Calculate Yield To Maturity And Evaluate The Cost
Calculate Yield to Maturity And Evaluate The Cost Of
The question is: Calculate Yield to maturity and evaluate the cost of capital. The scenario involves International Tile Importers, Inc., which is considering issuing a five-year interest-only bond. The bond has a principal of $1,000, pays 12% annual interest, and the principal is due at the end of Year 5. The investment banker estimates the bonds can be sold at $800 each under current market conditions. The assignment involves calculating the promised yield to maturity based on these terms, and then adjusting this calculation to account for default risk, with specified probabilities and recovery rates.
Paper For Above instruction
Introduction
Understanding the cost of debt and the yield to maturity (YTM) is crucial for firms when issuing bonds, as it reflects the true cost of borrowing and influences corporate financing decisions. For emerging and rapidly growing firms like International Tile Importers, accurately estimating YTM—both under ideal conditions and considering default risks—is essential for effective capital structure management and investor communication.
This paper analyzes the YTM of a proposed five-year interest-only bond, first under the assumptions of market pricing, and then factoring in default probabilities and recovery rates. The objective is to demonstrate how market perceptions of risk impact the yield and overall cost of capital for firms.
Calculation of Promised Yield to Maturity
The bond details indicate a principal of $1,000, an annual interest payment of 12% ($120), a five-year maturity, and an estimated sell price of $800 per bond today. Since the bond is interest-only, the principal is repaid at maturity alongside the final interest payment.
The promised YTM equates the present value of all cash flows to the bond's current price ($800). The cash flows include annual interest payments and the repayment of principal at the end of Year 5:
- Annual interest: $120
- Principal repayment: $1,000 in Year 5
- Current price: $800
The YTM can be found by solving:
\[
800 = \sum_{t=1}^{5} \frac{120}{(1 + y)^t} + \frac{1000}{(1 + y)^5}
\]
This is a standard financial present value equation, which requires iterative or financial calculator methods for precise solving. Using a financial calculator or Excel’s RATE function, we find:
```excel
=RATE(5, 120, -800, 1000)
```
which yields approximately 15.15%. Thus, the promised YTM based on current market conditions is roughly 15.15%.
Interpretation Of Promised Yield
The promised YTM exceeds the coupon rate (12%), suggesting that investors demand a premium for risk factors not reflected in the coupon rate. This premium likely arises from perceived default risk and market liquidity considerations. Since the bond’s current price is below face value, the bond is trading at a discount, consistent with a higher required yield to compensate investors for the risk.
Adjusting for Default Risk
Management expressed concern that the initial YTM may underestimate the true cost, since the firm’s speculative credit rating implies a default risk. To incorporate this, the expected yield must account for the probability of default and the potential recovery in such events.
Given:
- Annual default probability: 5%
- Recovery rate in default: 50% of face value
The expected cash flows need to be adjusted by the probability of default. Specifically, in each year, there is a 5% chance that the firm defaults, and only 50% of the principal is recovered if default occurs. The expected cash flow in each period is reduced proportionally.
The expected cash flow in Year t, considering default risk, becomes:
\[
\text{Expected payment} = (1 - p)^t \times \text{original payment}
\]
where \( p = 5\% \) is the default probability.
Additionally, in case of default, only 50% of the principal is recovered, which affects the final cash flow at Year 5.
Step-by-step approach:
1. Calculate the adjusted expected cash flows annually, considering the default probability and recovery rate.
2. Discount these expected cash flows at the new yield \( y_{expected} \), which must be found such that the present value matches the bond’s current market price of $800.
This involves solving a more complex equation that includes risk-adjusted expected payments. As an approximation, a risk premium is added to the initial YTM based on the default probability and recovery rate.
Approximate Calculation:
The risk premium can be estimated as:
\[
\text{Risk Premium} = p \times (1 - \text{Recovery Rate}) \times \text{Face Value}
\]
\[
= 0.05 \times (1 - 0.50) \times 1000 = 0.05 \times 0.50 \times 1000 = 25
\]
Adding this premium to the initial YTM:
\[
15.15\% + \frac{25}{800} \approx 15.15\% + 3.13\% = 18.28\%
\]
Thus, the expected yield to maturity considering default risk is approximately 18.28%.
Conclusion
The initial promised yield to maturity under market conditions is approximately 15.15%, reflecting the current discount and risk factors. When accounting for default probability and recovery rates, the expected yield increases to around 18.28%. This higher yield underscores the importance of credit risk assessment in the cost of capital calculations for firms with speculative-grade bonds. Accurate estimation of YTM, including default risk, enables firms like International Tile Importers to better evaluate their financing costs and optimize their capital structure.
References
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