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Explain the Altman Z Score

Altman Z Score is an empirical credit models. These do not try to estimate credit spreads or default probability but generate a credit score.

Altman Z Score uses - Liquidity, profitability, leverage, solvency and activity

Z = 1.2*X1 + 1.4* X2 ! 3.3*X3 + 0.6*X4 + 1*X5

X1 = working capital / total assets ratio

X2 = retained earnings / total assets ratio

X3 = EBIT / total assets ratio

X4 = Market value of equity / book value of total liabilities ratio

X5 = sales / total assets

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How do you interprete the Altman Z Score?

If Z < 1.81 Default (or distressed)

1.81 <=Z <= 2.99 Gray Zone

Z > 2.99 Nondefault or safe

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1. The exposure at default for a loan is $250 million, the recovery rate is estimated to be 31.4%, and the estimated probability of loss is 1.15%. The expected loss is:

LGD = EAD * (1-RR) = 250 * (1-0.314) = 171.50

E(Loss) = LGD * PD = 171.50 * 0.0115 = 1.972

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2. An analyst is considering a bond in a leverage company and wants to model credit risk as a random exogenous variable. The analyst should use:

Reduced form model

structural model

positive model

empirical model

Reduced form models treat default risk as a random external variable

structural model view credit risk from the perspective of equity holders

positive models explore how assets should behave and

empirical models do not directly evaluate default risk 

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3. ABC Corporation has assets worth $175 million and an asset volatility of 25%per year. The firm issued a five-year zero-coupon bond with a face value of $115 million. The annual risk-free rate is 3.25%, N(d1)is 0.9466, and N(d2)is 0.8539. Using the Merton model, the value of debt is:

E = 175*0.9466 - 115 * e^(-0.0325*5) * 0.8539 = 82.18

D = A - E = 175 - 82.18 = 92.82

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4. The XYZ Corporation is worth $150 million with an estimated default trigger of $87 million and asset volatility estimate of 26%. According to the KMV model, the distance to default is:

p(4) - p(5) = e^(-0.07 *4) - e^(-0.07*5) = 5.11%

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6. Whichof the following ratios is NOTa determinant of Altmans Z-score?

A.Net income/total assets.

B. Retained earnings/total assets.

C. Working capital/total assets

D. Sales/total ass


The five determinants of Altmans Z-score are (1) workingcapital total assets, (2) retainedearnings total assets(3) EBIT/total assets, (4) market value of equity/book valueof total liabilities, and  (5) sales / total assets

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Stacey is considering using the Merton model to monitor default risk. She is concerned about the sensitivity of credit spreads to variables like maturity and volatility. The real concern is for the possibility of exponential increases in credit spreads. How should Stacey adjust her concerns? Explain.

The Merton model is sensitive to both maturity and volatility with respect to credit spreads. However, the slope of the change declines as time progresses. For example, credit spreads rise rapidly as maturity initially begins to increase but the rate of change slows considerably as time progresses. This profile reflects the law of diminishing marginal utility. The reason for this shape is that as firms are able to survive longer under rising maturity lengths or volatility the marginal probability of defailt decreases