Answer-first summary for fast verification
Answer: 5.7%.
## Explanation To estimate the company's cost of debt with a 7-year maturity, we need to interpolate between the two available bonds: - Bond 1: 5 years maturity, 3.0% YTM - Bond 2: 8 years maturity, 7.0% YTM The company's debt matures in 7 years, which is 2 years after Bond 1 and 1 year before Bond 2. **Linear interpolation calculation:** Time difference between bonds: 8 - 5 = 3 years YTM difference: 7.0% - 3.0% = 4.0% For 7-year maturity (2 years after 5-year bond): Proportion = (7 - 5) / (8 - 5) = 2/3 Estimated YTM = 3.0% + (2/3) × 4.0% = 3.0% + 2.67% = 5.67% Rounded to one decimal place: **5.7%** Therefore, the estimated cost of debt is closest to 5.7%.
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A private company's capital structure is composed of 65% in debt and 35% in equity. The company's single debt issue matures in seven years. To estimate the company's cost of debt, an analyst summarizes the following matrix of bond yields issued by companies with similar capital structures and credit quality:
| Time to Maturity (Years) | Yield to Maturity (%) |
|---|---|
| Bond 1 | 5 |
| Bond 2 | 8 |
The estimated company's cost of debt is closest to:
A
3.7%.
B
4.3%.
C
5.7%.
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