Ch 09-19 Build a Model Solution								3/5/2001
Chapter 9. Solution to Ch 09-19 Build a Model
Rework Problem 9-9 using a spreadsheet. After completing questions a through d, answer the new question.
9-9. A 10-year 12 percent semiannual coupon bond, with a par value of $1,000, may be called in 4
years at a call price of $1,060. The bond sells for $1,100. (Assume that the bond has just been
issued.)
Work parts a through d with a spreadsheet. You can also work these parts with a calculator to check your
spreadsheet answers if you aren't confidient of your spreadsheet solution. You must then go on to work the
remaining parts with the spreadsheet.
a. What is the bond's yield to maturity?
Basic Input Data:
Years to maturity:		10
Periods per year:		2
Periods to maturity:		20
Coupon rate:		12%
Par value:		$1,000
Periodic payment:		$60
Current price		$1,100
Call price:		$1,060
Years till callable:		4
Periods till callable:		8
YTM =	10.37%		This is a nominal rate, not the effective rate. Nominal rates are generally
			quoted.
b. What is the bond's current yield?
Current yield =		Ann. Coupon /		Price
		$120	/	$1,100
		10.91%
c. What is the bond's capital gain or loss yield?
Cap. Gain/loss yield =		YTM	-	Current yield
Cap. Gain/loss yield =		10.37%	-	10.91%
Capital loss yield =		-0.54%
Note that this is an economic loss, not a loss for tax purposes.
d. What is the bond's yield to call?
Here we can again use the Rate function, but with data related to the call.
YTC =	5.07%
The YTC is much lower than the YTM because if the bond is called, the buyer will lose the difference between
the call price and the current price in just 4 years, and that loss will offset much of the interest imcome. Note
too that the bond is likely to be called and replaced, hence that the YTC will probably be earned.
NOW ANSWER THE FOLLOWING NEW QUESTIONS:
e. How would the price of the bond be affected by changing interest rates? (Hint: Conduct a sensitivity analysis of
price to changes in the yield to maturity, which is also the going market interest rate for the bond. Assume
that the bond will be called if and only if the going rate of interest falls below the coupon rate. That is an
oversimplification, but assume it anyway for purposes of this problem.)
Nominal market rate, k:			12%
Value of bond if it's not called:			$1,000.00
Value of bond if it's called:			$1,037.64	The bond would not be called unless k<coupon rate = 12%.
We can use the two valuation formulas to find values under different k's, in a 2-output data table, and then use an IF
statement to determine which value is appropriate:
	Value of Bond If:		Actual value,		Hint: Use function Wizard and pick IF function.
	Not called	Called	considering
Rate, k	$1,000.00	$1,037.64	call likehood:
0%	$2,200.00	$1,540.00	$1,540.00
2%	$1,902.28	$1,437.99	$1,437.99
4%	$1,654.06	$1,344.23	$1,344.23
6%	$1,446.32	$1,257.96	$1,257.96
8%	$1,271.81	$1,178.50	$1,178.50
10%	$1,124.62	$1,105.24	$1,105.24
12%	$1,000.00	$1,037.64	$1,000.00
14%	$894.06	$975.21	$894.06
16%	$803.64	$917.48	$803.64
18%	$726.14	$864.07	$726.14
20%	$659.46	$814.59	$659.46
We can graph the above data to get another idea of the bond's price sensitivity.
										Settlement (today)		10/25/2000
										Maturity		1/1/2020
										Coupon rate		8.00%
										Going rate, k		7.00%
										Par value		100
If you study the graph, you will see that the "not called" situation shows the greatest price sensitivity, the "called"										Frequency (for semiannual)		2
the least sensitivity, and the "modified" falls somewhere in between. Actually, the modified situation, which is										Basis (360 or 365 day year)		0
representative of most actual bonds because most bonds are callable, shows that bondholders will not win big if
rates fall because then the bond will be called, but they do lose big if rates rise because then the bonds will not be
called. In terms of the graph, the sensitivity line is not steep where we want it to be steep, to the left of the 12%
coupon rate, but it is steep where we do not want it to be steep, to the right of 12%. The clear conclusion is
that callable bonds are riskier than non-callable bonds, and their risk is asymmetric.
										Basic Input Data:
f. Now assume the date is 10/25/2001. Assume further that our 12%, 10-year bond was issued on 7/1/2001, will										Years to maturity:		10
mature on 7/1/2011, is callable on 7/1/2005 for $1,060, pays interest semiannually (January 1 and July 1), and										Periods per year:		2
sells for $1,100. Use your spreadsheet to find (a) the bond’s yield to maturity and (b) its yield to call.										Periods to maturity:		20
										Coupon rate:		12%
Refer to 07model for information about how to use Excel's bond valuation functions. The model finds the price of a										Par value:		$1,000
bond, but the procedures for finding the yield are similar. Begin by setting up the input data as shown below:										Periodic payment:		$60
				Call info:						Current price		$1,100
Settlement (today)			10/25/2001							Call price:		$1,060
Maturity			7/1/2011	7/1/2005	True maturity for YTM, call date for YTC					Years till callable:		4
Coupon rate			12%							Periods till callable:		8
Current price (% of par)			110
Redemption (par value)			100	106	Par for YTM, Call price for YTC
Frequency (for semiannual)			2
Basis (360 or 365 day year)			0
With the input data set, put the pointer on D133 and then click fx, Financial, YIELD, OK to get the yield menu. Fill in
the menu by using the point-and-click procedure, and then click OK to get the bond's yield, 10.34%:
Yield to Maturity:		10.34%	The completed menu is shown below.
Tip: Use Yield function.
To find the yield to call, use the YIELD function, but with the call price rather than par value as the redemption
value, and the call date rather than the maturity date.
Yield to call:		10.06%
You could also use Excel's "Price" function to find the value of a bond between interest payment dates.