(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, we need to determine the cash flows you received and compare them to the amount you initially paid for the bond. Let's calculate the realized returns for both scenarios:
a. Default Scenario:
- Coupon payments for 3 years: 3 * 9.5% * $500 = $142.50
- Distribution received after default at year 3.5: $150
Total cash flows received: $142.50 + $150 = $292.50
Investment cost: $500
Realized return = (Cash flows received - Investment cost) / Investment cost
Realized return = ($292.50 - $500) / $500
Realized return = -$207.50 / $500
Realized return = -41.50%
Therefore, the realized return on your investment in the default scenario would be -41.50%.
b. Successful Scenario:
In this scenario, we assume the bond performs as expected and all promised interest and principal payments are made.
- Coupon payments for 10 years: 10 * 9.5% * $500 = $475
- Principal repayment at the end of 10 years: $1,000
Total cash flows received: $475 + $1,000 = $1,475
Investment cost: $500
Realized return = (Cash flows received - Investment cost) / Investment cost
Realized return = ($1,475 - $500) / $500
Realized return = $975 / $500
Realized return = 195%
Therefore, the realized return on your investment in the successful scenario would be 195%.
Please note that these calculations only consider the cash flows received and the initial investment cost, and do not take into account the time value of money or other factors influencing the bond's risk and return profile. Real-life investments typically involve more complex considerations.
a. To calculate the realized return on your investment, we need to determine the total cash inflows and outflows.
1. Cash inflows:
- Coupon payments received for three years: 3 years * $1,000 principal * 9.5% coupon rate/year = $285
2. Cash outflows:
- Initial investment: $500
- Loss from the default: $1,000 principal - $150 distribution = $850
3. Total cash inflows: $285
4. Total cash outflows: $500 + $850 = $1,350
The realized return on your investment is calculated as follows:
Realized Return = (Total Cash Inflows / Total Cash Outflows) - 1
= ($285 / $1,350) - 1
= 0.21 or 21%
Therefore, the realized return on your investment is 21%.
b. In this scenario, since the firm does far better than expected, you will receive all of the promised interest and principal payments.
The realized return on your investment can be calculated as:
Realized Return = (Total Cash Inflows / Total Cash Outflows) - 1
= ($1,000 principal + $1,000 principal * 9.5% coupon rate * 10 years) / $500 initial investment - 1
= ($1,000 + $950 * 10) / $500 - 1
= $10,000 / $500 - 1
= 20 - 1
= 19
Therefore, the realized return on your investment is 19 times your initial investment, which equals a 1900% return.