Usha Manufacturing Co. has a bond of $1000 par value outstanding. It pays interest annually and carries an annual coupon rate of 8%. Bonds are issued 2 years ago & due in 10 years. If the market rate of return on bonds is 7%. Required:
a. What is the current price of the bond? Explain whether the bond will sell at a discount or a premium?
b. Would the price of the bond be any different if interest was paid semi-annually instead of annually? Explain?
c. Explain what would happen to the bond price 5 years from now if the market interest rate remained the same at 7%. Explain what would be the market value of the bond at maturity date.
a. To calculate the current price of the bond, we need to use the present value formula for a bond. The formula for the present value of a bond is:
PV = C / (1 + r)^1 + C / (1 + r)^2 + ... + C / (1 + r)^n + F / (1 + r)^n
Where:
PV = Present value (current price) of the bond
C = Annual coupon payment (interest payment)
r = Market interest rate
n = Number of periods (years)
F = Face value (par value) of the bond
Using the given information, the annual coupon payment is $1000 * 8% = $80, the market interest rate is 7%, the number of periods is 10 years, and the face value is $1000.
PV = $80 / (1 + 7%)^1 + $80 / (1 + 7%)^2 + ... + $80 / (1 + 7%)^10 + $1000 / (1 + 7%)^10
Calculating this using a financial calculator or spreadsheet gives us the current price of the bond. Note that in this case, the bond will sell at a premium because the coupon rate (8%) is higher than the market interest rate (7%).
b. If the interest was paid semi-annually instead of annually, the price of the bond would be slightly different. The formula for the present value of a bond with semi-annual payments is:
PV = (C/2) / (1 + (r/2))^1 + (C/2) / (1 + (r/2))^2 + ... + (C/2) / (1 + (r/2))^2n + F / (1 + (r/2))^2n
In this case, the coupon payment (C) should be divided by 2, and the market interest rate (r) should also be divided by 2. Everything else remains the same. Using this formula, the current price of the bond with semi-annual payments can be calculated.
c. If the market interest rate remains the same at 7% after 5 years, the bond price will not change significantly. The market value of the bond at the maturity date will still be the face value ($1000), assuming the issuer doesn't default on their obligations. The coupon payments will continue to be paid at the fixed rate of 8%, irrespective of the market interest rate.
a. To calculate the current price of the bond, we need to use the present value formula. The formula is:
P = C * (1 - (1 + r)^(-n)) / r + F / (1 + r)^n
Where:
P = Present value or current price of the bond
C = Annual coupon payment
r = Market rate of return or yield
n = Number of periods or years
F = Face value or par value of the bond
In this case, the coupon payment (C) is 8% of the par value, which is $1000. So, C = 0.08 * $1000 = $80.
The market rate of return (r) is 7%, which is 0.07.
The number of periods (n) is 10 years, and the bond was issued 2 years ago, so n = 8.
The face value (F) is $1000.
Using these values in the formula:
P = $80 * (1 - (1 + 0.07)^(-8)) / 0.07 + $1000 / (1 + 0.07)^8
Calculating this equation will give us the current price of the bond.
If the current price of the bond is higher than its face value ($1000), it is selling at a premium. If it is lower than the face value, it is selling at a discount. So, depending on the calculated price, we can determine whether the bond is selling at a premium or a discount.
b. If interest was paid semi-annually instead of annually, it would affect the calculation of the current price. The coupon payment (C) would be divided by the number of periods per year (2 in this case), and the market rate of return (r) would also be divided by 2.
The number of periods (n) would be multiplied by the number of periods per year (2 in this case).
So, with semi-annual payments, we would calculate the current price using the modified values and the present value formula.
c. If the market interest rate remains the same at 7% after 5 years, the bond price would not change significantly. The price of the bond may fluctuate slightly due to other market factors, but assuming all other factors remain constant, it would stay close to its current price.
At maturity, the market value of the bond would be equal to its face value or par value ($1000). This assumes that the issuer does not default on its bond obligation. So, if the bond is held until maturity, the investor will receive the face value as the market value of the bond.