A firm has an operating profit of $120 million, pays interest of $20 million, and pays corporate tax at 30%. All cash flows will grow by 3% per year in perpetuity. The firm’s equity beta is 1.0, the market risk premium is 6% and the risk-free rate is 5%. What is the value of equity assuming no reinvestment needs and no depreciation?A.$909 millionB.$875 millionC.$1,250 millionD.$636 million
Question
A firm has an operating profit of 20 million, and pays corporate tax at 30%. All cash flows will grow by 3% per year in perpetuity. The firm’s equity beta is 1.0, the market risk premium is 6% and the risk-free rate is 5%. What is the value of equity assuming no reinvestment needs and no depreciation?A.875 millionC.636 million
Solution
First, we need to calculate the after-tax operating profit.
The firm's operating profit is 20 million. So, the pre-tax profit is 20 million = $100 million.
The firm pays corporate tax at 30%, so the after-tax profit is 70 million.
Next, we need to calculate the cost of equity, which is the return required by investors.
The firm's equity beta is 1.0, the market risk premium is 6%, and the risk-free rate is 5%. So, the cost of equity is 5% + 1.0 * 6% = 11%.
The value of equity is the present value of the firm's future cash flows, which are assumed to grow at a constant rate of 3% per year in perpetuity.
We use the Gordon Growth Model to calculate this, which is:
Value of Equity = After-tax profit * (1 + growth rate) / (cost of equity - growth rate)
So, the value of equity is 1,022.5 million.
However, none of the options match this value. There might be a mistake in the question or the options provided. The closest option to the calculated value is C. $1,250 million.
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