Before-tax cost of debt and after-tax cost of debt Personal Finance Problem Davi

Question

Before-tax cost of debt and after-tax cost of debtPersonal Finance ProblemDavid Abbot is interested in purchasing a bond issued by Sony. He has obtained the following information on the security:

Sony Bond

Par value $1000

5.55.%

20%

$910

Years to maturity 10

Answer the following questions:

a.Calculate the before-tax cost of the Sony bond using the bond's yield to maturity (YTM).

b.Calculate the after-tax cost of the Sony bond given the corporate tax rate.

Sony Bond

Par value $1000

5.55.%

20%

$910

Years to maturity 10

Explanation / Answer

As we are not given whether annual or semi-annual coupons, I am wiritng both the cases

Case 1: Assuming semi-annual coupons,

Coupons=5.5%*1000/2=27.5

Price=27.5/(1+ytm/2)+27.5/(1+ytm/2)^2.......................27.5/(1+ytm/2)^20+1000/(1+ytm/2)^20

=>910=27.5/(1+ytm/2)+27.5/(1+ytm/2)^2.......................27.5/(1+ytm/2)^20+1000/(1+ytm/2)^20

=>ytm=6.7524%

So, before-tax cost of bond=6.7524%

after-tax cost of bond=6.7524%*(1-20%)=5.4019%

Case 2: Assuming annual coupons,

Coupons=5.5%*1000=55

Price=55/(1+ytm)+55/(1+ytm)^2.......................55/(1+ytm)^10+1000/(1+ytm)^10

=>910=55/(1+ytm)+55/(1+ytm)^2.......................55/(1+ytm)^10+1000/(1+ytm)^10

=>ytm=12.6083%

So, before-tax cost of bond=12.6083%

after-tax cost of bond=12.6083%*(1-20%)=10.0866%

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