Suppose that issuers in the bond market with A and BBB ratings pay (annual) interest rates equal to the risk-free rate (2%) plus 2.5% and 5%, respectively. Bank A can lower the credit risk of firm F from BBB to A. This annually costs the bank 1% of the loan’s outstanding principal (no borrower cost). Describe the interest rate on potential loans that would be attractive for both bank A and firm F.

Question

BlackTom AI · Accepted Answer

Bank A can borrow at the A-rated market rate of 4.5% (risk-free 2% + 2.5%), and reducing F’s credit risk costs the bank 1% per year.

1) Relevant knowledge points and concepts
- Market yields: A-rated borrowers pay 4.5% (2% + 2.5%), BBB pay 7% (2% + 5%).
- A loan is acceptable to firm F only if its offered rate is no higher than what F can obtain elsewhere (the BBB market rate of 7%).
- The bank will only make the loan if its net return after funding cost and the credit-reduction cost is nonnegative.
- Bank A’s funding cost is its A-rate (4.5%) if it finances at its own rating.

2) Complete reasoning step by step
- If the bank lends to F at interest rate r, the bank receives r annually on the loan principal.
- The bank finances this at its A-rating funding cost = 4.5% per year.
- The bank must also pay the 1% annual cost to lower F’s risk from BBB to A.

3) Calculations with intermediate steps
- Bank’s annual net return = r − funding cost − cost of risk reduction
- = r − 4.5% − 1%
- = r − 5.5%
- For the bank to be willing: r − 5.5% ≥ 0 ⇒ r ≥ 5.5%.
- For the firm to be willing: r ≤ 7% (otherwise F would borrow at BBB market rate of 7%).

4) Why the correct answer is correct
Combining both constraints gives 5.5% ≤ r ≤ 7%. Thus any interest rate between 5.5% and 7% makes the loan attractive to both bank A (nonnegative net return) and firm F (cheaper than the BBB market).

5) Why other options are incorrect
- "≤ 7%" is too weak: rates below 5.5% would lose money for the bank. 
- "Between 3.5% and 7%" and "between 5% and 6%" set lower bounds that are too low (bank would lose at r < 5.5%).
- "Above or equal to 5.5%" ignores the firm’s cap of 7%, allowing rates the firm would reject.

6) Conclusion
Therefore the mutually acceptable interest-rate range is between 5.5% and 7%, which matches the provided answer.

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