Question

Consider a firm with a ROE of 12%. The earnings next year are projected at $50 per share, and the firm’s earnings retention ratio is 0.70. The required rate of return is 10%. Compute the following for the firm:

a) Intrinsic value
b) Intrinsic P/E
c) Present value of growth opportunity (PVGO)

Answer 1

To calculate the intrinsic value, use the Gordon Growth Model: Intrinsic Value = Earnings per Share / (Required Rate of Return - Growth Rate). Using the provided values, the intrinsic value is $3,125 per share. The intrinsic P/E ratio is 62.5, and the PVGO cannot be calculated without the market price per share.

Step-by-step explanation:

To calculate the intrinsic value of a firm, we can use the Gordon Growth Model, which is given by the formula: Intrinsic Value = Earnings per Share / (Required Rate of Return - Growth Rate).

In this case, the earnings per share is $50, the required rate of return is 10%, and the growth rate can be calculated using the retention ratio. Since the retention ratio is 0.70 and the return on equity is 12%, the growth rate is 0.70 * 12% = 8.4%.

Plugging in these values, we get: Intrinsic Value = $50 / (10% - 8.4%) = $50 / 1.6% = $3,125 per share.

The intrinsic P/E ratio can be calculated by dividing the intrinsic value by the expected earnings per share: Intrinsic P/E = Intrinsic Value / Expected Earnings per Share = $3,125 / $50 = 62.5.

The present value of growth opportunity (PVGO) can be calculated by subtracting the intrinsic value from the market price per share: PVGO = Market Price - Intrinsic Value. However, the market price per share is not given in the question, so we cannot calculate the PVGO.