Finding Intrinsic Value of Security using EPS

CFA Level I Equities
#1

Hey all, stumbled across a tough question:

A company pays no cash dividends currently and is not expected to for the next four years. Its latest EPS was $5, all of which was reinvested in the company. The firm’s expected ROE for the next four years is 20% per year, during which time it is expected to continue to reinvest all of its earnings. Starting year 5, the firm’s ROE on new investments is expected to fall to 15% per year. The market capitalization rate is 15% per year.

  • What is this company’s intrinsic value per share?

I am lost on how to solve this.

#2

You must use a Dividend Discount Model.

Wait, what?

Remember that DDM is preferable for equity valuation when dividends are very correlated with EPS. In this case, the correlation is perfect, the company pays no dividend. So we will EPS directly.

First, prepare the EPS flow:

EPS was $5 last year and ROE is 20%, so, because there is no dividend distributions, EPS is expected to grow at a growth rate of 20% for the next 4 years.

5(1.2) , 5(1.2)2 , 5(1.2)3 , 5(1.2)4

Second, prepare the terminal value (using Gordon model):

The case says that at year 5 and ahead, the ROE will be 15% forever. Also, no cash dividend is expected, so the growth rate of EPS is 15%.

The terminal value is (5(1.2)4)(1.15) / (discount rate - growth rate)

We are not given with the discount rate directly, but with the capitalization rate which is 15%. By definition, the cap rate is equal to the discount rate - growth rate of the flow. So, completing the terminal value formula we get:

TV = (5(1.2)4)(1.15) / (0.15)

We deduce that the discount rate is 30%

Now, bring to present the flow shown in Step 1 and the TV to get the intrinsic value of the stock.

Hope this helps