Apple Residual Income

For informational and educational purposes only • Not investment advice.

Apple

iPhone, services, devices

Estimated Fair Value

$1374.08

Stock price: $333.69

Fair value above stock price

Residual Income estimates a company's fair value by combining its current Book Value per Share with the present value of future Residual Income.

Fair Value Composition

Fair Value Per Share consists of current Book Value Per Share, the present value of forecast residual income (RI), and the present value of terminal residual income (RI).

Key Valuation Metrics

Selected ROE

Time Horizon

Equity Risk Premium

Range: 2–10%

Notes

• Return on equity was normalized using recent historical results to better estimate the company's sustainable profitability.

Residual Income Formulas

Required Shareholder Earnings

\text{Required Shareholder Earnings} = \text{Book Value per Share} \times \text{Cost of Equity}

Residual Income

\text{Residual Income} = \text{Forecast EPS} - \text{Required Shareholder Earnings}

Terminal Value

\text{Terminal Value} = \frac{ \text{Terminal Residual Income} }{ \text{Cost of Equity} - \text{Terminal Growth} }

Fair Value per Share

\text{Fair Value per Share} = \text{Book Value per Share} + PV(\text{Forecast Residual Income}) + PV(\text{Terminal Value})

What is Residual Income Valuation?

Residual Income Valuation is based on the idea that a company creates value when it generates returns above the level required by its shareholders. This additional value is referred to as Residual Income.

When Return on Equity (ROE) exceeds the Cost of Equity, the company generates positive Residual Income and creates value beyond its existing Book Value. When ROE is below the Cost of Equity, Residual Income is negative.

The model uses Book Value and future Residual Income to estimate the company's intrinsic value. Unlike a Discounted Cash Flow model, it focuses on accounting earnings and Book Value rather than Free Cash Flow.

How the Residual Income Model Works

The Residual Income model starts with today's book value per share, estimates future economic profit by forecasting returns on equity above the Cost of Equity, discounts those future residual income streams to present value, adds a terminal value, and combines everything into an intrinsic value per share.

Book Value Per Share

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Estimate Return on Equity ROE

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Forecast Book Value & Residual Income

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Discount Residual Income

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Terminal Value

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Combine Values

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Fair Value Per Share

Key Model Assumptions

• Book Value per Share represents the current equity attributable to shareholders.
• Current EPS uses trailing twelve-month (TTM) earnings when available, with the latest annual EPS used as a fallback when calculating current ROE.
• Normalized ROE is based on the median of up to the five most recent valid historical ROEs and is adjusted using the selected ROE scenario.
• Forecast ROE gradually converges toward the Terminal ROE over the forecast period.
• Book Value grows through retained earnings based on the selected Payout Ratio.
• Positive Residual Income is created when forecast earnings exceed the required earnings implied by the Cost of Equity.
• Future Residual Income is discounted using the Cost of Equity.
• The Risk-Free Rate is based on the U.S. 10-Year Treasury yield published by the Federal Reserve Board.
• Terminal Value is included only when final-year Residual Income is positive.

Step 1 — Start With Book Value

Book Value Per Share = Total Shareholders' Equity / Shares Outstanding

Book Value Per Share = $107.5B / 14.69B shares

Book Value Per Share = $7.32

The Residual Income model begins with Apple's current book value per share of $7.32, representing the accounting value of shareholders' equity attributable to each share.

Step 2 — Estimate Return on Equity (ROE)

Current ROE = EPS / Book Value Per Share

$8.71 / $7.32 = 175.3%

Normalized ROE = Median of Up to the 5 Most Recent Valid Historical ROEs

Normalized ROE = 160.1%

Selected ROE = Normalized ROE × Selected ROE Scenario

160.1% × 100.0% = 160.1%

Terminal ROE = Cost of Equity + 1%

10.5% + 1.0% = 11.5%

Current ROE measures earnings in relation to Book Value per Share. The calculation uses trailing twelve-month (TTM) EPS as the current earnings measure. To reduce the effect of temporary fluctuations, the model then estimates a Normalized ROE based on the median of up to the five most recent valid historical ROEs.

The selected ROE scenario adjusts Normalized ROE to determine the starting ROE used in the forecast. Forecast ROE then gradually converges toward the Terminal ROE.

When Selected ROE exceeds the Cost of Equity, Terminal ROE is set to the Cost of Equity plus 1 percentage point. Otherwise, Terminal ROE equals the Cost of Equity.

Forecast ROE by Year

Return on Equity gradually fades toward the terminal ROE assumption.

Step 3 — Calculate the Cost of Equity

Cost of Equity = Risk-Free Rate + Beta × Equity Risk Premium

Cost of Equity = 4.7% + 1.17 × 5.0%

= 10.5%

The Cost of Equity represents the return shareholders require for investing in Apple and is estimated using CAPM.

Positive Residual Income is created when forecast earnings exceed the required earnings implied by the Cost of Equity.

Step 4 — Forecast Book Value and Residual Income

Forecast EPS = Forecast ROE × Beginning Book Value Per Share

Year 1 Forecast EPS = 160.1% × $7.32 = $11.72

Retained Earnings Per Share = Forecast EPS × (1 − Payout Ratio)

$11.72 × (1 − 12.2%) = $10.29

Next-Year Book Value Per Share = Current Book Value Per Share + Retained Earnings Per Share

$7.32 + $10.29 = $17.61

Required Shareholder Earnings = Cost of Equity × Book Value Per Share

10.5% × $7.32 = $0.77

Residual Income = Forecast EPS − Required Shareholder Earnings

$11.72 − $0.77 = $10.95

Year 1 Residual Income = $10.95

Forecast EPS is calculated from Forecast ROE and Beginning Book Value per Share. Earnings that are not distributed to shareholders are retained and added to Book Value.

The Cost of Equity is applied to Beginning Book Value to determine the earnings required by shareholders. Residual Income is the amount by which Forecast EPS exceeds these required earnings.

The complete year-by-year calculation is shown in the Residual Income Forecast Table.

Residual Income by Forecast Year

Residual income represents the economic profit created after covering shareholders' required return.

Step 5 — Discount Residual Income

Present Value of Residual Incomeₜ = Residual Income / (1 + Cost of Equity)^Year

Year 1 PV RI = $10.95 / (1 + 10.5%)¹ = $9.91

Present Value of Forecast Residual Income = $1226.43

Each year's Forecast Residual Income is discounted back to present value using the Cost of Equity.

The discounted values from all forecast years are then added together to calculate the Present Value of Forecast Residual Income. The complete year-by-year calculation is shown in the Residual Income Forecast Table.

Step 6 — Calculate Terminal Value

Terminal Residual Income = Final-Year Residual Income × (1 + Terminal Growth)

$25.72 × (1 + 3.5%) = $26.62

Terminal Value = Terminal Residual Income / (Cost of Equity − Terminal Growth)

$26.62 / (10.5% − 3.5%) = $380.65

Present Value of Terminal Value = Terminal Value / (1 + Cost of Equity)ⁿ

$380.65 / (1 + 10.5%)¹⁰ = $140.33

Present Value of Terminal Value = $140.33

Terminal Value represents the Residual Income expected after the explicit 10-year forecast period. The final Forecast Residual Income is grown at the Terminal Growth Rate and capitalized using the Cost of Equity.

The resulting Terminal Value is then discounted back to present value. If final-year Residual Income is not positive, the model assigns no Terminal Value.

The complete Terminal Value calculation is shown in the Residual Income Forecast Table.

Step 7 — Calculate Fair Value Per Share

Fair Value per Share = Book Value per Share + Present Value of Forecast Residual Income + Present Value of Terminal Value

Fair Value = $7.32 + $1226.43 + $140.33

Fair Value Per Share = $1374.08

Fair Value per Share is calculated by adding current Book Value per Share, the Present Value of Forecast Residual Income and the Present Value of Terminal Value.

For Apple, this results in an estimated Fair Value per Share of $1374.08.

Residual Income Forecast Table

The table below shows how Book Value Per Share, forecast earnings, required shareholder earnings and residual income develop throughout the explicit forecast period.

Year	Book Value per Share	Forecast ROE	Forecast EPS	Required Shareholder Earnings	Residual Income	PV Residual Income
Y1	$7.32	160.1%	$11.72	$0.77	$10.95	$9.91
Y2	$17.61	154.6%	$27.23	$1.85	$25.38	$20.79
Y3	$41.53	144.5%	$60.02	$4.36	$55.66	$41.26
Y4	$94.24	131.5%	$123.92	$9.89	$114.03	$76.50
Y5	$203.08	116.1%	$235.69	$21.31	$214.38	$130.17
Y6	$410.09	98.6%	$404.17	$43.03	$361.14	$198.45
Y7	$765.07	79.2%	$605.96	$80.28	$525.68	$261.43
Y8	$1297.29	58.2%	$754.52	$136.13	$618.39	$278.33
Y9	$1959.99	35.6%	$696.93	$205.68	$491.26	$200.11
Y10	$2572.10	11.5%	$295.63	$269.91	$25.72	$9.48
Total Present Value of Forecast Residual Income						$1226.43
Terminal RI	$2831.76	11.5%			$26.62	$140.33
The Terminal Value is $380.65 before being discounted back to its present value.
Estimated Fair Value Per Share = Book Value Per Share + PV Forecast Residual Income + PV Terminal Residual Income = $7.32 + $1226.43 + $140.33 = $1374.08