000
24,000
14,500
8,500
3,000
0
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aacdbbaabbbccbcaaaabadcaacddbaabbbabda1. primary activities and support activitiesthe five primary activities of a value chain. Inbound Logistics: the receiving and warehousing of raw materials, and theirdistribution to manufacturing as they are requ
Towson  ECON  101
ORGANIZATIONSTRATEGYANDPROJECTSELECTIONPRESENTEDBY:TUSHARRATHODBS(MECHANICAL),MBA(FINANCE),PMPSENIORPROJECTMANAGEREBAY/PAYPAL,INC.Study PlanWHYPROJECTMANAGERSNEEDTOUNDERSTANDTHESTRATEGICMANAGEMENTPROCESSCorporate Structure & PMOChanges in the
Towson  ECON  101
DEFININGTHEPROJECTPRESENTEDBY:TUSHARRATHODBS(MECHANICAL),MBA(FINANCE),PMPSENIORPROJECTMANAGEREBAY/PAYPAL,INC.Study PlanDEFININGTHEPROJECTStep 1: Defining the Project ScopeStep 2: Establishing Project PrioritiesStep 3: Creating the Work Breakdow
Towson  ECON  101
1. List the five primary activities of a value chain.Inbound Logistics: all processes associated with receiving. Storing, anddisseminating inputs to the production process of the product or service;Operations: all processes associated with transforming
Towson  ECON  101
TOWSONUNIVERSITYCollegeofBusinessandEconomics/DepartmentofManagementMNGT482.001/002BusinessEthicsandSustainabilityDr.W.SmithST118C;4107043875Fall2012officehours:11:00am12:00pmMWFemail:wsmith@towson.eduInanuglyandunhappyworldtherichestmancanpurch
Towson  ECON  101
Moral Claims: Madres de Plaza de MayoDoes this rightsupersedeA motherutilitarianhas a rightconsiderations?to knowwhathappens toher child.ooThe cost of doinginvestigations todetermine the guiltyparties.The cost to a nationof reliving past
Towson  ECON  101
MNGT 482, Fall 2012Sample Questions for Exam 1Exam 1 (Wednesday, September 19) will contain some multiple choice and four shortanswer questions. Eachstudent will be required to answer three of the four shortanswer questions. At least two of the follo
Towson  ECON  101
Two Project Options1. a video project that is submitted to PlanetForward.2. an eighthour service learning assignmentat a local nonprofit organizationProjects will be discussed on Fridays.Information presented on these days isyour responsibility.V
Towson  ECON  101
Ethical Dilemma Faced By StudentsProf.DenisCollins,EdgewoodCollegeYou work at a furniture store. The previous twomonths you were below sales quota, mostly due tothe recession, and if you fail to meet the sales quotaa third consecutive month you will
Towson  ECON  101
September 3, 2012Towson, Maryland 21252Dept. of ManagementMNGT. 375 International Business: Theory and PracticeSections 001 and 002: Fall 2012 Class ScheduleThis schedule presents the planned dates for lectures, readings, and courseassignments. It m
Towson  ECON  101
September 3, 2012Towson, Maryland 21252Dept. of ManagementMNGT. 375 International Business: Theory and PracticeFall 2012COURSE SECTION, MEETING TIME, AND LOCATIONSections 001 and 002,MondayWednesdayFriday,10:00 to 10:50 am, and 11:00 to 11:50 am
Towson  ECON  101
FEEDBACK SOLICITATION FOR SERVICE LEARNING PROJECTTo Whom It May Concern:Thank you very much for allowing _, a student in my Management 482 classto participate in a service learning project at your organization. We hope this project provides aworthwhi
Towson  ECON  101
Business WritingThe Final Electronic PortfolioYour Final Electronic Portfolio (FEP) is the final project for our course. The FEP is your chance to addany final revisions/commentary to your assignments and to archive your work.A note about revisions: D
Towson  ECON  101
TOWSON UNIVERSITYDepartment of FinancePrinciples of Financial ManagementFIN331Fall 2012Instructor:Office:Work Phone:Class Hours:MoonWhoan Stephen Rhee, Ph.D.Stephens Hall (ST) 316H4107044075MWF 8:008:50am (331.001 ST309)MWF 10:0010:50am
Towson  ECON  101
Chapter 2Financial Markets andInstitutionsTopics:Financial MarketsFinancial InstitutionsThe Capital Allocation ProcessStock Markets and ReturnsStock Market Efficiency21 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied, or
Towson  ECON  101
FIN331Fall 2012 Exam #1Dr. RheeNAME_ ID#_1. Identify which financial statements are appropriate to use for each event listed below.Event 1: Can the firm meet all its shortterm obligations?Event 2: How much of the firms earnings are put back into th
Towson  ECON  101
ExampleForeign ExchangeProblemsFall 20121Transaction 1 Chocolate PurchaseFAT CANDY of USA purchases chocolatefrom Switzerland. FAT CANDY will pay SF25,000,000 in 90 days. The present spotexchange rate is US$1.0814/SF. The 90day forward contract
Towson  ECON  101
MNGT 375  International Business, Fall 2012, Mr. KopkaForeign Exchange Rate AssignmentDUE Wednesday, October 31, 2012In completing this assignment, follow the writing guidelines on p. 7 of thesyllabus.For each of the following two foreign exchange s
Towson  ECON  101
Global FinancialCrisisDon Kopka, PhDManagement DeptTowson University1Types of Financial CrisesCurrency Sharp currency depreciationBanking Loss of confidence in bankingsystemForeign Debt Country unable to serviceforeign debt obligations2Previo
Towson  ECON  101
Job DescriptionFraud Analysts for Bank of AmericaJob Description:Fraud Analysts review potential fraudulent accounts for the prevention and detection ofFraud and verify account activity with customers over the phone. The incumbent willtake appropriat
Towson  ECON  101
Guidance for Preparing forMidterm Exam 2 Fall 2012MNGT 375Sections 001 and 0021Exam will be on Wednesday, October17Exam will be all EssayBring your own paper do not usebluebooksMidterm Exam 2 covers Chapters 5, 6,7, and 8 and class discussions
Towson  ECON  101
Guidance for Preparing forMidterm Exam 2 Fall 2012MNGT 375Sections 001 and 0021Exam will be on Wednesday, October17Exam will be all EssayBring your own paper do not usebluebooksMidterm Exam 2 covers Chapters 5, 6,7, and 8 and class discussions
Towson  ECON  101
External analysis:It had lost its 65yearsold leadership among imported beers in the USA to GroupModelos CoronaOther brewers started reaching out to make acquisitions all over the world,Heineken has been running the risk of falling behind its more ag
Towson  ECON  101
Homework IIINgan BuiFIN 423Chapter 10: Residential Mortgage LoansQuestion 1: For the following fixedrate levelpayment mortgage, construct anamortization schedule for the first 10 months:Maturity = 360 monthsAmount borrowed = $150,000Note rate =
Towson  ECON  101
Huy DinhEBTM 443 Monday 6:30 PM 9:10 PMCase StudyHector Gaming Company1. What is our major problem?Hector Gaming Company, HGC, has an ineffective project portfolio managementsystem. The major problem with the HGC is the organizational politics. Ther
Towson  ECON  101
Table of Content:Executive SummaryPassword ProtectorOur marketing team of Production Development proposes production and marketing ofPassword Protector for distribution to two target markets.Business Mission: Password Protector To provide secure pas
Towson  ECON  101
TO: Marketing DepartmentFROM: Product DevelopmentDATE: April 5, 2012SUBJECT: Password Protector market researchOverviewIn the development of the Password Protector suite of applications for personal computers andmobile devices, we have decided to co