Company A wants to issue new 20-year bonds for needed projects. The company currently has 10 percent coupong bonds on the market that sell for $1,063, make semiannual payments, and mature in 20 years. What coupon rate should the company set on its new bonds if it wants them to sell at par?

To determine the coupon rate that Company A should set on its new bonds in order for them to sell at par, we need to use the information provided about the existing bonds.

First, let's understand the concept of par value. Par value, also known as face value, is the amount that is paid to the bondholder at the bond's maturity. In this case, we are looking for the coupon rate that will make the new bonds sell at par, which means their price will be equal to their face value.

Given that the existing bonds are selling for $1,063, we need to calculate the present value of these bonds. The present value is the current worth of future cash flows.

The existing bonds have a coupon rate of 10%, a maturity of 20 years, and make semiannual payments. This means the bondholders receive interest payments twice a year.

To calculate the present value, we can use the present value formula for a bond:

PV = (C / (1 + r)^n) + (C / (1 + r)^(n-1)) + ... + (C / (1 + r)^2) + (C / (1 + r)) + (C + F) / (1 + r)^n

Where PV is the present value, C is the coupon payment, r is the discount rate (which is the required rate of return for similar bonds), n is the number of periods, and F is the face value.

In this case, n is 20 years, r is unknown (the coupon rate we are solving for), and F is $1,000 (since par value is usually set at $1,000).

The coupon payment (C) is calculated as the coupon rate multiplied by the face value (F):

C = Coupon Rate * Face Value

First, let's calculate the coupon payment:

C = 0.10 * $1,000 = $100

Now, let's calculate the present value of the existing bonds:

PV = ($100/ (1 + r)^1) + ($100 / (1 + r)^2) + ... + ($100 / (1 + r)^39) + ($100 + $1,000) / (1 + r)^40

To simplify the calculation, we can use financial software or a financial calculator to find the value of r that makes the present value equal to $1,063.

To determine the coupon rate that should be set on the new bonds for them to sell at par, we need to calculate the coupon rate on the existing bonds. Here are the steps:

Step 1: Calculate the price of the existing bonds at par value:
The existing bonds are selling for $1,063, which is above their par value. Since the bonds make semi-annual payments and mature in 20 years, there are 40 coupon payments remaining (2 payments per year for 20 years).
Par Value = $1,000 (since bonds are selling at par)
Semi-Annual Coupon Payment = (Coupon Rate x Par Value) / 2
Price at Par Value = (Semi-Annual Coupon Payment x PVIFA) + (Par Value / (1 + (YTM / 2))^40)
$1,063 = (Semi-Annual Coupon Payment x PVIFA) + ($1,000 / (1 + (YTM / 2))^40

Step 2: Calculate the coupon payment on the existing bonds:
We can rearrange the equation from the previous step to solve for the semi-annual coupon payment.
Semi-Annual Coupon Payment = ($1,063 - (Par Value / (1 + (YTM / 2))^40)) / PVIFA

Step 3: Calculate the coupon rate on the existing bonds:
Coupon Payment = (Coupon Rate x Par Value) / 2
Coupon Rate = (Coupon Payment x 2) / Par Value

Once we have the coupon rate on the existing bonds, we can set the same rate on the new bonds if the company wants them to sell at par.