B18. (Default risk) You buy a very risky bond that promises a 9.5% coupon and return of the
$1,000 principal in 10 years. You pay only $500 for the bond.
a. You receive the coupon payments for three years and the bond defaults. After liquidating
the firm, the bondholders receive a distribution of $150 per bond at the end of 3.5
years. What is the realized return on your investment?
b. The firm does far better than expected and bondholders receive all of the promised
interest and principal payments. What is the realized return on your investment?
To calculate the realized return on your investment in both scenarios, we need to use the formula for realized return. The formula is:
Realized Return = (Ending Value - Beginning Value) / Beginning Value
In this case, the beginning value is the price you paid for the bond, which is $500. The ending value depends on the scenario:
a. In scenario a, the bond defaults after 3 years and bondholders receive a distribution of $150 per bond at the end of 3.5 years. Since you receive the coupon payments for 3 years and then receive a distribution of $150, the ending value is $150. Therefore, the realized return is:
Realized Return = ($150 - $500) / $500
Realized Return = -$350 / $500
Realized Return = -0.7 or -70%
b. In scenario b, the firm does better than expected and bondholders receive all of the promised interest and principal payments. Since the bond promises a 9.5% coupon and a return of the $1,000 principal in 10 years, the ending value is $1,000. Therefore, the realized return is:
Realized Return = ($1,000 - $500) / $500
Realized Return = $500 / $500
Realized Return = 1 or 100%
Therefore, in scenario a, the realized return on your investment is -70%, indicating a negative return because the bond defaults and you receive less than what you paid for it. In scenario b, the realized return is 100%, indicating a positive return as you receive all of the promised payments.