Question

Bond Valuation and Changes in Maturity and Required Returns Suppose Hillard Manufacturing sold an issue of bonds with a 10-year maturity, a $1,000 par value, a 10% coupon rate, and semiannual interest payments. Two years after the bonds were issued, the going rate of interest on bonds such as these fell to 7%. At what price would the bonds sell? Round your answer to the nearest cent. $

Answer 1

Answer:

It will be sold at $1,186.71

Explanation:

We will calculate the present value of the cuopon payment and the maturity at the new market rate of 7%

The coupon payment will be calcualte as the PV of ordinary annuity

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

C $50 (1,000 x 10%/2 as there are 2 payment per year)

time    16 (8 years x 2 payment per year)

rate     0.035 (7% rate / 2 payment per year)

$50 \times \frac{1-(1+0.035)^{-16} }{0.035} = PV$

PV $604.7058

The maturity will be calculate as the PV of a lump sum

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

Maturity  1,000.00

time         8 years

rate  0.07

$\frac{1000}{(1 + 0.07)^{8} } = PV$  

PV   582.01

The market price will be the sum of both:

PV cuopon $604.7058

PV maturity  $582.0091

Total $1,186.7149