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Call Provisions and Sinking Funds
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Annual Pmt: $100
Par value = FV: $1,000
menu items as shown in our snapshot in the screen shown just below.
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A B C D E F G H
Situation
Finding the “Fair Value” of a Bond
First, we list the key features of the bond as “model inputs”:
Years to Mat: 10
Coupon rate: 10%
Chapter 5. Mini Case
Sam Strother and Shawna Tibbs are vice-presidents of Mutual of Seattle Insurance Company and co-directors
company‘s pension fund management division. A major new client, the Northwestern Municipal Alliance, ha
requested that Mutual of Seattle present an investment seminar to the mayors of the represented cities, and S
and Tibbs, who will make the actual presentation, have asked you to help them by answering the following que
Because the Boeing Company operates in one of the league’s cities, you are to work Boeing into the present
pay more and lenders require more on callable bonds.
In a sinking fund provision, the issuer pays off the loan over its life rather than all at the maturity date. A si
reduces the risk to the investor and shortens the maturity. This is not good for investors if rates fall after is
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A B C D E F G H
(2.) What would happen to the value of the 10-year bond over time if the required rate of return remained a
$1,500
$2,000
$2,500
0% 5% 10% 15% 20%
Interest Rate Sensitivity of a 10-Year Bond
Value at 13%
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4$1,143 $1,000 $880
5$1,123 $1,000 $894
6$1,102 $1,000 $911
7$1,079 $1,000 $929
8$1,054 $1,000 $950
9$1,028 $1,000 $973
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$581
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$640
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$917
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A B C D E F G H
N7% 10% 13%
0$1,211 $1,000 $837
1$1,195 $1,000 $846
2$1,179 $1,000 $856
3$1,162 $1,000 $867
10 $1,000 $1,000 $1,000
You pick the rate for
Your choice:
20%
Resulting bond pri
$597
$616
$667
$701
$741
$789
$847
Use the Rate function to solve the problem.
Years to Mat: 10
Coupon rate: 9%
Value of Bond in Given Year:
If rates fall, the bond goes to a premium, but it moves towards par as maturity approaches. The reverse hold i
rise and the bond sells at a discount. If the going rate remains equal to the coupon rate, the bond will cont
at par. Note that the above graph assumes that interest rates stay constant after the initial change. That is
unlikely–interest rates fluctuate, and so do the prices of outstanding bonds.
$200
$400
$600
$800
$1,000
$1,400
Price
Value of the bond over time Rates fall to 7%
Rates stay the same
Rates increase to 13%
Your choice
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account for any capital gains or losses that will be realized if the bond is held to maturity or call.
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Capital Gains Yield = 0.76%
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Periods to maturity = 10*2 = 20
Coupon rate: 10%
Use the Rate function with adjusted data to solve the problem.
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A B C D E F G H
Current and Capital Gains Yields
Par value $1,000.00
Coupon rate: 9%
Current Yield =
10.15%
Annual Pmt: $90.00
Current price: $887.00
YTM =
Current Yield
+ Capital Gains Yield
Capital Gains Yield = YTM – Current Yield
Capital Gains Yield = 10.91% – 10.15%
Bonds with Semiannual Coupons
Semiannual pmt = $100/2 = $50.00 PV = $834.72
Future Value: $1,000.00
Periodic rate = 13%/2 = 6.5%
Note that the bond is now more valuable, because interest payments come in faster.
Excel Bond Functions
(2.) What are the total return, the current yield, and the capital gains yield for the discount bond? (Assume
is held to maturity and the company does not default on the bond.)
Since most bonds pay interest semiannually, we now look at the valuation of semiannual bonds. We must
modifications to our original valuation model: (1) divide the coupon payment by 2, (2) multiply the years to m
2, and (3) divide the nominal interest rate by 2.
semiannual payment, 10 percent coupon bond if nominal rd = 13%.
The current yield is the annual interest payment divided by the bond’s current price. The current yield prov
information regarding the amount of cash income that a bond will generate in a given year. However, it doe
The current yield provides information on a bond’s cash return, but it gives no indication of the bond’s tota
see this, consider a zero coupon bond. Since zeros pay no coupon, the current yield is zero because there
interest income. However, the zero appreciates through time, and its total return clearly exceeds zero.
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Value of bond = $83.6307 or $836.31
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Going rate, r 13.00%
Redemption (par value) 100
Frequency (for semiannual) 2
Basis (360 or 365 day year) 0
Accrued interest = $2.3333 or $23.33
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Coupon rate 10.00%
Redemption (par value) 100
Frequency (for semiannual) 2
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A B C D E F G H
Settlement (today) 1/1/2014
Maturity 12/31/2023
Coupon rate 10.00%
Going rate, r 13.00%
Redemption (par value) 100
Frequency (for semiannual) 2
Basis (360 or 365 day year) 0
Value of bond = $83.4737 or $834.74
Settlement (today) 3/25/2014
Maturity 12/31/2023
Coupon rate 10.00%
Going rate, r 13.00%
Redemption (par value) 100
Frequency (for semiannual) 2
Basis (360 or 365 day year) 0
Issue date 1/1/2014
First interest date 6/30/2014
Settlement (today) 3/25/2014
Maturity 12/31/2023
Coupon rate 10.00%
Suppose the bond’s price is $1,150. You can also calculate the yield using the YIELD function, as shown be
Curent price 1,150.00$
Settlement (today) 1/1/2014
Maturity 12/31/2023
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years to maturity is replaced with years to call, and the maturity value is replaced with the call price.
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Call price = FV $1,050.00
Par value $1,000.00
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k. Describe a way to estimate the inflation premium (IP) for a T-Year bond. Answer: See Chapter 5 Mini Ca
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A B C D E F G H
Yield 7.81%
Use the Rate function to solve the problem.
Number of semiannual periods to call: 10
Seminannual coupon rate: 5% Semiannual Rate = I = YTC = 3.77%
Seminannual Pmt: $50.00 Annual nominal rate = 7.53%
Current price: $1,135.90
(1.) What is the bond’s nominal yield to call (YTC)?
(2.) If you bought this bond, do you think you would be more likely to earn the YTM or the YTC? Why?
l. What is a bond spread and how is it related to the default risk premium? How are bond ratings related to
risk? What factors affect a company’s bond rating? Answer: See Chapter 5 Mini Case Show.
i. Write a general expression for the yield on any debt security (rd) and define these terms: real risk-free rat
interest (r*), inflation premium (IP), default risk premium (DRP), liquidity premium (LP), and maturity risk pre
(MRP). Answer: See Chapter 5 Mini Case Show.
j. Define the real risk-free rate (r*). What security can be used as an estimate of r*? What is the nominal risk
(rRF)? What securities can be used as estimates of rRF? Answer: See Chapter 5 Mini Case Show.
same maturity, the one with the smaller coupon payment will have more interest rate sensitivity.
m. What is interest rate (or price) risk? Which bond has more interest rate risk, an annual payment 1-year bon
year bond? Why?
h. Suppose a 10-year, 10 percent, semiannual coupon bond with a par value of $1,000 is currently selling for
producing a nominal yield to maturity of 8 percent. However, the bond can be called after 5 years for a price
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As the interst rate goes from 5% to 15%, the price changes are bigger for the 10-year bond.
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n. What is reinvestment rate risk? Which has more reinvestment rate risk, a 1-year bond or a 10-year bond?
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A B C D E F G H
Your Choice of Maturity
Years to Mat: 10 Rate Price Rate Price Rate
Coupon rate: 10% $966.65 $946.77
Annual Pmt: $100.00 5.0% 1,216.47 5.0% $1,386.09 5.0%
Current price: $946.77 7.0% 1,123.01 7.0% $1,210.71 7.0%
Par value = FV: $1,000.00 10.0% 1,000.00 10.0% $1,000.00 10.0%
YTM = 10.9% 13.0% 894.48 13.0% $837.21 13.0%
Years to Mat: 1
Coupon rate: 10%
Annual Pmt: $100.00
Current price: $991.88
Par value = FV: $1,000.00
YTM = 10.9%
rd10-Year P Change 1-Year P Change
5.0% $1,048 $1,386
4.8% 38.6%
10.0% $1,000 $1,000
4.5% 33.5%
15.0% $957 $749
p. What is the term structure of interest rates? What is a yield curve?
1-Yr Ma
10-Yr Maturity
o. How are interest rate risk and reinvestment rate risk related to the maturity risk premium? Answer: See
Mini Case Show.
$700.00
$800.00
$1,200.00
$1,300.00
$1,400.00
$1,500.00
5.0% 7.0% 10.0% 13.0% 15.0
YTM
10 Yr. versus 1 Yr.
Y
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A B C D E F G H
Hypothetical Inputs See to right for actual date use
Real risk free rate 3.00%
Expected inflation of 5% for the next 1 years.
Expected inflation of 6% for the next 1 years.
Expected inflation of 8% thereafter.
Hypothetical Treasury Yield Curve
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I J K L M N O P
10/28/2015
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I J K L M N O P
going rate is
ted inflation
a discount or
nterest rates.
ned at 13
tion? You
rates in cells
tually just
range of cells
(A73:B78).
the menu.
olumn input cell”