Bond valuation
Nungesser Corporation’s outstanding bonds have a $1,000 par value, a 9 percent semiannual coupon, 8 years to maturity, and an 8.5 percent YTM. What is the bond’s price?
1060
To calculate the price of a bond, we can use the present value formula for a bond's cash flows. The cash flows in the case of a bond are the periodic coupon payments and the final maturity value.
The formula for calculating the price of a bond is:
Bond Price = (C / (1 + r)^1) + (C / (1 + r)^2) + ... + (C / (1 + r)^n) + (M / (1 + r)^n)
Where:
C = Coupon payment (in this case, semiannual coupon payment)
r = Yield to Maturity (YTM) rate (in this case, 8.5%, which is 8.5/2 = 4.25% semiannual rate)
n = Number of periods (in this case, 8 years to maturity, or 8 periods, and since coupons are paid semiannually, there will be 2 * 8 = 16 periods)
M = Maturity value (in this case, the par value of $1,000)
In this case, the bond has a $1,000 par value, and the coupon payments are semiannual, so we need to calculate the semiannual coupon payment.
Semiannual Coupon Payment = (Par Value * Coupon Rate) / Number of Payments per Year
= (1000 * 9%) / 2
= $45
Now, we can plug in these values into the bond pricing formula:
Bond Price = (45 / (1 + 4.25%)^1) + (45 / (1 + 4.25%)^2) + ... + (45 / (1 + 4.25%)^16) + (1000 / (1 + 4.25%)^16)
Using a financial calculator or spreadsheet software, we can calculate this sum to find the bond's price. The result will be the present value of all the coupon payments plus the present value of the maturity value.
Therefore, the bond's price can be calculated using the formula mentioned above.