Ying Import Has Several Bond Issues Outstanding Each Making
Ying Import Has Several Bond Issues Outstanding Each Making Semiannua
Ying Import has several bond issues outstanding, each making semiannual interest payments. The bonds are listed in the table below. Bond Coupon Rate Price Quote Maturity Face Value 1 8.60% 106.1 6 years $20,000,.60 94.3 9 years 38,000,..9 16.5 years 43,000,.80 94.7 26 years 58,000,000 Required: If the corporate tax rate is 30 percent, what is the aftertax cost of the company’s debt?
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The calculation of the after-tax cost of debt is a fundamental aspect of corporate finance, as it helps to determine the true cost of borrowing for a company, considering the tax shield benefits associated with debt financing. For Ying Import, which has multiple bond issues, each with different characteristics, a weighted average approach is necessary to accurately estimate the company's overall cost of debt after taxes.
To begin, we need to determine the yield to maturity (YTM) for each bond, since the coupon rate alone does not accurately reflect the current market cost of debt. The YTM can be approximated using the bond's price, coupon payments, time to maturity, and face value. The formula involves solving for the discount rate that equates the present value of future cash flows (coupon payments and face value) to the bond's current price. Since this can be complex, financial calculators or iterative methods are typically employed; however, for this example, approximate calculations are sufficient.
Step 1: Calculate the Yield to Maturity (YTM)
For each bond, the bond's current market price indicates the market's required yield. The bonds are quoted at prices expressed as a percentage of face value.
Bond 1:
- Coupon Rate: 8.60%
- Price Quote: 106.1% of face value
- Face Value: $20,000
- Maturity: 6 years
The bond price is:
\[ P = 106.1\% \times 20,000 = \$21,220 \]
Annual coupon payment:
\[ C = 8.60\% \times 20,000 = \$1,720 \]
Since the bond pays semiannually, semiannual coupon:
\[ C_{semi} = \frac{1,720}{2} = \$860 \]
The number of periods:
\[ N = 6 \times 2 = 12 \]
The face value at maturity:
\[ FV = \$20,000 \]
Using a financial calculator or Excel's RATE function, approximate YTM:
\[
\text{YTM (semiannual)} \approx 4.0\%
\]
Annual YTM:
\[
YTM_{annual} = 4.0\% \times 2 = 8.0\%
\]
Bond 2:
- Price Quote: 94.3% of face value
- Face Value: $38,000
- Maturity: 9 years
Price:
\[ P = 94.3\% \times 38,000 = \$35,834 \]
Coupon payment:
\[ C = 8.60\% \times 38,000 = \$3,268 \]
Semiannual coupon:
\[ C_{semi} = \frac{3,268}{2} = \$1,634 \]
Number of periods:
\[ N = 9 \times 2 = 18 \]
Approximated semiannual YTM:
\[
\text{YTM (semiannual)} \approx 4.35\%
\]
Annual YTM:
\[
YTM_{annual} = 4.35\% \times 2 = 8.7\%
\]
Bond 3:
- Price Quote: 94.7% of face value
- Face Value: $43,000
- Maturity: 16.5 years
Price:
\[ P = 94.7\% \times 43,000 = \$40,721 \]
Coupon payment:
\[ C = 8.60\% \times 43,000 = \$3,698 \]
Semiannual coupon:
\[ C_{semi} = \frac{3,698}{2} = \$1,849 \]
Number of periods:
\[ N = 16.5 \times 2 = 33 \]
Approximate semiannual YTM:
\[
\text{YTM (semiannual)} \approx 4.0\%
\]
Annual YTM:
\[
YTM_{annual} = 8.0\%
\]
Bond 4:
- Price Quote: 94.7% of face value
- Face Value: $58,000,000
- Maturity: 26 years
Price:
\[ P = 94.7\% \times 58,000,000 = \$54,926,000 \]
Coupon payment:
\[ C = 8.60\% \times 58,000,000 = \$4,988,000 \]
Semiannual coupon:
\[ C_{semi} = \frac{4,988,000}{2} = \$2,494,000 \]
Number of periods:
\[ N = 26 \times 2 = 52 \]
Approximate semiannual YTM:
\[
\text{YTM (semiannual)} \approx 4.0\%
\]
Annual YTM:
\[
YTM_{annual} = 8.0\%
\]
---
Step 2: Compute the After-Tax Cost of Debt for Each Bond
The cost of debt is the yield to maturity (YTM), adjusted for the tax shield:
\[
\text{After-tax cost of debt} = YTM \times (1 - \text{Tax rate})
\]
Given the corporate tax rate of 30%:
\[
\text{After-tax YTM} = YTM_{annual} \times (1 - 0.30) = YTM_{annual} \times 0.70
\]
Applying this:
- Bond 1: \( 8.0\% \times 0.70 = 5.6\% \)
- Bond 2: \( 8.7\% \times 0.70 \approx 6.09\% \)
- Bond 3: \( 8.0\% \times 0.70 = 5.6\% \)
- Bond 4: \( 8.0\% \times 0.70 = 5.6\% \)
---
Step 3: Calculate the Weighted Average Cost of Debt
Next, weight each bond's after-tax cost by its proportion of the total debt:
Total face value:
\[
20,000 + 38,000 + 43,000 + 58,000,000 = 58,101,000
\]
Weights:
- Bond 1:
\[
\frac{20,000}{58,101,000} \approx 0.000344
\]
- Bond 2:
\[
\frac{38,000}{58,101,000} \approx 0.000654
\]
- Bond 3:
\[
\frac{43,000}{58,101,000} \approx 0.000741
\]
- Bond 4:
\[
\frac{58,000,000}{58,101,000} \approx 0.998261
\]
Weighted average after-tax cost:
\[
(5.6\% \times 0.000344) + (6.09\% \times 0.000654) + (5.6\% \times 0.000741) + (5.6\% \times 0.998261)
\]
\[
\approx 0.000019 + 0.000040 + 0.000042 + 0.005591 \approx 0.005692
\]
Expressed as a percentage:
\[
\boxed{0.569\%}
\]
Given the dominance of the large bond issue, the overall after-tax cost of debt for Ying Import is approximately 0.57%.
Conclusion:
The calculated after-tax cost of Ying Import’s debt, considering the multiple bond issues and their market yields, is approximately 0.57%, reflecting the beneficial impact of tax deductions on its borrowing expenses. This low rate underscores the advantage of debt financing, especially for large-scale bond issues, through tax shields.
This comprehensive analysis highlights the importance of using market-based YTM for an accurate assessment of a firm’s true cost of debt, which is crucial for effective capital budgeting and financial strategy.
References
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