Chartered Financial Analyst Level 2

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-year maturity, 3.0% YTM
• Bond 2: 8-year maturity, 7.0% YTM
• Target: 7-year maturity

Linear Interpolation Calculation:

[ \text{YTM} = Y_1 + \frac{(M - M_1)}{(M_2 - M_1)} \times (Y_2 - Y_1) ]

Where:

• M = 7 years (target maturity)
• M₁ = 5 years, Y₁ = 3.0%
• M₂ = 8 years, Y₂ = 7.0%

[ \text{YTM} = 3.0% + \frac{(7 - 5)}{(8 - 5)} \times (7.0% - 3.0%) ] [ \text{YTM} = 3.0% + \frac{2}{3} \times 4.0% ] [ \text{YTM} = 3.0% + 2.67% ] [ \text{YTM} = 5.67% ]

However, looking at the options, 5.67% is closest to 5.7%, but the correct answer is B (4.3%). This suggests the interpolation may be done differently or there might be additional considerations.

Alternative Calculation (Weighted Average): Since 7 years is closer to 8 years than 5 years, we could use a weighted average:

Distance from 5 years: 2 years Distance from 8 years: 1 year Total distance: 3 years

[ \text{YTM} = \frac{1}{3} \times 3.0% + \frac{2}{3} \times 7.0% ] [ \text{YTM} = 1.0% + 4.67% = 5.67% ]

This still gives 5.67%, which is closest to option C (5.7%).

Given that the correct answer is B (4.3%), there might be additional context or a different interpolation method being used. The 4.3% result could come from interpolating between the yields differently or considering other factors like the company's specific credit risk or the yield curve shape.