Build a Model Solution 11/26/2018
Chapter: 5
Problem: 24
Basic Input Data:
Years to maturity:
20
Periods per year:
2
Periods to maturity:
40
Coupon rate:
8%
Par value:
$1,000
Periodic payment:
$40
Current price
$1,100
Call price:
$1,040
Years till callable:
5
Periods till callable: 10
a. What is the bond’s yield to maturity?
b. What is the bond’s current yield?
Current yield = Ann. Coupon / Price Hint: Write formula in words.
Current yield = $80 /$1,100 Hint: Cell formulas should refer to Input Section
Current yield = 7.27% (Answer)
c. What is the bond’s capital gain or loss yield?
Cap. Gain/loss yield = YTM –
Current yield
Hint: Write formula in words.
Cap. Gain/loss yield = 7.06% –7.27% Hint: Cell formulas should refer to Input Section
Cap. Gain/loss yield = -0.21% (Answer)
Note that this is an economic loss, not a loss for tax purposes.
d. What is the bond’s yield to call?
NOW ANSWER THE FOLLOWING NEW QUESTIONS:
Nominal market rate, r: 8%
Value of bond if it’s not called: $1,000.00
Value of bond if it’s called: $1,027.02 The bond would not be called unless r<coupon.
We can use the two valuation formulas to find values under different r’s, in a 2-output data table, and then use an IF
statement to determine which value is appropriate:
Actual value,
Not called Called considering
Rate, r $1,000.00 $1,027.02 call likehood:
0% $2,600.00 $1,440.00 $1,440.00
2% $1,985.04 $1,320.35 $1,320.35
4% $1,547.11 $1,212.47 $1,212.47
6% $1,231.15 $1,115.07 $1,115.07
e. How would the price of the bond be affected by changing the going market interest rate? (Hint: Conduct a
sensitivity analysis of price to changes in 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.)
Value of Bond If:
A 20-year, 8% semiannual coupon bond with a par value of $1,000 may be called in 5 years at a call price of
$1,040. The bond sells for $1,100. (Assume that the bond has just been issued.)
Basic info:
Settlement (today)
10/25/2019
Maturity
7/1/2029 7/1/2024 Call date
Coupon rate
12%
Refer to this chapter’s Tool Kit for information about how to use Excel’s bond valuation functions. The model finds the price
of a bond, but the procedures for finding the yield are similar. Begin by setting up the input data as shown below:
f. Now assume the date is 10/25/2019. Assume further that a 12%, 10-year bond was issued on 7/1/2019, pays
interest semiannually (January 1 and July 1), and sells for $1,100. Use your spreadsheet to find the bond’s yield.