Assume that Pelon Inc. has issued a 10 year maturity bond with a yield of 8%. Its coupon rate is 5% and the coupons are paid semi annually. Its par value is the value of this bond at the issue date?
To calculate the par value of the bond at the issue date, we need to understand the relationship between the coupon rate, yield, and the price of the bond.
The coupon rate is the fixed interest rate that the bond pays annually or semiannually. In this case, the bond has a 5% coupon rate, which means it pays 5% of the par value as interest annually or semiannually.
The yield of a bond represents the annual return, expressed as a percentage, that an investor can expect to earn by holding the bond until maturity. In this case, the bond has a yield of 8%.
To calculate the price of the bond at the issue date, we need to discount the future cash flows (coupons and the final payment of the face value) by the yield. Since the coupons are paid semiannually, we need to adjust the yield accordingly.
The formula to calculate the price of a bond using semiannual yields is as follows:
Price = (Coupon Payment / (1 + Yield/2)^n) + (Coupon Payment / (1 + Yield/2)^(n-1)) + ... + (Coupon Payment / (1 + Yield/2)) + (Face Value / (1 + Yield/2)^n)
In this formula:
- Coupon Payment refers to the coupon amount received each period.
- Yield/2 refers to the adjusted semiannual yield.
- n refers to the number of periods until maturity.
Since the bond has a 10-year maturity and pays semiannual coupons, n would be 10 years multiplied by 2 (to convert to semiannual periods), which equals 20.
Let's plug in the given values into the formula:
Coupon Payment = 5% * Par Value / 2 (since the coupon is paid semiannually)
Adjusted Yield = 8% / 2 (to convert the annual yield to semiannual yield)
n = 20
We can now calculate the price of the bond at the issue date.