Question

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:

IRR = 10.75%

Explanation:

The yield to maturity will be the rate at which the present value of the coupon payment and the maturity equals the market price.

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 57.50

time 24

$57.5 \times \frac{1-(1+r)^{-24} }{r} = PV$

PVc

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity   1,000.00

time   24.00

 PVm

$\frac{1000}{(1 +r)^{24} } = PV$  

PV c $765.3158

PV m  $284.6842

Total $1,050.0000

rate ?

The only way to solve this equation is with trial and error. Because of technological advance we can do it using excel goal seek.

we write the formula for the PV of an ordinary annuity

and the formula for a lump sum

below them we add them both together

then we define a cell for the rate

and we determinate that we want the cell which contain the sum to match 1,050 changing the rate cell

this will give us an IRR of 0.10749 = 10.75%