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Solution
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?
Peridodic YTM = 3.53%
Annualized Nominal YTM = 7.06% Hint: This is a nominal rate, not the effective rate. Nominal rates are generally quoted.
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.)
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:
The YTC is 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.
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:
You could also use Excel's "Price" function to find the value of a bond between interest payment dates.
7/16/2015
Hint: This is a nominal rate, not the effective rate. Nominal rates are generally quoted.
Hint: Cell formulas should refer to Input Section
Hint: Cell formulas should refer to Input Section
This is a nominal rate, not the effective rate. Nominal rates are generally quoted.
The YTC is 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.
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.)
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
The YTC is 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.
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.)
