Question

1. Renfro Rentals has issued bonds that have an 8% coupon rate, payable semiannually. The bonds mature in 14 years, have a face value of $1,000, and a yield to maturity of 10%. What is the price of the bonds?

Answer 1

The formula to calculate price of a bond is:

$Price=C\left [ \frac{1-(1+r)^{-n}}{r} \right ]+\frac{Par\: value}{(1+r)^{n}}$

Where,

• C is the coupon payment
• r is the yield
• n is the time till maturity

The formula may seem complicated but all it is trying to do is to discount all future coupon payments and the final principal with the yield to maturity to calculate their present value.

Since, the bond is semiannual, coupon payment, time till maturity and yield will have to be adjusted.

$Semiannual \:coupon\: payment=\frac{Annual\: coupon \:payment}{2}=\frac{80}{2}$

So, semiannual coupon payment = $40

$Timeperiod = 2* no.\: of\: years=28$

$Semiannual\: yield = \frac{Annual\: yield}{2}=0.05$

Now, we substitute the values:

$Price=40\left [ \frac{1-(1+0.05)^{-28}}{0.05} \right ]+\frac{1000}{(1+0.05)^{28}}$

On solving, we get price = $851.02