If a firm has a large quantity of different debt contracts, how do you proceed to compute the r_d ?

Question

BlackTom AI · Accepted Answer

Compute the firm's overall cost of debt by taking a weighted average of the individual yields on each debt contract, with weights equal to the value (preferably market value) of each debt. This ensures each contract contributes to the firm’s r_d in proportion to the amount of debt outstanding at that rate.

Relevant concepts:
- Cost of debt r_d for a firm with multiple debt instruments is the portfolio yield: r_d = Σ(r_i * weight_i).
- Weights should be the market values of each debt instrument (book values acceptable if market values are unavailable).
- WACC typically uses the after-tax cost of debt r_d*(1 − Tc), but the raw r_d is the value-weighted average of contract rates/yields.

Step-by-step reasoning and formula:
1. List all debt contracts i = 1..n, find each instrument’s yield r_i and market value D_i.
2. Compute total debt D_total = Σ D_i.
3. Compute value-weighted r_d = Σ (r_i * D_i) / D_total.

Numeric example (intermediate steps):
- Suppose D1 = 100, r1 = 4%; D2 = 50, r2 = 6%; D3 = 150, r3 = 5%.
- D_total = 100 + 50 + 150 = 300.
- Numerator = 100*0.04 + 50*0.06 + 150*0.05 = 4 + 3 + 7.5 = 14.5.
- r_d = 14.5 / 300 = 0.048333 = 4.833%.

Why this is correct:
- Value-weighting reflects the economic impact of each contract on the firm’s financing costs: larger debts should influence the aggregate yield more.
- Market values are preferred because they reflect current yields and prices.

Why other options are incorrect:
- Valuing the firm as equity-only ignores the cost and presence of debt and would misstate WACC; it’s not a method for computing r_d.
- Using a single Libor+bps contract is arbitrary and ignores the contribution of other contracts with different amounts and rates.
- Maturity-weighting weights by time-to-maturity, not the monetary size, so it misrepresents the cost contribution of each obligation.

Conclusion: therefore the correct approach is: You use a value-weighted r_d based on all debt contracts. This matches the provided answer.

If a firm has a large quantity of different debt contracts, how do you proceed to compute the r_d ?单项选择题

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