Question

# Company B had issued 10-year bonds a year ago at the coupon rate 4%. The bond...

Company B had issued 10-year bonds a year ago at the coupon rate 4%. The bond makes annual payments. The yield to maturity (YTM) of these bonds is 5%. The face value of the bond is \$1000.

Calculate the current bond price.

Company B has a second debt issue on the market, a zero coupon bond with 9.6 years left to maturity. The yield to maturity (YTM) of these bonds is 8 %. The face value of the bond is \$1000. Calculate the current bond price.

Refer back to previous two questions. If the market value of the 10-year bonds is \$ 18 million and the market value of the zero coupon bond is \$ 44 million (these are the two bond issues outstanding for the company B) what is the after tax cost of debt of company B? The tax rate is 30%. Express your answer as %.

Solution : - (1)

Time to Maturity of Bond = 9 Years

Yield to Maturity = 5%

Coupon Rate = 6%

Face Value of Bond = \$1,000

Coupon Payment = \$1,000 * 6% = \$60

Current Price of Bond = \$60 * PVAF ( 5% , 9 ) + \$1,000 * PVF ( 5% , 9 )

= ( \$60 * 7.108 ) + ( \$1,000 * 0.6446 )

= \$426.67 + \$644.61

= \$1,071.08

Current Price of Bond = \$1,071.08

(2)

Current Price of Zero Coupon Bond = Face Value / ( 1 + YTM )n

X = \$1,000 / ( 1 + 0.08 )9.6

X = \$1,000 / ( 1 + 0.08 )9 * ( 1 + 0.08 )0.6

= \$1,000 * 0.47734

= \$477.34

(3) Weight of 10- Year Bond = \$18 / ( 18 + 44 ) = 0.29

Weight of Zero Coupon Bond = 0.71

After tax cost of 10 - Year Bond = 5% * ( 1 - 0.30 ) = 3.50%

After tax cost of Zero Coupon Bond = 8% * ( 1 - 0.30 )= 5.60%

After tax cost of debt of Company B = ( 0.29 * 3.50% ) + ( 0.71 * 5.60% ) = 4.99%

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