Question

Marwick Corporation issues 15%, 5 year bonds with a par value of $1,070,000 and semiannual interest payments. On the issue date, the annual market rate for these bonds is 13%. What is the bond's issue (selling) price, assuming the Present Value of $1 factor for 6.5% and 10 semi-annual periods is 0.5327 and the Present Value of an Annuity factor for the same rate and period is 7.1888?

Answer 1

Answer:

The bond's issue (selling) price = $1,146,890.2

Explanation:

The selling price of the bond is equivalent to the present value of all the cash flows that are likely to accrue to an investor once the bond is bought. These cash-flows are the periodic coupon payments that are paid semi anually and the par value of the bond that will be paid at the end of the 10 years.

During the 5 years, there are 10 equal periodic coupon payments that will be made. In each  year, the total coupon paid will be $1,070,000*0.15= 160,500$ and this payment will be split into two equal payments equal to  $\frac{160,500}{2}= 80,250$. this stream of cashflows is an ordinary annuity

The periodic annual market rate is equal to $\frac{0.13}{2}=0.065$

The  PV of the cashflows = PV of the coupon payments + PV of the par value of the bond

=$80,250*PV Annuity Factor for 10 years at 6.5% + $\ 1,070,000*\frac{1}{(1+0.065)^10}$

$= 80,250*7.1888+ 1,070,000*0.5327 = 1,146,890.2$