UNIVERSITY OF GHANA
2ND SEMESTER: 2022/2023
FINC 302: BUSINESS FINANCE II
TUTORIAL SET 1: BOND VALUATION
SECTION A
The Nitty-Gritty of BONDS
1) Discuss the following
a) What is Bond all about?
b) Bond Indenture
•
Terms of a bond
•
Security and seniority
•
Call provisions
•
Sinking funds
•
Protective covenants
c) Bond Security
d) Bond Ratings
e) Call provisions vs Put provisions
f) Relationship between bond prices and interest rates
g) Bond sensitivity and interest rate risks
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SECTION B
BOND PRICE & CURRENT YIELD
1. Atomoh Baby Inc. just issued a bond with a 3-year term to maturity. The face value is
$1000 and it pays a 12% coupon. The interest rate in the market is 10%.
a) Compute the price of the bond
b) What is its current Yield today?
c) Now assume the coupons are paid semi-annually.
i.
Compute the new bond price
ii.
Compute the new current yield
2. To finance a new line of products, Tangshan Toys has issued a bond with a par value of
$1,000, a coupon rate of 8 percent, and a maturity of 30 years. If the opportunity cost is 11
percent.
a) Compute the price of the bond
b) What is its current Yield today?
c) What will be its Current Yield, 5 years to maturity?
3. To expand its business, the Kingston Outlet factory would like to issue a bond with a par
value of $1,000, coupon rate of 10 percent, and maturity of 10 years from now. If the
required rate of return is 10 percent:
a) What is the value of the bond?
b) What is its current Yield today?
c) What will be its Current Yield after 3 years?
Use the table below to answer questions 3 to 5
Annual Coupon
Bond
Par Value ($)
Interest Rate (%)
L
1000
9
M
100
10
N
500
18
Years to
Maturity
5
8
17
Required
Return (%)
6
10
15
4. a) What is the value of Bond L?
b) What is its current Yield today?
c) What will be its Current Yield after 2 years?
5. Find the price of Bond M
6. What is the maximum price you will pay for Bond N?
7. Yantai Food, Inc. has issued a bond with a par value of $1,000, a coupon rate of 9 percent
that is paid semi-annually, and that matures in 10 years. What is the value of the bond if
the required rate of return is 12 percent? What is its current Yield today? What will be its
Current Yield, 5 years to maturity?
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8. The $1,000 face value Mega-World Company bond has a coupon rate of 6%, with interest
paid semi-annually, and matures in 5 years. If the bond is priced to yield 8%, what is the
bond's value today? What is its current Yield today? What will be its Current Yield after 3
years?
9. Hewitt Packing Company has an issue of $1,000 par value bonds with a 14 percent coupon
interest rate outstanding. The issue pays interest semi-annually and has 10 years remaining
to its maturity date. Bonds of similar risk are currently selling to yield a 12 percent rate of
return. What is the value of these Hewitt Packing Company bonds? What is its Current
Yield today? What will be its Current Yield, 6 years to maturity?
10. The La Carolina bond has an 8% coupon rate (with interest paid semi-annually), a maturity
value of $1,000, and matures in 5 years. If the bond is priced to yield 6%, what is the bond's
current price? What is its Current Yield today? What will be its Current Yield, in 2 years
to maturity?
11. Burger King Company has issued a bond with a par value of $1,200, a coupon rate of 9
percent that is paid semi-annually, and that matures in 10 years. What is the value of the
bond if the required rate of return is 12 percent?
.
12. Zhen Yi Computers has an outstanding issue of bond with a par value of $1,000, paying a
12 percent coupon rate semi-annually. The bond was issued 25 years ago and has 5 years
to maturity. What is the value of the bond assuming a 14 percent rate of interest?
SECTION C
COUPON AMOUNT AND RATE
13. The La Antonio Company bond has a current price of $800, a maturity value of $1,000 and
matures in 5 years. If interest is paid semi-annually and the bond is priced to yield 8%, what
is the bond’s annual coupon rate?
14. What is the coupon rate of a bond that sells at $1200 with a par value of $1000 and a YTM
of 15%?
15. What is the coupon rate of a bond that sells at $1200 with a par value of $1000 and a YTM
of 15%? Assume interests are paid semi-annually.
16. How much coupon is paid by a bond worth $950 with a face value of $1000, a YTM of
10%, if coupons are paid semi-annually?
17. How much coupon is paid by a bond worth $950 with a face value of $1000, a YTM of
10%, if coupons are paid quarterly?
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SECTION D
YIELD TO MATURITY
18. Find the approximate YTM of a bond with a face value of $1,000 and pays a $100 coupon.
It sells at 1050 and will mature in 4 years.
19. The $1,000 face value Ayala Company bond has a coupon of 10% (paid semi-annually),
matures in 4 years, and has a current price of $1,140. What is the bond's yield to maturity?
20. The Jollibee Foods Corporation bond has an 8% coupon rate (semi-annual interest), a
maturity value of GHS1,000, matures in 5 years, and a current price of GHS1,200. What is
the bond’s yield-to-maturity?
21. Find the approximate YTM of a bond with a face value of $1,000 and pays a $100
coupon. It sells at $900 and will mature in 5 years.
SECTION E
GENERAL OBJECTIVE TEST ON BONDS
1. What's the value to you of a $1,000 face-value bond with an 8% coupon rate when your
required rate of return is 15 percent?
A. More than its face value.
B. Less than its face value.
C. $1,000.
D. Inadequate information to determine
2. When the market's required rate of return for a particular bond is much less than its coupon
rate, the bond is selling at:
A. a premium.
B. a discount.
C. cannot be determined without more information.
D. face value.
3. If an investor may have to sell a bond prior to maturity and interest rates have risen since
the bond was purchased, the investor is exposed to
A. the coupon effect.
B. interest rate risk.
C. perpetuity.
D. an indefinite maturity.
4. If a bond sells at a high premium, then which of the following relationships hold true? (P0
represents the price of a bond and YTM is the bond's yield to maturity.)
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A.
B.
C.
D.
P0 < par and YTM > the coupon rate.
P0 > par and YTM > the coupon rate.
P0 > par and YTM < the coupon rate.
P0 < par and YTM < the coupon rate.
5. Interest rates and bond prices
A. move in the same direction.
B. move in opposite directions.
C. sometimes move in the same direction, sometimes in opposite directions.
D. have no relationship with each other (i.e., they are independent).
6. In the United States, most bonds pay interest ………… a year, while many European bonds
pay interest …………. a year.
A. once; twice
B. twice; once
C. once; once
D. twice; twice
7. The expected rate of return on a bond if bought at its current market price and held to
maturity.
A. yield to maturity
B. current yield
C. coupon yield
D. capital gains yield
8. The value of a bond is calculated using the present value of discounted cash flows. What is
the discount rate?
A. The discount rate is the rate of return required for an investor to purchase the bond.
B. The discount rate is the difference between the face value and the purchase price
expressed as a percentage.
C. The discount rate is the amount above the face value an investor is willing to pay
for the bond.
D. The discount rate is the interest paid to the investor.
9. When the coupon rate is above the discount rate, the bond value is _____ the face value
and is considered to be at a _____.
A. Above; discount
B. Below; discount
C. Below; premium
D. Above; premium
10. Smith Darby has issued a five-year bond with a coupon rate of 8% and a face value of
$5,000. As a personal investor, you require a rate of return of 10%. What is the value of the
bond?
A. $5,000.00
B. $5,399.37
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C. $4,620.94
D. $3,050.00
11. The annual interest payment divided by the present or current price of a bond is termed as
A. Yield to Maturity
B. Current Yield
C. Maturity yield
D. Earnings Yield
12. The price of an outstanding bond increases when the market rate
A. Never changes
B. Increases
C. Decreases
D. Changes
13. Bonds that may be exchanged for common stock at the option of the bondholders are called
A. options.
B. stock bonds.
C. convertible bonds.
D. callable bonds.
14. The contractual interest rate on a bond is often referred to as the
A. callable rate.
B. the maturity rate.
C. market rate.
D. stated rate.
15. If the market interest rate for a bond is higher than the stated interest rate, the bond will sell
at
A. a premium.
B. a discount.
C. par.
D. either a discount or premium
16. Long-term bonds are …….... than short-term bonds.
A. subject to more uncertainty
B. less risky
C. less sensitive to interest rate changes
D. more liquid
17. If a bond's yield to maturity is lower than its coupon rate, the bond will sell at a discount.
A. False
B. True
C. Inadequate information to decide
D. It depends
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18. As a bond approaches its maturity date, its price approaches par value.
A. False
B. True
C. Inadequate information to decide
D. It depends
19. Which of the following statements is FALSE regarding bonds?
A. If the par value is lower than the market price, then the yield-to-maturity must be
lower than the coupon rate.
B. If the market price is lower than the par value, then the coupon rate must be lower
than the yield-to-maturity.
C. Both A and B are false.
D. None of the above is false.
20. When the price of a bond is calculated below its par value, it is classified as...
A. classified bond
B. discount bond
C. consideration earnings
D. compound bond
21. What is a bond?
A. a type of debt a company issues to investors
B. an agreement or friendship
C. something that binds, fastens, confines, or holds together
D. binding security
22. When you purchase a municipal bond, you are:
A. diversifying your portfolio
B. buying a portion of a municipality
C. loaning money to a municipality
D. investing in an index fund
23. A bond issued by a corporation is called a ________
A. share of stock
B. market share
C. corporate bond
D. stock option
24. The rate of interest on a bond is called the ________
A. interest rate
B. coupon rate
C. discount rate
D. bond rate
25. A 15-year bond pays 11% on a face value of $1,000. If similar bonds are currently yielding
8%, what is the market value of the bond? Use annually.
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A.
B.
C.
D.
Under $1,000
Over $1,200
Not enough information to tell
Equal $1,000
26. A bond which has a yield to maturity greater than its coupon rate will sell for a price
A. above par
B. equal to the face value of the bond plus the interest payments
C. at par
D. below par
27. What is the value of a zero-coupon bond with 800 face value, which matures in 7 years
with a discount rate of 14%?
A. 1000
B. 450
C. 5600
D. 320
28. What will the value of a bond with a coupon rate of 8%, and a market rate of 8% be?
A. at par (or face value)
B. at a discount
C. not enough information
D. at a premium
29. What is a coupon?
A. the interest rate on a bond at the time it is issued
B. an asset bought in the stock market
C. something you use in a supermarket to decrease your cost
D. used in the stock market to lessen the initial cost of stocks
30. If a coupon rate is 10%, how much would a semi-annual coupon payment be?
A. $100
B. $1000
C. $25
D. $50
31. If a bond was issued with a 5% coupon rate and the market rate is now 8%, the coupon
payment:
A. Stays the same
B. Goes up
C. Coupon changes
D. Goes down
32. A bond which has a yield to maturity greater than its coupon rate will sell for a price
A. below par
B. at par
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C. equal to the face value of the bond plus the interest payments
D. above par
33. What will happen to the market value of a bond if interest rates rise?
A. market value will increase
B. market value will decrease
C. No idea
D. Stay the same
34. A bond which has a yield to maturity lower than its coupon rate will sell for a price
A. equal to the face value of the bond plus the interest payments
B. above par
C. at par
D. below par
35. What is usually the relationship between a bond's rating and the interest rate?
A. there is no relationship
B. the rating is the same as the rate
C. higher ratings mean higher interest
D. Higher ratings mean lower interest
36. A type of long-term financing used by both corporations and government entities is
A. bonds
B. common stock
C. preferred stock
D. retained earnings
37. Bonds are
A. a hybrid form of financing used to raise large sums of money from a diverse group
of lenders.
B. a form of equity financing that pays interest.
C. long-term debt instruments.
D. a series of short-term debt instruments.
38. The ________ value of a bond is also called its face value. Bonds which sell at less than
face value are priced at a ________, while bonds which sell at greater than face value sell
at a ________.
A. coupon; premium; discount
B. premium; discount; par
C. par; discount; premium
D. discount; par; premium
39. The value of a bond is the present value of the
A. dividends and maturity value.
B. interest and dividend payments.
C. interest payments and maturity value.
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D. maturity value
40. A firm has an issue of $1,000 par value bonds with a 12 percent stated interest rate
outstanding. The issue pays interest annually and has 10 years remaining to its maturity
date. If bonds of similar risk are currently earning 8 percent, the firm's bond will sell for
________ today.
A. $851.50
B. $1,000
C. $1,268.40
D. $805.20
41. A firm has an issue of $1,000 par value bonds with a 9 percent stated interest rate
outstanding. The issue pays interest annually and has 20 years remaining to its maturity
date. If bonds of similar risk are currently earning 11 percent, the firm's bond will sell for
________ today.
A. $1,123.33
B. $1,000
C. $716.67
D. $840.73
42. Hewitt Packing Company has an issue of $1,000 par value bonds with a 14 percent annual
coupon interest rate. The issue has ten years remaining to the maturity date. Bonds of
similar risk are currently selling to yield a 12 percent rate of return. The current value of
each Hewitt bond is ________.
A. $1,000
B. $791.00
C. $1,113.00
D. $1,052.24
43. What is the approximate yield to maturity for a $1,000 par value bond selling for $1,120
that matures in 6 years and pays 12 percent interest annually
A. 13.2 percent
B. 8.5 percent
C. 9.4 percent
D. 12.0 percent
44. Tangshan Industries has issued a bond which has a $1,000 par value and a 15 percent annual
coupon interest rate. The bond will mature in ten years and currently sells for $1,250. Using
this information, the yield to maturity on the Tangshan Industries bond is ________.
A. 12.19 percent
B. 11.39 percent
C. 13.29 percent
D. 10.79 percent
45. A bond with a coupon rate of 7% and a discount rate of 6% is trading ...
A. Par
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B. Discount
C. Premium
D. None of the above
46. Which of the following is not a characteristic of a zero-coupon bond?
A. can sell for more than the par value
B. The entire YTM comes from the difference between the par value and the purchase
price.
C. coupon rate = zero
D. There are no periodic payments
47. Which of the following are characteristics of a bond when traded at a premium?
i.
YTM=coupon rate
ii. YTM< coupon rate
iii. Bond traded at a price below face value
iv.
Bond traded at a price above face value
A.
B.
C.
D.
i and ii
i and iii only.
ii and iv only
ii and iii
48. If the Bond Value = PV of coupons + PV of par
What is the value of a 3-year, $100 par value, 7% annual coupon bond, when the discount rate
is 6%?
A. $100
B. $89.83
C. $102.67
D. $110.50
49. Which of the following bonds have a higher coupon (all else equal)?
A. senior debt
B. A bond without a sinking fund
C. callable bond
D. debenture
50. The ______ is used to calculate the present value of a bond.
A. Nominal yield
B. Current yield
C. Yield to call
D. Yield to maturity
51. A bond has a coupon rate of 6%, matures in 6 years, and currently sells for $1,000 (par
value). Therefore, the yield to maturity is also 6%.
A. True
B. False
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C. Maybe
D. None
52. Generally speaking, short-term bonds have lower yields than long-term bonds.
A. True
B. False
C. Maybe
D. None
53. Bond duration refers to the remaining life of a bond.
A. True
B. False
C. Maybe
D. None
54. A major advantage of passive bond strategies is low transaction costs
A. True
B. False
C. Maybe
D. None
55. The market price of a bond changes according to which of the following reasons?
A. Market price changes due to the supply-demand of the bond in the market.
B. Market price changes due to investors’ perceptions.
C. Market price changes due to changes in the interest rate.
D. All of the above.
56. A bond will sell at a discount when ____?
A. The coupon rate is greater than the current yield and the current yield is greater than
the yield to maturity.
B. The coupon rate is greater than the yield to maturity.
C. The coupon rate is less than the current yield and the current yield is less than the
yield to maturity.
D. The coupon rate is less than the current yield and the current yield is greater than
the yield to maturity.
57. The long-term bonds issued by the government are called
A. Corporate bonds
B. Junk bonds
C. Zero coupon bonds
D. Treasury bonds
58. The expected rate of return on a bond if bought at its current market price and held to
maturity.
A. Yield to maturity
B. Current yield
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C. Coupon yield
D. Capital gains yield
59. The _____ feature permits the issuer to repurchase bonds at a stated price prior to maturity.
A. Call
B. Conversion
C. Put
D. Capitalization
60. The ____ feature allows the bondholder to change each bond into a stated number of shares
of stock.
A. Call
B. Conversion
C. Put
D. Capitalization
61. A low or deep/zero–discounted bond is a
A. Junk bond
B. Floating rate bond
C. Zero coupon bond
D. Subordinated debenture
62. The stated interest payment, in dollars, made on a bond each period is called the bond’s
A. Coupon
B. Face value
C. Maturity
D. Yield to maturity
E. Coupon rate
63. Which of the following statements is most correct?
A. All else equal, if a bond’s yield to maturity increases, its price will fall
B. All else equal, if a bond’s yield to maturity increases, its price will rise.
C. If a bond’s yield to maturity exceeds the coupon rate, the bond will sell at a premium
over par.
D. All of the statements above are correct.
64. A bond with a face value of P1,000 that sells for less than P1,000 in the market is called a
A. Par bond
B. Discount bond
C. Premium bond
D. Floating rate bond
65. These are corporate bonds where the coupon can be adjusted at pre-determined intervals.
A. Foreign bonds
B. Floating rate notes
C. Junk bonds
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D. Index-linked bond
66. A technique for determining the theoretical fair value of a particular bond, including the
present and future value of its cash flows.
A. Bond convexity
B. Bond Immunization
C. Bond Valuation
D. None of the above.
67. An investor or the owner of debt securities that are typically issued by corporations and
governments and are essentially lending money to the bond issuers.
A. Broker
B. Agent
C. Bondholder
D. Bank
68. In a practical sense, the longer the term of a bond, the greater the default risk associated
with the bond
A. True
B. False
C. Maybe
D. None
69. The volatility of the price of a bond is measured by the duration
A. True
B. False
C. Maybe
D. None
70. Since a puttable bond gives its holder the right to “put the bond” at specified times or
actions by the firm, the bond’s yield is lower than that of a non-puttable bond.
A. True
B. False
C. Maybe
D. None
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APPENDIX A: USEFUL FORMULAE
𝑃𝑟𝑖𝑐𝑒 =
𝐶
1
𝐹𝑉
(1 −
)+
𝑛
𝑟
(1 + 𝑟 )
(1 + 𝑟)𝑛
𝐹𝑉
(1 + 𝑟)𝑛
𝐶=
1
1
(1
)
𝑟 − (1 + 𝑟)𝑛
𝑃−
𝐹𝑉 − 𝑃
𝐶+
𝑛
𝑟 = 𝑌𝑇𝑀 =
𝐹𝑉 + 𝑃
2
𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑌𝑖𝑒𝑙𝑑 =
𝐴𝑛𝑛𝑢𝑎𝑙 𝐶𝑜𝑢𝑝𝑜𝑛 (𝑇ℎ𝑒 𝐴𝑚𝑜𝑢𝑛𝑡)
𝐵𝑜𝑛𝑑 𝑃𝑟𝑖𝑐𝑒
where:
C = The coupon Amount (NOT the rate)
r = The Yield to Maturity (YTM), Opportunity Cost, Discount rate
n = The Term to Maturity
FV = Face Value or the Par Value
P = Price of Bond
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APPENDIX B: SAMPLE BOND CERTIFICATES
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