Fran
Administrator
AIMs: Describe the Merton Model, and use it to calculate the value of a firm, the values of a firm’s debt and equity, and default probabilities. Explain the drawbacks and assess possible improvements to the Merton Model, and identify proprietary models of rating agencies that attempt to address these issues.
Questions:
303.1. A firm's current asset value is $120.0 million with asset volatility of 44.0% per annum. The expected return on the firm's assets are 15.0%. Debt consists of a singe zero-coupon bond that matures in one (1.0) year with face (par) value of $100.0 million. The riskfree rate is 3.0% per annum. According to the Merton Model, which is nearest to the value of the firm's debt? Recall that d1 = [ln(S/K) + (r+sigma^2/2)*T]/(sigma*SQRT[T]) and d2 = d1 - sigma*SQRT(T). Please note: you will need to retrieve your own N(.) values; but an exam would provide N(.) or give you a Z-lookup table snippet.
a. $67.40
b. $79.36
c. $87.51
d. $94.19
303.2. A firm's current asset value is $62.0 million with an asset volatility of 38.0%. Expected return on the firm's assets are 10.0% per annum. Debt consists of a single zero-coupon bond that matures in one (1.0) year with a face (par) value of $40.0 million. The riskfree rate is 2.0% per annum. What is the firm's probability of default (PD) according to the Merton model?
a. 1.05%
b. 4.38%
c. 9.15%
d. 11.00%
303.3. According to Malz, the basic "out-of-the-box" Merton Model suffers from drawback(s) and unrealistic assumptions, although they can be fixable with modifications or improvements. Each of the following is one of Malz's drawbacks of the basic Merton EXCEPT for:
a. In contrast to other applications of Black-Scholes (BSM), the underlying firm's asset value and asset volatility are not directly observable
b. By relying on the risk-neutral theory of the BSM, Merton ignores the real-world (physical) reality that a higher expected asset return (ROA or mu) would tend to realistically decrease default probability
c. The capital structure of a typical firm is "more much complex" than the basic Merton assumes, especially with regard to a firm's debt structure
d. For firms with high leverage (leverage = assets/equity), the Merton model tends to produce default probabilities that are unrealistically low and recovery rates that are unrealistically high
(Source: Allan Malz, Financial Risk Management: Models, History, and Institutions (Hoboken, NJ: John Wiley & Sons, 2011))
Answers:
Questions:
303.1. A firm's current asset value is $120.0 million with asset volatility of 44.0% per annum. The expected return on the firm's assets are 15.0%. Debt consists of a singe zero-coupon bond that matures in one (1.0) year with face (par) value of $100.0 million. The riskfree rate is 3.0% per annum. According to the Merton Model, which is nearest to the value of the firm's debt? Recall that d1 = [ln(S/K) + (r+sigma^2/2)*T]/(sigma*SQRT[T]) and d2 = d1 - sigma*SQRT(T). Please note: you will need to retrieve your own N(.) values; but an exam would provide N(.) or give you a Z-lookup table snippet.
a. $67.40
b. $79.36
c. $87.51
d. $94.19
303.2. A firm's current asset value is $62.0 million with an asset volatility of 38.0%. Expected return on the firm's assets are 10.0% per annum. Debt consists of a single zero-coupon bond that matures in one (1.0) year with a face (par) value of $40.0 million. The riskfree rate is 2.0% per annum. What is the firm's probability of default (PD) according to the Merton model?
a. 1.05%
b. 4.38%
c. 9.15%
d. 11.00%
303.3. According to Malz, the basic "out-of-the-box" Merton Model suffers from drawback(s) and unrealistic assumptions, although they can be fixable with modifications or improvements. Each of the following is one of Malz's drawbacks of the basic Merton EXCEPT for:
a. In contrast to other applications of Black-Scholes (BSM), the underlying firm's asset value and asset volatility are not directly observable
b. By relying on the risk-neutral theory of the BSM, Merton ignores the real-world (physical) reality that a higher expected asset return (ROA or mu) would tend to realistically decrease default probability
c. The capital structure of a typical firm is "more much complex" than the basic Merton assumes, especially with regard to a firm's debt structure
d. For firms with high leverage (leverage = assets/equity), the Merton model tends to produce default probabilities that are unrealistically low and recovery rates that are unrealistically high
(Source: Allan Malz, Financial Risk Management: Models, History, and Institutions (Hoboken, NJ: John Wiley & Sons, 2011))
Answers:
