Question

Yield to Maturity and Call with Semiannual Payments Thatcher Corporation's bonds will mature in 12 years. The bonds have a face value of $1,000 and an 11.5% coupon rate, paid semiannually. The price of the bonds is $1,050. The bonds are callable in 5 years at a call price of $1,050. Do not round intermediate calculations. Round your answers to two decimal places. What is their yield to maturity?

Answer 1

Answer:

rounding to two decimal places: 11.11%

Explanation:

we can se the approximate formula for YTM

$YTM = \frac{C + \frac{F-P}{n }}{\frac{F+P}{2}}$

C=  57.5 (1,000 x 11.5%/2)

Face value = 1000

P= 1050 (market value)

n= 24 (12 years x 2 payment per year)

$YTM = \frac{57.5 + \frac{1,00 - 1,050}{24}}{\frac{1,000+1,050}{2}}$

semiannual YTM =  5.4065041%

This is a semiannual rate as we consider semiannula payment.

We need to convert into annual rate:

$(1 + 0.054065041)^{2}  - 1$

YTM 11.1053109921343000%

rounding to two decimal places: 11.11%