Step 1: Book Value of Equity Roll-Forward
Because the clean surplus relation holds, book equity grows exactly by the net income the bank retains:
BVE1 = $500.0m + $60.0m = $560.0m
BVE2 = $560.0m + $65.0m = $625.0m
| Point in Time | Book Value of Equity |
|---|
| Start of Year 1 | $500.0m |
| Start of Year 2 | $560.0m |
| Start of Year 3 | $625.0m |
This roll-forward is what lets the Residual Income Model track economic value creation directly on the balance sheet — something free cash flow struggles to do for a bank, which has no intuitive capex or working-capital cycle and whose reported "cash flow" is shaped heavily by regulatory capital and funding decisions rather than operating performance.
Step 2: Residual Income (EVA)
Where: NI = Net Income, Re = Cost of Equity, BVE = Book Value of Equity at the start of the period.
Using the beginning-of-period book value as the capital base for each year's charge:
RI1 = $60.0m - (10.0% x $500.0m) = $60.0m - $50.0m = $10.0m
RI2 = $65.0m - (10.0% x $560.0m) = $65.0m - $56.0m = $9.0m
RI3 = $70.0m - (10.0% x $625.0m) = $70.0m - $62.5m = $7.5m
| Year | Net Income | Capital Charge (Re x Beginning BVE) | Residual Income |
|---|
| Year 1 | $60.0m | $50.0m | $10.0m |
| Year 2 | $65.0m | $56.0m | $9.0m |
| Year 3 | $70.0m | $62.5m | $7.5m |
Residual income is the profit left over after charging the business for the opportunity cost of the equity capital it employs. It isolates genuine value creation from mere profitability — net income alone doesn't tell you whether the bank earned more than shareholders could get elsewhere for the same risk. Notice that residual income is declining even though net income is rising: the capital charge is growing faster than earnings, a warning sign for future value creation that a simple net income trend would miss entirely.
Step 3: Present Value of Residual Income
Discounting each year's residual income at the cost of equity:
PV(RI1) = $10.0m / 1.10^1 = $9.1m
PV(RI2) = $9.0m / 1.10^2 = $7.4m
PV(RI3) = $7.5m / 1.10^3 = $5.6m
Sum of PV (Years 1-3) = $9.1m + $7.4m + $5.6m = $22.2m
This step converts a series of annual excess-return figures into a single present-value contribution — the same discounting logic as a DCF, but applied to a profit measure that is already capital-charge-adjusted, so there is no separate step needed to subtract reinvestment or capex.
Step 4: Terminal Value of Residual Income
Using the Year 3 residual income and a 2.0% (0.02) terminal growth rate:
TV3 = [$7.5m x 1.02] / (10.0% - 2.0%) = $7.65m / 8.0% = $95.6m
PV(TV3) = $95.6m / 1.10^3 = $71.8m
The terminal value captures residual income beyond the explicit forecast using the same Gordon growth perpetuity formula as a DCF terminal value. The key difference is that it compounds a shrinking excess-return figure rather than a growing free cash flow figure — which is why RI-based terminal values are typically far less sensitive to the terminal growth assumption than DCF terminal values are, and why interviewers like this model for capital-intensive businesses.
Final Results
- Sum of PV of Residual Income (Years 1-3 + Terminal Value): $94.0m
- Equity Value = BVE0 + PV(Residual Income) = $500.0m + $94.0m = $594.0m
This equity value can be compared directly against the bank's market capitalization to test whether the market is pricing in the same value-creation trajectory implied by the forecast — and unlike a DCF, it gets there without ever forecasting dividends, buybacks, or a standalone free cash flow line, all of which are heavily shaped by regulatory capital requirements for a bank rather than by underlying operating performance.
Would you like to explore how this valuation changes if the bank's ROE falls below its cost of equity in the terminal year?
No comments yet — be the first to ask a question.