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Suppose the Current Value of a Firm's Assets Is $100

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Suppose the current value of a firm's assets is $100 million, and the value of equity in the firm is $40 million. Suppose too that the firm has only one issue of debt outstanding: zero-coupon debt with a maturity of three years, and a face value of $70 million. Finally, suppose that the risk-free rate of interest is 4% (continuously-compounded terms) for all maturities. Assuming that firm value evolves according to a lognormal diffusion (as in Merton, 1974) , what is the volatility of the firm's assets?


Definitions:

Stationary Object

An object that is not in motion; remaining in the same place relative to its surroundings.

Just Noticeable Difference

The minimum difference in stimulation that a person can detect 50% of the time, also called the difference threshold.

Ounce

A unit of weight in the avoirdupois system, equivalent to 1/16th of a pound or approximately 28.35 grams.

Sensory Adaptation

The gradual decrease in sensory receptors' sensitivity to unvarying stimuli as time goes on.

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