Residual Income Valuation

Question 1

Residual Income

Answer 1

RI = “economic profit” = NI of firm less a charge for stockholders oppy. cost of capital

Question 2

Economic Value Added (EVA)

Answer 2

EVA = NOPAT - ( WACC * invested capital )

EVA = [ EBIT * (1-tax) ] - $WACC

where:

NOPAT = “net operating profit after tax”

Question 3

Market Value Added (MVA)

Answer 3

MVA = market value - invested capital

Question 4

Difference between RI and EVA

Answer 4

RI:

• Net Income (after interest expense)
• minus a charge for EQUITY capital based on cost of equity

EVA:

• NOPAT (before interest expense)
• minus a charge for EQUITY and DEBT based on WACC

Question 5

Calculation of Residual Income

Answer 5

RI_t = E_t - ( r * B_t-1)
RI_t = ( ROE - r ) * B_t-1

Difference between end-of-period earnings and equity charges based on begin-of-period book value.

Question 6

Valuation using RI Model

Answer 6

V0 = B0 + [ RI1/(1+r)^1 + RI2/(1+r)^2 + … ]

Value is equal to book value PLUS te PV of all future residual income.

Question 7

Forecast Book Value Per Share

Answer 7

Forecast BVPS = B_t-1 + E_t - D_t

Question 8

RI Model that highlights the drivers of Residual Income

Answer 8

V0 = B0 + [ ( ROE - r ) * B0 ] / ( r - g )

Second part is the additional value generated by the firm’s ability to produce returns in excess of the cost of capital.

Important: this model assumes:

• constant ROE
• constant g

Question 9

Tobin’s Q

Answer 9

Q = [ MV(debt) + MV(equity) ] / replacement cost of total assets

Question 10

Re-arrange Single-Stage RI model to calculate implied growth rate for a stock

Answer 10

g = r - [ [ B0 *( ROE - r ) ] / (V0 - B0) ]

Gives you the market’s expectation of growth implied by current market price

Question 11

Multi-stage RI Models

Answer 11

V0 = B0 + [ PV of high growth RI ] + [ PV of continuing residual income ]

Question 12

PV of Continuing Residual Income

Answer 12

PV Continuing RI in year T-1 = RI_t / ( 1 + r - w)

where:
w is persistence factor between 0 and 1

Question 13

PV of Continuing Residual Income that PERSISTS FOREVER

Answer 13

PV Continuing RI in year T-1 = RI_t / ( 1 + r - w )

= RI_t / ( 1 + r - 1 )
= RI_t / r

Question 14

PV of Continuing Residual Income that DROPS IMMEDIATELY to ZERO

Answer 14

PV Continuing RI in year T-1 = RI_t / ( 1 + r - w )

= RI_t / ( 1 + r - 0 )
= RI_t / ( 1 + r )

Question 15

PV of Continuing Residual Income that DECLINES OVER TIME TO ZERO

Answer 15

PV Continuing RI in year T-1 = RI_t / ( 1 + r - w )

= RI_t / ( 1 + r - w )

Question 16

PV of Continuing Residual Income that DECLINES TO LONG-RUN LEVEL in MATURE INDUSTRY

Answer 16

PV future RI = difference between market value and book value

= P_t - B_t

PV Continuing RI in year T-1 = [ (P_t - B_t) + RI_t ] / ( 1 + r )

Question 17

Clean Surplus Relation

Answer 17

Ending book value of equity equals beginning book value of equity PLUS earnings LESS dividends

B_t = B_t-1 + E_t - D_t