Troy University Bond Valuation Economics Market Worksheet

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7-1. BOND VALUATION Madsen Motors’s bonds have 23 years remaining to maturity. Interest is paid
annually, they have a $1,000 par value, the coupon interest rate is 9%, and the yield to maturity is 11%.
What is the bond’s current market price?
7-2. YIELD TO MATURITY AND FUTURE PRICE A bond has a $1,000 par value, 12 years to maturity, and
an 8% annual coupon and sells for $980.
a. What is its yield to maturity (YTM)?
b. Assume that the yield to maturity remains constant for the next three years. What will the price
be 3 years from today?
7-3. BOND VALUATION Nesmith Corporation’s outstanding bonds have a $1,000 par value, an 8%
semiannual coupon, 14 years to maturity, and an 11% YTM. What is the bond’s price?
7-4. YIELD TO MATURITY A firm’s bonds have a maturity of 8 years with a $1,000 face value, have an 11%
semiannual coupon, are callable in 4 years at $1,154, and currently sell at a price of $1,283.09. What are
their nominal yield to maturity and their nominal yield to call? What return should investors expect to
earn on these bonds?
7-8. YIELD TO CALL Seven years ago the Templeton Company issued 20-year bonds with an 11% annual
coupon rate at their $1,000 par value. The bonds had a 7.5% call premium, with 5 years of call
protection. Today Templeton called the bonds. Compute the realized rate of return for an investor who
purchased the bonds when they were issued and held them until they were called. Explain why the
investor should or should not be happy that Templeton called them.
Bonds and Their
Valuation
Chapter 7
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Overview
Key Features of Bonds
Bond Valuation
Measuring Yield
Assessing Risk
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What is a bond?
? A long-term debt instrument in which a
borrower agrees to make payments of principal
and interest, on specific dates, to the holders of
the bond.
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Key Features of a Bond
? Par value: face amount of the bond, which
is paid at maturity (assume $1,000).
? Coupon interest rate: stated interest rate
(generally fixed) paid by the issuer. Multiply by
par value to get dollar payment of interest.
? Maturity date: years until the bond must be
repaid.
? Issue date: when the bond was issued.
? Yield to maturity: rate of return earned on
a bond held until maturity (also called the
“promised yield”).
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Other Types (Features) of Bonds
? Convertible bond: may be exchanged for
common stock of the firm, at the holder’s
option.
? Warrant: long-term option to buy a stated
number of shares of common stock at a
specified price.
? Putable bond: allows holder to sell the bond
back to the company prior to maturity.
? Income bond: pays interest only when interest
is earned by the firm.
? Indexed bond: interest rate paid is based upon
the rate of inflation.
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Effect of a Call Provision
? Allows issuer to refund the bond issue if rates
decline (helps the issuer, but hurts the
investor).
? Bond investors require higher yields on callable
bonds.
? In many cases, callable bonds include a
deferred call provision and a declining call
premium.
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What is a sinking fund?
? Provision to pay off a loan over its life rather
than all at maturity.
? Similar to amortization on a term loan.
? Reduces risk to investor, shortens average
maturity.
? But not good for investors if rates decline after
issuance.
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How are sinking funds executed?
? Call x% of the issue at par, for sinking
fund purposes.
• Likely to be used if rd is below the coupon
rate and the bond sells at a premium.
? Buy bonds in the open market.
• Likely to be used if rd is above the coupon
rate and the bond sells at a discount.
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The Value of Financial Assets
0
1
2
N
r%
Value
…
CF1
Value =
CF2
CF1
+
CF2
(1 + r )1 (1 + r )2
CFN
+?+
CFN
(1 + r )N
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What is the opportunity cost of debt capital?
? The discount rate (ri) is the opportunity cost of
capital, and is the rate that could be earned on
alternative investments of equal risk.
ri = r* + IP + MRP + DRP + LP
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What is the value of a 10-year, 10% annual coupon
bond, if rd = 10%?
0
VB = ?
10%
1
2
N
…
100
VB =
100
$100
(1.10 )
1
+?+
100 + 1,000
$100
(1.10 )
10
+
$1,000
(1.10 )10
VB = $90.91 + ? + $38.55 + $385.54
VB = $1,000
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Calculating the Value of a Bond
? This bond has a $1,000 lump sum (the par
value) due at maturity (t = 10), and annual
$100 coupon payments beginning at t = 1 and
continuing through t = 10. The price of the
bond can be found by solving for the PV of
these cash flows.
INPUTS
OUTPUT
10
10
N
I/YR
PV
100
1000
PMT
FV
-1000
Excel: =PV(.10,10,100,1000)
© 2019 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
What’s the value of a 10-year bond outstanding with
the same risk but a 13% annual coupon rate?
? The annual coupon payment is $130. Since the
risk is the same it has the same yield to
maturity as the previous bond (10%). This
bond sells at a premium because the coupon
rate > the yield to maturity.
INPUTS
OUTPUT
10
10
N
I/YR
PV
130
1000
PMT
FV
-1184.34
Excel: =PV(.10,10,130,1000)
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What’s the value of a 10-year bond outstanding with
the same risk but a 7% annual coupon rate?
? The annual coupon payment is $70. Since the
risk is the same it has the same yield to
maturity as the previous bonds (10%). This
bond sells at a discount because the coupon
rate < the yield to maturity. INPUTS OUTPUT 10 10 N I/YR PV 70 1000 PMT FV -815.66 Excel: =PV(.10,10,70,1000) © 2019 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Changes in Bond Value over Time ? What would happen to the value of these three bonds if the required rate of return remained at 10%? VB 1,184 1,000 13% coupon rate 10% coupon rate 7% coupon rate 816 10 5 0 Years to Maturity © 2019 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Bond Values over Time ? At maturity, the value of any bond must equal its par value. ? If rd remains constant: • The value of a premium bond would decrease • • over time, until it reached $1,000. The value of a discount bond would increase over time, until it reached $1,000. The value of a par bond stays at $1,000. © 2019 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. What is the YTM on the following bond? • 10-year; 9% annual coupon; $1,000 par value; selling for $887. • Must find the rd that solves this model. VB = $887 = INT (1 + rd ) 1 90 (1 + rd ) 1 +?+ +?+ INT (1 + rd ) N 90 (1 + rd ) 10 + + M (1 + rd ) N 1,000 (1 + rd )10 © 2019 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Solving for the YTM ? Solving for I/YR, the YTM of this bond is 10.91%. This bond sells at a discount, because YTM > coupon rate.
INPUTS
10
N
OUTPUT
I/YR
-887
90
1000
PV
PMT
FV
10.91
Excel: =RATE(10,90,-887,1000)
© 2019 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Find YTM If the Bond Price is $1,134.20
? Solving for I/YR, the YTM of this bond is 7.08%.
This bond sells at a premium, because YTM < coupon rate. INPUTS 10 N OUTPUT I/YR -1134.20 90 1000 PV PMT FV 7.08 Excel: =RATE(10,90,-1134.20,1000) © 2019 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Definitions Annual coupon payment Current yield (CY) = Current price Change in price Capital gains yield (CGY) = Beginning price Expected total return = YTM = Expected CY + Expected CGY © 2019 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. An Example: Current and Capital Gains Yields Find the current yield and the capital gains yield for a 10-year, 9% annual coupon bond that sells for $887, and has a face value of $1,000. $90 Current yield = $887 = 0.1015 = 10.15% © 2019 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Calculating Capital Gains Yield YTM = Current yield + Capital gains yield CGY = YTM ? CY = 10.91% ? 10.15% = 0.76% Could also find the expected price one year from now and divide the change in price by the beginning price, which gives the same answer. © 2019 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. What is price risk? Does a 1-year or 10-year bond have more price risk? ? Price risk is the concern that rising rd will cause the value of a bond to fall. rd 1-year 5% $1,048 10% 1,000 15% 956 Change + 4.8% – 4.4% 10-year $1,386 1,000 749 Change +38.6% –25.1% ? The 10-year bond is more sensitive to interest rate changes, and hence has more price risk. © 2019 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Illustrating Price Risk Value ($) 1,600 1,400 1,200 1,000 800 600 400 200 0 10-year Bond 1-year Bond YTM(%) 0 5 10 15 20 © 2019 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. What is reinvestment risk? ? Reinvestment risk is the concern that rd will fall, and future CFs will have to be reinvested at lower rates, hence reducing income. EXAMPLE: Suppose you just won $500,000 playing the lottery. You intend to invest the money and live off the interest. © 2019 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Reinvestment Risk Example ? You may invest in either a 10-year bond or a series of ten 1-year bonds. Both 10-year and 1-year bonds currently yield 10%. ? If you choose the 1-year bond strategy: • After Year 1, you receive $50,000 in income and have $500,000 to reinvest. But, if 1-year rates fall to 3%, your annual income would fall to $15,000. ? If you choose the 10-year bond strategy: • You can lock in a 10% interest rate, and $50,000 annual income for 10 years, assuming the bond is not callable. © 2019 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Conclusions about Price Risk and Reinvestment Risk Price risk Reinvestment risk Short-term AND/OR High-coupon Bonds Low High Long-term AND/OR Low-coupon Bonds High Low © 2019 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Semiannual Bonds 1. Multiply years by 2: Number of periods = 2N 2. Divide nominal rate by 2: Periodic rate (I/YR) = rd/2 3. Divide annual coupon by 2: PMT = Annual coupon/2 INPUTS 2N rd/2 OK cpn/2 OK N I/YR PV PMT FV OUTPUT © 2019 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. What is the value of a 10-year, 10% semiannual coupon bond, if rd = 13%? 1. Multiply years by 2: N = 2 x 10 = 20 2. Divide nominal rate by 2: I/YR = 13/2 = 6.5 3. Divide annual coupon by 2: PMT = 100/2 = 50 INPUTS 20 6.5 N I/YR OUTPUT PV 50 1000 PMT FV -834.72 Excel: =PV(.065,20,50,1000) © 2019 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Would you prefer to buy a 10-year, 10% annual coupon bond or a 10-year, 10% semiannual coupon bond, all else equal? The semiannual bond’s effective rate is: M 2 ? rNOM ? ? 0.10 ? EFF% = ?1 + ? ? 1 = ?1 + ? ? 1 = 10.25% M 2 ? ? ? ? Excel: =EFFECT(.10,2) = 10.25% 10.25% > 10% (the annual bond’s effective rate),
so you would prefer the semiannual bond.
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If the proper price for this semiannual bond is
$1,000, what would be the proper price for the
annual coupon bond?
? The semiannual bond has a 10.25% effective
rate, so the annual bond should earn the same
EAR. At these prices, the annual and
semiannual bonds are in equilibrium.
INPUTS
OUTPUT
10
10.25
N
I/YR
PV
100
1000
PMT
FV
-984.80
Excel: =PV(.1025,10,100,1000)
© 2019 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
A 10-year, 10% semiannual coupon bond selling for
$1,135.90 can be called in 4 years for $1,050, what
is its yield to call (YTC)?
? The bond’s yield to maturity is 8%. Solving for
the YTC is identical to solving for YTM, except
the time to call is used for N and the call
premium is FV.
INPUTS
8
N
OUTPUT
I/YR
-1135.90
50
1050
PV
PMT
FV
3.568
Excel: =RATE(8,50,-1135.90,1050)
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Yield to Call
? 3.568% represents the periodic semiannual
yield to call.
? YTCNOM = rNOM = 3.568% x 2 = 7.137% is the
rate that a broker would quote.
? The effective yield to call can be calculated.
• YTCEFF = (1.03568)2 – 1 = 7.26%
• Excel: =EFFECT(.07137,2) = 7.26%
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If you bought these callable bonds, would you be
more likely to earn the YTM or YTC?
? The coupon rate = 10% compared to YTC =
7.137%. The firm could raise money by selling
new bonds which pay 7.137%.
? Could replace bonds paying $100 per year with
bonds paying only $71.37 per year.
? Investors should expect a call, and to earn the
YTC of 7.137%, rather than the YTM of 8%.
© 2019 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
When is a call more likely to occur?
? In general, if a bond sells at a premium, then
(1) coupon > rd, so (2) a call is more likely.
? So, expect to earn:
• YTC on premium bonds.
• YTM on par and discount bonds.
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Default Risk
? If an issuer defaults, investors receive less than
the promised return. Therefore, the expected
return on corporate and municipal bonds is less
than the promised return.
? Influenced by the issuer’s financial strength and
the terms of the bond contract.
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Evaluating Default Risk:
Bond Ratings
Moody’s
Investment Grade
Aaa Aa A Baa
Junk Bonds
Ba B Caa C
S&P
AAA AA A BBB
BB B CCC C
Bond ratings are designed to reflect the probability of
a bond issue going into default.
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Factors Affecting Default Risk and Bond Ratings
? Financial performance
• Debt ratio
• TIE ratio
• Current ratio
? Qualitative factors: Bond contract terms
•
•
•
•
Secured vs. unsecured debt
Senior vs. subordinated debt
Guarantee and sinking fund provisions
Debt maturity
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Other Factors Affecting Default Risk
? Miscellaneous qualitative factors
• Earnings stability
• Regulatory environment
• Potential antitrust or product liabilities
• Pension liabilities
• Potential labor problems
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Chapter 11 Bankruptcy
? If company can’t meet its obligations…
• It files under Chapter 11 to stop creditors from
•
•
foreclosing, taking assets, and closing the
business and it has 120 days to file a
reorganization plan.
Court appoints a “trustee” to supervise
reorganization.
Management usually stays in control.
? Company must demonstrate in its
reorganization plan that it is “worth more alive
than dead.”
• If not, judge will order liquidation under Chapter
7.
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Priority of Claims in Liquidation
1. Secured creditors from sales of secured assets
2. Trustee’s costs
3. Wages, subject to limits
4. Taxes
5. Unfunded pension liabilities
6. Unsecured creditors
7. Preferred stock
8. Common stock
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Reorganization
? In a liquidation, unsecured creditors generally
receive nothing. This makes them more willing
to participate in reorganization even though
their claims are greatly scaled back.
? Various groups of creditors vote on the
reorganization plan. If both the majority of the
creditors and the judge approve, the company
“emerges” from bankruptcy with lower debts,
reduced interest charges, and a chance for
success.
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End of Chapter 7
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Cover image attribution: “Finance District” by Joan Campderrós-i-Canas (adapted) https://flic.kr/p/6iVMd5

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Bond Valuation

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