Answer-first summary for fast verification
Answer: I only
## Explanation In the Merton model: **Assumption I is CORRECT:** An increase in the risk-free rate will increase the firm's equity value. This is because equity is valued as a call option on the firm's assets, and the value of a call option increases with higher risk-free rates (due to the reduced present value of the strike price). **Assumption II is INCORRECT:** An increase in the risk-free rate does NOT affect the estimated physical default probability. The physical default probability (PD) is calculated using the actual expected return on assets (8% in this case), not the risk-free rate. The risk-free rate is only used in the risk-neutral valuation of equity, not in the calculation of the physical distance to default. **Key points:** - Equity value = Call option value = f(asset value, strike price, risk-free rate, volatility, time) - Physical default probability = f(asset value, strike price, expected return, volatility, time) - Only risk-neutral default probabilities are affected by the risk-free rate Therefore, only Assumption I is correct.
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Analyst Greg is employing the Merton model to both value a firm's equity and estimate a physical default probability. He has collected the following information:
$10 million; e.g., face value of short-term debt is $10 million.$12.75 million with an expected return of 8% per annum with continuous compoundingHis exercise includes two components: one, valuation of the firm's equity market value by treating equity as a call option on the firm's assets; two, estimate of default probability by calculation of a forward distance to default. Greg makes two assumptions: I. An increase in the risk-free rate will increase an estimate of the firm's current equity market value, and II. An increase in the risk-free rate will decrease the estimated default probability.
Which of Greg's two assumptions is correct?
A
Neither
B
I only
C
II only
D
Both
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