### CFA Practice Question

There are 151 practice questions for this study session.

### CFA Practice Question

Consider a 100% equity financed firm that has physical assets valued at \$200 million. The market believes that all physical assets the firm has will produce earnings of 12.5% of the value of the assets. The firm reinvests an unknown amount of earnings into physical capital, and pays out the rest as dividends. There are no taxes. What is the P/E ratio for the firm?
A. 6
B. 8
C. 12
Explanation: As it turns out, the rate of retention doesn't matter. The earnings of the firm for the first year are 200M * 12.5% = 25M.
Say the retention rate is b.
Amount of earnings retained to reinvest in physical capital = b*25M
Amount of earnings paid out as dividends = (1-b)*25M
Growth rate = b*25M/200M = 12.5%*b
Then we have the price of total equity = (1-b)*25M/(12.5% - b*12.5%) = (25M/12.5%)*((1-b)/(1-b)) = 200M
And PE ratio = 200M/25M = 8
So what happened here? This is simply Modigliani-Miller in action. The firm can either pay out dividends or keep the money and re-invest in physical assets that produce a 12.5% return, and have the cash flows produced discounted at 12.5%. So essentially when the firm re-invests \$1, it produces cash flows whose discounted value is \$1. Therefore it does not matter how much the firm retains, it doesn't change the value of equity, therefore does not change P/E ratio. In other words, the dividend policy is irrelevant.

### User Contributed Comments6

User Comment
leftcoast I wouldn't rank this question as easy.
somk leftcoast, ranking is based on the percentage of users getting it right. so it seems u r over estimating this question.
adamrej A somewhat implicit assumption here is that the applicable discount rate is equal the expected return on equity. Not sure why this should hold ...
daverco Or to get to the P/E ratio, you take the inverse of the E/P ratio. The E/P ratio is a proxy for the cost of equity, which is here 25/200 (because 200 is all equity) = 0.125. Then, 1/0.125 = 8. That's how I reasoned through it at least.
darbyland thank you for that daverco
darbyland can anyone explain how the growth rate is calculated (as b*25M/200M) ?