To compute the current price of the bonds, we need to calculate the present value of the bond's cash flows, which includes the periodic interest payments (coupons) and the face value (par value) at maturity.
The bond pays annual interest of 8% of the $1,000 par value, which is equal to $80 per year. Given the current yields to maturity, we can calculate the present value of these coupon payments using the following formula:
Present Value of Coupons = C * (1 - (1 + YTM) ^ -N) / YTM,
where C is the coupon payment, YTM is the yield to maturity, and N is the number of years to maturity.
We also need to calculate the present value of the face value at maturity using the following formula:
Present Value of Face Value = M / (1 + YTM) ^ N,
where M is the face value (par value) of the bonds.
Finally, we add these two present values together to determine the current bond price.
Here are the calculations for each yield to maturity:
A. 7% yield to maturity:
Present Value of Coupons = $80 * (1 - (1 + 0.07) ^ -25) / 0.07 = $832.41
Present Value of Face Value = $1,000 / (1 + 0.07) ^ 25 = $349.41
Current Bond Price = $832.41 + $349.41 = $1,181.82
B. 10% yield to maturity:
Present Value of Coupons = $80 * (1 - (1 + 0.10) ^ -25) / 0.10 = $611.66
Present Value of Face Value = $1,000 / (1 + 0.10) ^ 25 = $228.30
Current Bond Price = $611.66 + $228.30 = $839.96
C. 13% yield to maturity:
Present Value of Coupons = $80 * (1 - (1 + 0.13) ^ -25) / 0.13 = $441.41
Present Value of Face Value = $1,000 / (1 + 0.13) ^ 25 = $111.27
Current Bond Price = $441.41 + $111.27 = $552.68
So, the current bond prices for different yields to maturity are:
A. 7% yield to maturity: $1,181.82
B. 10% yield to maturity: $839.96
C. 13% yield to maturity: $552.68
Midland Oil has $1,000 par value bonds outstanding at 8 percent interest. The bonds will mature in 25 years. Compute the current price of the bonds if the present yield to maturity is:
A. 7 percent.
B. 10 percent.
C. 13 percent.
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