# Question

Mr. K, a risk- neutral investor, is contemplating a one- year 8% loan of $ 500 to firm J. Mr. K demands at least a 6% expected return per annum on loans like this. K is concerned that the firm may not be able to pay the interest and/ or principal at the end of the year. A further concern is that if he makes the loan, firm J may engage in additional borrowing. If so, K’s security would be diluted and the firm would become more risky. Since firm J is growing rapidly, K is sure that the firm would engage in additional borrowing if he makes the loan.

K examines firm J’s most recent annual report and calculates an interest coverage ratio (the ratio of net income before interest and taxes to interest expense) of 4, including his contemplated $ 500 loan. Upon considering all of these matters, K assesses the following probabilities:

PAYOFF PROBABILITY.

01: Interest and principal repaid ............ 0.80.

02: Reorganization, principal repaid but not interest.... 0.18.

03: Bankruptcy, nothing repaid............ 0.02

......................................... 1.00

Required

a. Should Mr. K make the loan? Show calculations.

b. Firm J offers to add a covenant to its lending agreement with Mr. K, undertaking not to engage in any additional borrowing if its interest coverage ratio falls below 4 before the next year- end. Mr. K estimates that there is a 60% probability that the interest coverage ratio will fall below 4. If it does, there would be no dilution of his equity by additional borrowing under the firm J offer, and he feels the lower coverage ratio would still be adequate. He assesses that his payoff probabilities would then be

PAYOFF PROBABILITY .

01 ............ 0.95.

02 ............ 0.04.

03 ............ 0.01

............. 1.00

If the coverage ratio does not fall below 4, the resulting additional borrowing and dilution of security would cause him to assess payoff probabilities as

PAYOFF PROBABILITY.

01 ........... 0.87.

02 ........... 0.12.

03 ........... 0.01

............ 1.00

Should Mr. K now make the loan? Show calculations.

K examines firm J’s most recent annual report and calculates an interest coverage ratio (the ratio of net income before interest and taxes to interest expense) of 4, including his contemplated $ 500 loan. Upon considering all of these matters, K assesses the following probabilities:

PAYOFF PROBABILITY.

01: Interest and principal repaid ............ 0.80.

02: Reorganization, principal repaid but not interest.... 0.18.

03: Bankruptcy, nothing repaid............ 0.02

......................................... 1.00

Required

a. Should Mr. K make the loan? Show calculations.

b. Firm J offers to add a covenant to its lending agreement with Mr. K, undertaking not to engage in any additional borrowing if its interest coverage ratio falls below 4 before the next year- end. Mr. K estimates that there is a 60% probability that the interest coverage ratio will fall below 4. If it does, there would be no dilution of his equity by additional borrowing under the firm J offer, and he feels the lower coverage ratio would still be adequate. He assesses that his payoff probabilities would then be

PAYOFF PROBABILITY .

01 ............ 0.95.

02 ............ 0.04.

03 ............ 0.01

............. 1.00

If the coverage ratio does not fall below 4, the resulting additional borrowing and dilution of security would cause him to assess payoff probabilities as

PAYOFF PROBABILITY.

01 ........... 0.87.

02 ........... 0.12.

03 ........... 0.01

............ 1.00

Should Mr. K now make the loan? Show calculations.

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