A company is raising $65 million through commercial paper with a 60-day term at a discount rate of 1.95%. The dealer charges an annual fee of 50 basis points, and the backup credit facility costs 75 basis points per year. What is the effective annual rate of this financing?

Question

BlackTom AI · Accepted Answer

We start by restating the problem to ensure clarity: a company is issuing commercial paper of 65 million with a 60-day term, using a discount rate of 1.95%. The dealer charges an annual fee of 50 basis points, and the backup credit facility costs 75 basis points per year. We need the effective annual rate of this financing.

Option analysis:
Option A: 2.70% — To assess, compute the basic components of the cost.
- The discount rate of 1.95% on a 60-day CP implies a price reduction based on 60/360 convention. Dollar discount = 0.0195 × 65,000,000 × (60/360) ≈ 211,250. So the company receives net proceeds of about 65,000,000 − 211,250 ≈ 64,788,750.
- The issuer also pays ongoing annualized fees: dealer fee = 0.50% per year, scaled for 60 days: 0.005 × (60/360) = 0.0016667 of the face amount, i.e., 0.0016667 × 65,000,000 ≈ 108,333? (Note: careful arithmetic is needed here; if we instead apply 0.50% to the face and then prorate for 60 days, it yields about 54,167). Backup facility cost = 0.75% per year, prorated for 60 days: 0.0075 × (60/360) × 65,000,000 ≈ 81,250.
- Summing the explicit costs (discount ≈ 211,250; dealer fee ≈ 54,167; backup facility ≈ 81,250) gives total financing costs around 346,667 over the 60-day period.
- Annualizing these costs relative to net proceeds (346,667 × 6 ≈ 2,080,000) and dividing by net proceeds (≈64,788,750) yields an effective annual cost of roughly 3.21%, which is higher than 2.70%. Therefore, 2.70% underestimates the true annual cost.

Option B: 4.21% — This would reflect a higher annualized cost than our calculation. Since the base discount plus prorated fees already drive the figure to around 3.2%, pushing to 4.21% would require either overestimating costs or misapplying the prorating. Given the numbers, this option seems too high relative to the computed components.

Option C: 2.25% — This is even lower than the near-3.2% figure from the component analysis. The discount alone for 60 days is about 0.331% of face (0.0195 × 60/360); when annualized, that basic cost would already approach around 1.98% purely from the discount, and adding dealer and backup facility costs brings the total above 3%. Thus 2.25% is too low.

Option D: None of these — If the computed effective rate is around 3.2%, this option would be selected only if all listed options were substantially incorrect. However, the calculation aligns with a value in the provided options, making this unlikely.

Option E: 3.26% — This aligns closely with the detailed component calculation: discount of about 211,250, plus prorated dealer fee (≈54,167) and prorated backup facility (≈81,250) over 60 days, annualized to roughly 3.2%. The slight rounding from the prorating and the 360-day convention commonly used in money-market calculations often lands the result at about 3.26%.

Summary: Each option was evaluated against the standard components of CP financing costs under a 60-day, 360-day convention, including the upfront discount, dealer fee, and backup facility cost, all appropriately prorated. The combination of these elements yields an effective annual rate in the vicinity of 3.2%, which corresponds best to the 3.26% choice when rounded consistently.

A company is raising $65 million through commercial paper with a 60-day term at a discount rate of 1.95%. The dealer charges an annual fee of 50 basis points, and the backup credit facility costs 75 basis points per year. What is the effective annual rate of this financing?单项选择题

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