A company has a zero coupon bond issue with a face value of $1 million that matures in one year. The assets of the firm are currently valued at $1.3 million, but this amount is expected to either decrease to $1.2 million or increase to $1.7 million in a year's time. Assume the risk-free rate is 4%. What is the value of the equity?
Total assets of a firm are equal to the sum of total liabilities and total equity.
The present value of debt will be the discounted value of the face value. Irrespective of the value of the asset of the firm, the debt value in a year would be $1 million.
The present value of debt = Cash flow in one year/(1+risk free interest rate) = $1 million/1.04 = $0.961538 million
Therefore, the total equity value = Total asset - Total debt = ($ 1.3 - $0.961538) million = $0.33846 million
Thus, the value of equity is $338,461.54
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