Assume that a firm's earnings are expected to be $1 million next year, but that this number is expected to shrink by 2% a year indefinitely. If the appropriate cost of capital is 20%, what is
This firm's P/E ratio?

Question

Quizplus · Accepted Answer

We can use the dividend discount model to estimate the P/E ratio. Since the firm's earnings are expected to shrink indefinitely, we can assume that it will pay out its entire earnings as dividends. Therefore, the dividend in the first year will be $1 million, and it will shrink by 2% a year indefinitely.

The present value of the perpetual stream of dividends can be calculated as:

PV = D / (r-g)

where PV is the present value, D is the dividend in the first year, r is the cost of capital, and g is the growth rate of dividends. Plugging in the numbers, we get:

PV = $1 million / (20% - 2%) = $5 million

The P/E ratio can be calculated as:

P/E = Price per share / Earnings per share

Since the present value of the firm's future dividends is equal to the current price of the firm's shares, we can use the present value to estimate the price per share. Therefore, the P/E ratio can be calculated as:

P/E = $5 million / $1 million = 5.0

Therefore, the answer is C (4.5 is not one of the options, and D is not correct because we were able to calculate a P/E ratio using the dividend discount model).

Assume That a Firm's Earnings Are Expected to Be $1