Question

Fizgerald's 30-year bonds pay 7 percent interest annually on a $1,000 par value. If the bonds sell at $925, what is the bond's yield to maturity? What would be the yield to maturity if the bonds paid interest semiannually? Explain the difference..

Answer 1

Annual Coupon Payment: Annual Coupon Rate = 7%, Bond Tenure = 30 years, Par Value = $ 1000, Bond Price = $ 925

Annual Coupon = 0.07 x 1000 = $ 70

Let the yield to maturity be y %

Therefore, 925 = 70 x (1/y) x [1-{1/(1+y)^(30)}] + 1000 / (1+y)^(30)

Using EXCEL's Goal Seek Function to solve the above equation, we get:

y = 0.07644 or 7.644 %

Semi-Annual Coupon Payment:

nnual Coupon Rate = 7%, Bond Tenure = 30 years or (30 x 2) = 60 half-years, Par Value = $ 1000, Bond Price = $ 925

Semi-Annual Coupon = 0.5 x 0.07 x 1000 = $ 35

Let the yield to maturity be 2r %

Therefore, 925 = 35 x (1/r) x [1-{1/(1+r)^(60)}] + 1000 / (1+r)^(60)

Using EXCEL's Goal Seek Function to solve the above equation, we get:

r = 0.038203 or 3.8203 % ~ 3.82 %

Yield to Maturity = 2 x r = 2 x 3.82 = 7.641 %