Broke Benjamin Co. has a bond outstanding that makes semiannual payments with a coupon rate of 6.2 percent. The bond sells for $1,020.37 and matures in 18 years. The par value is $1,000. What is the YTM of the bond?

What is the YTM of the bond?

3,01 % Semiannual rate

6,02% Anual rate

Explanation:

To know the YTM of the bond we need first to calculate the Present Value of the Principal and then through the annuity method calculate the Present Value of the coupons.

Bond Value

Principal Present Value = F / (1 + r) ^t

Coupon Present Value = C x [1 - 1 / (1 + r) ^t] / r

As the payments of the coupons are semiannual we could calculate the present value of the bonds using a semiannual rate and a semiannual coupon, which will be coupon of usd 31,0 and a rate of 3,1%.

YTM = $344 + $676 = $1,020,37

Bond $1,000

Coupon $62,00

Annual Rate 6,2%

Years 18

Semiannual rate 3,01%

Period 36

Present Value of Bonds $344 = 1,000 / (1+0,0301) ^36

Bond 1.000

Semiannual Rate 3,01%

Periods 36

Present Value of Coupons $676 = 31 x 21,81

21,81 = [1 - 1 / (1+0,0301) ^36 ] / 0,031

Bond 1.000

Semiannual Rate 3,01%

Periods 36