Question

BP has a bond outstanding with 15 years to maturity, a $1,000 par value, a coupon rate of 6.8%, with coupons paid semiannually, and a price of 95.49 (percent of par).

What is the cost of debt?

answer 3+ decimals

Answer 1

Solution

Price of bond=Present value of coupon payments+Present value of face value

Price of bond=Coupon payment*((1-(1/(1+r)^n))/r)+Face value/(1+r)^n

Here

Face value =1000

n=number of periods to maturity=15*2=30

r-intrest rate per period=Semiannual YTM

Semi annual Coupon payment=coupon rate *face value/2=6.8%*1000/2=34

Price of bond=1000*95.49%=954.9

Putting values in formuLA

954.9=34*((1-(1/(1+r)^30))/r)+1000/(1+r)^30

Solving we get

r=3.6498%(Semiannual YTM)

Now to find the cost of debt,the effective rate of intrest annually will be calculated

Annual effective rate=(1+semiannual rate)^2-1

Annual effective rate=(1+3.6498%)^2-1

Annual effective rate=7.433%

Thus cost of debt=7.433%