Question

A firm has an issue of $1,000 par value bonds with a 8 percent stated interest rate outstanding. The issue pays interest annually and has 10 years remaining to its maturity date. If bonds of similar risk are currently earning 8 percent, the firm's bond will sell for __________ today.

Answer 1

Answer: $1268.20

Explanation:

value of the bond today = Present value of coupon (interest) payments + present value of principal = 120[PVOAIF8%, 10] + 1000[PVIF8%, 10] =1,268

Answer 2

The firm's bond having an issue price of 1,000 with an 8% interest rate will be sold today for $1,000.

Computation:

Given,

$PV$ Par value =$1,000

$r$ Interest rate =8%

$n$ Number of years =10 years

$\begin{aligned}\text{Coupon Amount}&=\text{Par Value}\times\text{Interest Rate}\\&=\ 1,000\times8\%\\&=\ 80\end{aligned}$

First, the Present Value of the interest payments will be determined:

The formula used is:

$PV=\dfrac{\text{Coupon Amount}}{(1+\frac{r}{n})^{n.t}}$

The formula will be repeated for 10 years and the values will be cumulated.

$\begin{aligned}PV(\text{Coupon})&=\dfrac{\ 80}{(1+0.08)^1}+\dfrac{\ 80}{(1+0.08)^2}+\dfrac{\ 80}{(1+0.08)^3}+...+\dfrac{\ 80}{(1+0.08)^{10}}\\&=\ 536.81\end{aligned}$

Now, the Present Value of the principal amount will be determined:

$\begin{aligned}PV&=\dfrac{\text{Par Value}}{(1+\frac{r}{n})^{n.t}}\\&=\dfrac{\ 1,000}{(1+0.08)^{20}}\\&=\ 463.19\end{aligned}$

Now, the value of a bond is determined:

$\begin{aligned}\text{Sale Value of Bond}&=PV\text{Coupon}+PV\\&=\ 536.81+\ 463.19\\&=\ 1,000\end{aligned}$

So, the value of a bond for selling today is $1,000.

To know more about the present value of a bond, refer to the link:

https://brainly.com/question/25365327