Definition of RoE in (Equity & FRA) as per CFAI

CFA Level II
#1

Guys,

Just wanna confirm this: So, RoE = Net Income/Avg. Book Value of S.E. - that’s how CFAI defines & calculates in Equity & FRA readings, correct?

But on Page-244 (footnote 22) of EQUITY (Reading 35), where they talk about how increase in shareholder wealth occurs only when investments have a net positive present value (i.e. RoE > required return on equity) - So far good. But in the footnote, they explain that this RoE is calculated based on Mkt Value of Equity (rather than BV of equity)…

Can somebody please look into this and reconcile it…both concept wise and also what should be used on exam as a general rule.

#2

Usually, RoE is calculated based on beginning book value for the period; or for average book value for the period as the denomintor.

I have no idea why CFAI would consider market value (MV) of equity when calculating RoE or how they justify it. Maybe some professor type showing off.

Off-hand, the two places where you consider MV of equity is when (1) calculating entrprise value and (b) deciding if book value will go up after buybacks.

#3

Thanks,

#4

shareholder wealth will only increase if the ROE is greater than the cost of equity at MARKET VALUE of equity.

book value will increase if the ROE is greater than the cost of equity calculated using BOOK VALUE of equity.

Think about it this way, if a companies book value increases will a shareholder make money? maybe, or maybe not. The only way shareholder wealth increases if if they make a ROE of the market value that is greater than their cost of equity.

BV of equity = $10

MV of equity = $20

Earnings = $1

P/B = 2x

ROE based on BV = 10%

ROE based on MV = 5%

if cost of equity is 8% book value will be increasing however the wealth of the shareholder will not as they have only earning 5% on they capital when they could have deployed it elsewhere and got 8% (the problem lays in the fact that they paid 2x book value)

#5

Also note that ROE as calculated using market value of equity is the same as earnings yield. From the example i gave you the P/E is 20/1 or 20x earnings, which is the same as an earnings yield of 5%…

#6

RoE means Return on Equity i.e. how much return is generated on the investments made by equityholders . This is equal to Net Income divided by Average value of equity . Where the market value is given we use the market value and if the market value is not given we use the book value of equity to calculate the RoE. The higher it is the better is the ratio.