Residual Income

Summaries

Residual income is just the economic profit, i.e. the net income less the opportunity cost of the equity.

EVA – Economic Value Added

= NOPAT – WACC * Invested capitals

= EBIT (1-t) – $ value of invested capitals

Invested capitals = net WC + net fixed assets

=BV of long-term debt + BV of equity

MVA = Market value – invested capital

(Include both long term debts and equity)

Residue income

RI_t = E_t – r*BV_(t-1) = (ROE – r) *B_(t-1)

Residual income model:

V0 = BV0 + sum(RI_t/(1+r)^t) (last term is the economic profit)

Special case: V0 = BV0 + (ROE-r)*BV0/(r-g) or V0 = BV0*(ROE-g)/(r-g)

Not using NI because BV need to increase with the required rate of return also (r).

The current BV (BV0) contributes a substantial portion of V0 (compared to other DCF methods, in which terminal values have a large weight)

BV doesn’t not need forecasting but subjected to manipulation. And many adjustments are needed.

Clean Surplus Relation: BV_t = BV_(t-1) + E_t – D_t

If there is comprehensive income (under the clean surplus accounting), the Residual income model will be affected. *** happens when items are directly charged to shareholders’ equity but not going through the income statement

1)      Foreign currency translation gains under all-current-method

2)      Minimum liability adjustment in pension accounting

3)      Change of market values for debts and equity securities classified as available-for-sale

Balance sheet adjustments for fair values

1. Operating leases be capitalized
2. Special Purpose Entity be consolidated
3. Reverse and allowance be adjusted
4. LIFO+LIFO reserve => FIFO for inventory
5. Pension asset or liability
6. Deferred tax liabilities

Goodwill should be included and NOT amortized.

R&D should be included

V0 = BV0 + PV of RI (high growth for T years) + PV of continuing residual income

PV of continuing residual income at T-1 year = RI_T/(1+r-w)

w is the persistent factor between 0 and 1

w=1 if RI_T is constant for ever

w =0 if RI_T dropped to zero the following year

If the residual income falls gradually to the mature industry level, we can estimate the price at year T, P_T = BV_T * P/BV ratio.

Then PV of continuing residual income at T-1 year = (RI_T + (P_T-BV_T))/(1+r)

*** Note that the last year’s RI is included!!!

*** Distinguish Residual Income and Retention Earnings in the calculations!