Question

Dufner Co. issued 15-year bonds one year ago at a coupon rate of 7.1 percent. The bonds make semi-annual payments. If the YTM on these bonds is 5.4 percent, what is the current dollar price assuming a par value of $1,000?

Answer 1

Answer:

Total $1,173.2544

Explanation:

The price of the bond will be equivalent to the coupon payment and maturity discounted at the YTM

Coupon payment PV will be an annuity:

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

C 35.50 (1,000 x 7.1% / 2 )

time 30 (15 years x 2 payment per year)

rate 0.027 (YTM /2 )

$35.5 \times \frac{1-(1+0.027)^{-30} }{0.027} = PV$

PV $723.5919

The maturity will be the present value of a lump sum

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

Maturity   1,000.00

time   30.00

rate  0.027

$\frac{1000}{(1 + 0.027)^{30} } = PV$  

PV   449.66

We add bot h to gett the market value

PV c $723.5919

PV m  $449.6625

Total $1,173.2544