Question

3. Consider the following semiannual bond: Coupon rate = 6.5% Maturity = 20 years Par value = $1,000 Market price = $1,035 Can be called in 8 years at $1,032.5 Can be called in 15 years at par Only put date in 8 years and putable at par value (1) What is the yield to maturity for this bond? (1 point) (2) What is the yield to first call? (1 point) (3) What is the yield to second call? (1 point) (4) What is the yield to worst for this bond? (2 points)

Answer 1

Answer to Finance Question 3(1)

Yield to Maturity.

First we will calculate the maturity value and the formula is shown below

Maturity Value = Face Value*(1+r)^n where "r" is interest rate per month and "n" is total period in months means "r"=6.5%/12=0.065/12 = 0.0054 and "n" is 20*12=240. Putting all the values in formula

Maturity Value = $1000*(1+0.065)^240

=$1000*(1.065)^240

=$3641.93

Market Price = $1035

Total earning = Maturity Value - Current Price

= $3641.93-$1035=$2606.93

Earning per year= Total earning divided by period

= 2606.93/20=$130.35

Yield = Earning per year divided by Market Price =( $130.35/1035)*100 = 12.59%

Hence the yield to maturity is 12.59%

Answer to Finance Question 3(2)

Yield to first call

First we will calculate the maturity value and the formula is shown below

Maturity Value = Face Value*(1+r)^n where "r" is interest rate per month and "n" is total period in months means "r"=6.5%/12=0.065/12 = 0.0054 and "n" is 8*12=96. Putting all the values in formula

Maturity Value = $1000*(1+0.065)^96

=$1000*(1.065)^96

=$1677

Market Price = $1035

Total earning = Maturity Value - Current Price

= $1677-$1035=$642

Earning per year= Total earning divided by period

= $642/8=$80.25

Yield = Earning per year divided by Market Price =( $80.25/1035)*100 = 7.75%

Hence the yield to First call is 7.75%

Answer to Finance Question 3(3)

Yield to Second call

First we will calculate the maturity value and the formula is shown below

Maturity Value = Face Value*(1+r)^n where "r" is interest rate per month and "n" is total period in months means "r"=6.5%/12=0.065/12 = 0.0054 and "n" is 15*12=180. Putting all the values in formula

Maturity Value = $1000*(1+0.065)^180

=$1000*(1.065)^180

=$2636.32

Market Price = $1035

Total earning = Maturity Value - Current Price

= $2636.32-$1035=$1601.32

Earning per year= Total earning divided by period

= $1601.32/15=$106.75

Yield = Earning per year divided by Market Price =( $106.75/1035)*100 = 10.31%

Hence the yield to Second call is 10.31%

Answer to Finance Question 3(4)i

First we need to understand the yield to worst meaning. Yield to worst means in any given scenario, what is the lowest yield.

Scenarios means the provision under the bond contract and in this question, yield on first call is the lowest hence the yield to first call is the yield to worst.

Babbel, D. F., Merrill, C., & Panning, W. (1997). Default risk and the effective duration of bonds. Financial Analysts Journal, 53(1), 35-44.

Dunetz, M. L., & Mahoney, J. M. (1988). Using duration and convexity in the analysis of callable bonds. Financial Analysts Journal, 44(3), 53-72.