Question

Whitesell Athletic Corporation's bonds have a face value of $1,000 and a 9% coupon paid semiannually; the bonds mature in 8 years. What current yield would be reported in The Wall Street Journal if the yield to maturity is 8%?

PLEASE SHOW ALL WORK

NO EXCEL

Answer 1

Face Value = $1,000

Coupon rate = 9%

Coupon paid = semi annually

Thus, semi annual coupon payments = $1,000*9%/2 = $45

Maturity (years) = 8

Thus, number of semi-annual payments = 8 * 2 = 16 payments

Yield to maturity = 8% per annum or 4% (8%/2) per semi-annual

Step 1: Find the current price of the bond

Current price of bond = Present value of coupon payments for 16 semi-annual payments + present value of face value of bond at the end of 16th payment

=(C*(1-(1+r)^T)/4)+(FV*1/(1+r)^T) where C = semi annual coupon payments of $45; r = semi annual Yield to maturity of 4%; T = tenure of 16; FV = face value of $1,000

=($45*(1-(1.04^-16))/4%)+($1,000*1/(1+4%)^16)

=$524.35+$533.91 = $1,058.26

Current price of the bond = $1,058.26

Step 2: Current yield

Current yield = Annual coupon payment / current price of the bond = $45/$1,058.26 = 4.252% semi annually or 8.50% annually