Question

4. The current yield on bond B, which has semiannual coupons, is 7.08% and the bond was sold at par (i.e., at a price of $1,000) three years ago, when the YTM on similar bonds was 8.0%. If there are 12 years until maturity, what would be the YTM to an investor who buys the bond today? (Hint: If the bond's price was $1,000 three years ago, when the market interest rate was 8.0%, what must be the coupon rate? If you know the coupon and the current yield, you can solve for the price. Remember that to find the current yield on a bond with semiannual coupons, you must divide the yearly payment - two coupons - by the price. Now you can enter numbers in your financial calculator to find the periodic interest rate. Remember that for bonds with semiannual coupon payments, the YTM is the APR.)

Answer 1

4]

The bond was sold at par 3 years ago. A bond sells at par if its YTM equals its coupon rate. Therefore, the coupon rate of the bond is 8%.

Annual coupon payment = face value * coupon rate = $1,000 * 8% = $80

Current yield = annual coupon payment / bond price

7.08% = $80 / bond price

bond price = $1,129.94

YTM is calculated using financial calculator with these inputs :

N = 24 (12 years to maturity with 2 semiannual coupon payments each year. Total number of semiannual coupon payments until maturity = 12 * 2 = 24)

PMT = 40 (Semiannual coupon payment = face value * annual coupon rate / 2 = $1000 * 8% / 2 = $40. This is a positive figure as it is an inflow to the bondholder)

PV = -1129.94 (Current bond price. This is a negative figure as it is an outflow to the buyer of the bond)

FV = 1000 (Face value of the bond receivable on maturity. This is a positive figure as it is an inflow to the bondholder)

CPT --> I/Y

I/Y is calculated to be 3.21%. This is the semiannual YTM. To calculate the annual YTM, we multiply by 2. Annual YTM is 6.43%

YTM to investor is 6.43%