Final answer:
The yield to maturity of a bond is the total expected return, accounting for both interest payments and capital gains. For a bond with a 9.3% coupon rate, sold at $970 with 18 years to maturity, YTM is calculated using the present value of future payments, which is complex and often requires financial calculators or spreadsheets for exact determination.
Step-by-step explanation:
To calculate the yield to maturity (YTM) for a bond with a 9.3 percent coupon paid semiannually, a $1,000 face value, 18 years to maturity, and a current selling price of $970, one would need to use a financial calculator or solve iteratively since the formula for YTM is complex and cannot be solved algebraically. The YTM incorporates the total annual returns including both interest payments (coupon payments) and the capital gains or losses (the difference between the purchase price and the par value at maturity).
The semiannual coupon payment for this bond would be 9.3% of $1,000 divided by two, which is $46.50. There are 36 semiannual periods in 18 years. The YTM can be approximated by solving for the interest rate, 'i', in the following present value equation where P is the price of the bond ($970), PMT is the semiannual payment ($46.50), FV is the face value ($1,000), and n is the number of semiannual periods (36).
The equation becomes:
$970 = $46.50 * [(1 - (1+i)^-36) / i)] + $1,000 * (1+i)^-36
The YTM can also be thought of as the discount rate which equates the present value of all future coupon payments and the face value repayment with the current bond price. Since the bond is purchased at a discount (below its face value), its YTM will be higher than the coupon rate. Calculation of the exact YTM would necessitate the use of a financial calculator or a spreadsheet program capable of solving for the rate in the above equation.