4.3 Per-Share Metrics and Growth

Basic and Diluted Earnings Per Share

A margin is profit per sales dollar. Earnings per share (EPS) is profit per share of common stock. FMVA cases use EPS when they move from firm-level statements to owner-level results, and again when they build a residual-income or P/E walk in valuation. CFI does not publish a passing-score market multiple, and this course does not treat any P/E or EV/EBITDA figure as an official FMVA hurdle. Learn the per-share mechanics. Leave trading multiples to the comparable-valuation core.

Basic EPS = Net income attributable to common / weighted-average basic shares outstanding.

Harbor Year 3 net income is $10,500,000. Weighted-average basic shares are 10,000,000. Basic EPS = 10,500,000 / 10,000,000 = $1.05.

Weighted-average matters. If Harbor had 10,000,000 shares for the first nine months and issued 2,000,000 new shares on 1 October, the weighted average is 10,000,000 × 9/12 + 12,000,000 × 3/12 = 10,500,000, and basic EPS would be 10,500,000 / 10,500,000 = $1.00. Using year-end 12,000,000 shares in basic EPS would understate EPS. Using beginning 10,000,000 shares after a mid-year issue would overstate it.

Diluted EPS includes securities that could become common shares if the effect is dilutive: in-the-money options and warrants, convertible debt, convertible preferred. Employee options use the treasury-stock method:

1. Count the options as if exercised.
2. Pretend the company takes the strike proceeds and buys back shares at the average market price for the period.
3. Incremental diluted shares = options − shares hypothetically bought back.

Harbor has 800,000 options outstanding with a $12 strike. Average market price during the year is $20 (in the money).

• Proceeds = 800,000 × $12 = $9,600,000
• Hypothetical buyback = 9,600,000 / 20 = 480,000 shares
• Incremental shares = 800,000 − 480,000 = 320,000
• Diluted shares = 10,000,000 + 320,000 = 10,320,000
• Diluted EPS = 10,500,000 / 10,320,000 = $1.017 ≈ $1.02

If the average price had been $10, below the $12 strike, the options are antidilutive and are excluded. Diluted EPS is never higher than basic EPS when you have applied the tests correctly. A choice that shows diluted EPS above basic EPS is wrong.

Convertible debt, if it exists, uses the if-converted method: add back after-tax interest to the numerator and add the conversion shares to the denominator, then keep the convertibles only if the result is dilutive. Harbor has none. Do not invent a conversion just to have a fifth factor.

Book Value Per Share

Book value per share (BVPS) = Common book equity / shares.

Harbor: 42,000,000 / 10,000,000 = $4.20 using year-end basic shares. BVPS is a stock (balance-sheet) metric, so the usual share count is period-end shares, not the EPS weighted average. If 2,000,000 shares were issued on the last day of the year, basic EPS barely moves and BVPS falls immediately: 42,000,000 / 12,000,000 = $3.50 if the issue proceeds are not yet in equity, or a higher figure if cash and equity both rose by the issue amount.

Some analysts quote diluted BVPS (equity / diluted shares). Harbor diluted BVPS = 42,000,000 / 10,320,000 = $4.07. Name which share count you used. Mixing basic EPS with diluted BVPS in the same sentence is sloppy, not conservative.

BVPS is not a valuation. It is accounting equity per share. A profitable firm trading above book is common; that gap is a market multiple, which is a later chapter, not an FMVA passing statistic.

Dividends, Payout, and Retention

Harbor pays $4,200,000 of common dividends in Year 3.

Dividend per share (DPS) = Total common dividends / shares = 4,200,000 / 10,000,000 = $0.42. (If shares changed during the year, DPS is often computed on the shares that actually received the dividend, not on the EPS weighted average. Read the case.)

Payout ratio = Dividends / Net income = 4,200,000 / 10,500,000 = 40%.

Retention ratio (plowback) b = 1 − payout = 60%. Retention is also (Net income − Dividends) / Net income = 6,300,000 / 10,500,000 = 60%. That $6.3 million is the increase in retained earnings when there are no other equity items.

Payout and retention split one residual. They are not independently chosen once NI and dividends are known. A 40% payout is not a 40% of revenue distribution; it is 40% of net income. 4,200,000 / 80,000,000 = 5.3% of revenue, which is a different ratio and the wrong one for sustainable growth.

Exam trap: putting dividends in SG&A so EBIT falls. Dividends are not an expense. They never touch EBIT, EBITDA, or net income. They reduce retained earnings and cash (cash from financing).

Sustainable Growth Rate

The sustainable growth rate is the growth the firm can fund internally without issuing new equity and without changing leverage, payout, or operating returns:

g = ROE × retention ratio = ROE × (1 − payout)

Harbor, using the 25% ending-equity ROE and 60% retention:

g = 25% × 0.60 = 15%

If next year's sales are to grow at 15% from $80 million to $92 million, assets at a constant 70/80 turnover would need to grow 15% as well, to $80.5 million. That $10.5 million of new assets is funded by $6.3 million of retained earnings plus a 15% increase in liabilities, including a 15% increase in the $20 million of debt. Leverage (D/E) stays constant because debt and equity both grow at 15%. That is the identity's hidden assumption: the firm draws enough new debt to keep the equity multiplier unchanged.

If Harbor instead holds debt at $20 million (no new borrowing), equity still grows $6.3 million and leverage falls. Growth that can be funded with no new debt and no new equity is lower than 15%. If Harbor pays out 100%, retention is 0 and g = 0 under the formula: all earnings leave as dividends, book equity does not grow, and asset growth has to be funded by new capital or by sweating the existing base harder (higher turnover, which is a change in the model).

Assumptions baked into g = ROE × b:

• ROE stays constant (margins, turnover, and leverage stay constant)
• Payout stays constant
• No new common equity issuance
• Depreciation reinvestment and working-capital needs scale with sales

It is a planning identity, not a forecast guarantee. A firm can grow faster than g by issuing shares, raising leverage, or lifting ROE. It can grow slower by holding cash. On the exam, compute g from the two inputs you are given; do not replace ROE with ROA or ROIC unless the question explicitly redefines the formula.

Worked variant: if Harbor lifts payout to 70%, retention is 30% and g = 25% × 0.30 = 7.5%. Owners take more cash now; the book can support less growth. If ROE is computed on average equity (27.0%) with the same 60% retention, g = 16.2%. Stay consistent with the ROE definition you used in DuPont.

Year-over-Year Growth versus CAGR

CFI's horizontal tool is the one-period growth rate:

YoY = Period N / Period N-1 − 1

The course example remains 55,749 / 53,494 − 1 = 4.2%. Harbor's Year 3 revenue YoY is 80,000,000 / 76,000,000 − 1 = 5.3%. When someone says growth, ask: growth of which line, over how many periods?

Compound annual growth rate (CAGR) compresses several periods into one annualized rate:

CAGR = (Ending / Beginning)^(1/n) − 1

n is the number of intervals, not the number of year-labels on a page. From the end of Year 0 to the end of Year 3 is n = 3.

Harbor revenue three years earlier was $60,000,000. Ending Year 3 is $80,000,000.

CAGR = (80,000,000 / 60,000,000)^(1/3) − 1 = (1.3333)^(1/3) − 1 ≈ 10.1%.

That 10.1% is not 80/60 − 1 = 33.3% (the three-year cumulative change). It is also not automatically the average of the yearly rates.

Path that still starts at 60 and ends at 80:

Arithmetic average of the three YoY rates = (20.0 − 2.8 + 14.3) / 3 = 10.5%. CAGR is still 10.1%, because compounding cares about the start and the end, not the order of the bumps. A year of −2.8% has to be earned back. Averaging the percentages treats a 20% up year and a 2.8% down year as if they were symmetric; they are not.

When n = 1, CAGR equals YoY. CFI's 4.2% example is that special case. For a three-statement forecast, you usually drive Year 4 revenue with a YoY growth rate, not with a historical CAGR pasted into every year. CAGR is the right summary of a history. YoY is the right driver of the next period unless the case says otherwise.

Exam trap: dividing by n without the exponent: (80/60 − 1) / 3 = 11.1%, which is the average annual simple change and not CAGR. Another trap: using n = 4 because four years are listed (Year 0 through Year 3). Four labels, three intervals.

Option Dilution in Concept

Dilution is not only an EPS formula. It is a claim on future cash flows and on governance.

• Options and warrants add shares only when they are in the money (treasury-stock method). Out-of-the-money options are ignored for diluted EPS but still exist as potential future dilution if the stock rises.
• Restricted stock units (RSUs) typically enter the diluted count as whole shares (no strike proceeds to buy back). 200,000 RSUs would add 200,000 diluted shares, not a treasury-method haircut.
• Buybacks retire shares and reverse dilution if the company actually repurchases. The treasury-stock method's hypothetical buyback is not a real buyback.
• When you move from enterprise value to equity value per share in a DCF, the denominator is diluted shares (and you must be consistent about whether option proceeds are already in cash). Using basic shares overstates value per share.
• Stock-based compensation is often added back in an adjusted EBITDA. That add-back does not cancel dilution. You cannot both add the expense back and ignore the extra shares.

Harbor illustration of the per-share stack:

Payout on a per-share basis is DPS / basic EPS = 0.42 / 1.05 = 40%, the same 40% as dividends / NI, because both numerator and denominator were divided by the same 10 million shares. If you mix DPS with diluted EPS, 0.42 / 1.02 = 41%, a false payout increase created by the share count, not by the board.

What the FMVA Exam Does Not Publish

CFI's final exam is 50 multiple-choice questions, 70% to pass, with Finance among the heavier domains. That is logistics. CFI does not publish a required market P/E, a passing EV/EBITDA, or a magic PEG that every model must hit. Do not memorize 15× or 8× as if they were exam facts. Comparable-valuation courses teach how to build a multiple from peers; they do not certify a universal multiple.

What this section does expect you to compute under time pressure:

• Basic versus diluted EPS with a treasury-stock option overlay
• BVPS with the correct share count
• Payout, retention, and g = ROE × b
• YoY with CFI's Period N / Period N-1 − 1 formula, including the 55,749 / 53,494 = 4.2% pattern
• CAGR with the correct n, and the refusal to average volatile yearly rates and call the result a compound rate

Those are analysis identities. They survive an open-book exam because the case numbers change and the identities do not.