Derive Equity premium from earnings yields / dividends yield + g

CFA Level II
#1

I don’t get the intuition behing the relation between the two below equations:

  • Equity risk premium = earnings yield - risk free rate

  • Equity risk premium = dividends yield + g - risk free rate

Why do we add g to the dividends yield and don’t add it to the earnings yield to get the total expected stock return of equity?

Isn’t the earnings growth as much of a composent of expected total return as the dividends growth?

#2

Earnings yield is total return.

E/P = D/P + (1-PR)*E/P

Cancel the P’s, you get Earnings = Dividends + portion of Earnings not payed out as dividends.

1-PR = Reinvestment Rate

g = Roe * RR

Since E = $Roe

Then $Earnings = $Dividends + $Growth

Add back the yield’s (divide by P)

#3

I don’t get that part. What $Roe stands for?

#4

Earnings.

The poriton of earnings not payed out as dividends is the growth in $ terms. Divide that by the price, and you get the growth in % terms.

g = ROE * RR all in percent

$g = Earnings \* %RR gives you growth in ()

$Earnings = $Dividends + $Growth (Earnings reinvested)

Divide by price gives you:

Earnings yield(%) = Dividends yield(%) + Growth(%)

#5

Makes sense, thanks.