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Consider a single period problem where the riskless interest rate is zero, and there are no taxes. A firm consists of a machine that will produce cash flows of $210 if the economy is good and $80 if the economy is bad. The good and bad states occur with equal probability and the covariance of these states with the market portfolio is zero (no systematic risk). Initially, the firm has 100 shares outstanding and debt with a face value of $50 due at the end of the period. What is the share price of the firm

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Assuming the firm has 100 shares outstanding and debt with a face value of $50 due at the end of the period. The share price of the firm is $0.95.

Share price

First step is to calculate the expected payoff to equity

Expected equity=[($80 ×0.5) + ($210 × 0.5)]-$50

Expected equity=($40+$105)-$50

Expected equity = $145-$50

Expected equity=$95

Now let calculate the share price

Share price=$96/100 shares

Share price=$0.95

Inconclusion the share price of the firm is $0.95.

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