calculation of the price-to-book ratio

Question

You are analysing a firm. The firm has a book value of $20.00 per share. You expect a dividend payout of 100 percent to have a return on common equity of 12 percent per year indefinitely in the future. Its cost of equity capital is 10 percent.

 

1)Calculate the intrinsic price-to-book ratio.

 

2)Suppose this firm announced that it was reducing its payout to 50 percent of earnings in the future. How would this affect your calculation of the price-to-book ratio?

Answer 1

Lets start with the dividend growth model:

 

P = DPS1/(K-G)

 

Where, P = stock price today

           DPS1 = Expected dividend next year

           K = Cost of equity capital

           G = Growth rate in dividends

 

Now, we can write, DPS1 = EPS1 * Payout Ratio

 

 

We can also write, Return on equity (ROE) =EPS1/(Book value of Equity today)

Or, EPS1 = ROE * Book Value of equity today

 

With this much theoretical background, lets start the first part of the problem:

 

(1) We are given:   Payout Ratio = 100% = 1.0

                             Book Value of equity today = $20

                             Cost of equity capital = K = 10% = 0.10

                             ROE = 12% = 0.12

 

We first calculate EPS1 = ROE * Book Value of Equity today = 0.12*$20 = $2.4

Now we calculate DPS1 = EPS1* Payout Ratio = $2.4 *1.0 = $2.4

 

We can also calculate G = Growth rate in dividends = Return on Equity * Earnings retention = ROE * (1-Payout Ratio)

Since in our case Payout Ratio = 100%, G will be zero.

 

So, Stock price today, P = DPS1/(K-G) = $2.4/(0.10-0) = $24

 

Intrinsic Price to Book Value = P/BV = $24/$20 = 1.2

 

 

(2) If Payout Ratio = 0.50, then two things will be changed

 

First, G = ROE * (1-Payout Ratio ) = 0.12*(1-0.5) = 0.12*0.5 = 0.06

Then, DPS1 = EPS1* Payout Ratio = $2.4*0.5 = $1.2

 

So, Stock Price Today = DPS1/(K-G) = $1.2/(0.10-0.06) = $1.2/(0.04) = $30

 

New Intrinsic Price to Book Value = $30/$20 =1.5

 

 

This means as the company announces a reduction in payout ratio from 100% to 50%, my intrinsic price to book value increases from 1.2x to 1.5x. This is logical because as a growing company retains more cash for future growth, its valuation should improve. I hope this helps you.

 

Thanks,

 

Swaraj Chowdhury