Final answer:
The price of a bond when its interest rate is lower than the market rate is determined by the present value of the expected cash flows. A bond with a payment of $1,080 next year and a market interest rate of 12% is worth $964. The yield is calculated as the percentage gain on this price, which also comes to 12% in this case.
Step-by-step explanation:
Calculating Bond Price and Yield
To calculate the price of a bond when its interest rate is less than the market interest rate, you would find the present value of the expected cash flows from the bond.
Given the expected payment of $1,080 from the bond in one year and the market interest rate of 12%, the price you would be willing to pay for the bond is the amount that would grow to $1,080 in one year at that interest rate, which is $964.
This calculation is based on the formula $964(1 + 0.12) = $1080. Consequently, you will not pay more than $964 for a bond with a face value of $1,000.
The yield or total return on the bond is calculated by taking the difference between what the bond pays out, which is $1,080 ($1,000 face value plus $80 interest), and the price paid for the bond, which is $964.
The yield, therefore, is ($1080 - $964)/$964 = 12%. The yield takes into account both interest payments and any capital gains which, in this case, is the increase in value from the purchase price to the face value.
It's important to note that the bond's coupon rate does not change, and remains at 8% irrespective of the current market interest rate.
The market's interest rate, however, affects the selling price of the bond on the market: when market rates go up, the price of existing bonds with lower rates will often sell for less than their face value.
Your complete question is: Cost of debt using both methods (YTM and the approximation formula) Currently, Warren Industries can S 20-year, \$1,000-par-value bonds paying annual interest at a 11% coupon rate. Because current market rates for similar bonds are just under 11%. Warren can sell its bonds for $970 each; Warren will incur flotation costs of $2C bond. The firm is in the 29% tax bracket. a. Find the net proceeds from the sale of the bond, N
d
. b. Calculate the bond's yield to maturity (YTM) to estimate the before-tax and after-tax costs of debt. c. Use the approximation formula to estimate the before-tax and after-tax costs of debt. a. The net proceeds from the sale of the bond, N
d
, is S (Round to the nearest dollar.)