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LM3 Free Cash Flow Valuation Question Notes

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EQUITY VALUATION > LM3 Free Cash Flow Valuation Question Notes

Variant: Match the Cash Flow, Discount Rate, and Value

Abstract: First identify who gets the cash. FCFF belongs to all capital providers and uses WACC; FCFE belongs only to common shareholders and uses the required return on equity.

An analyst has forecasts of both FCFF and FCFE. Which cash flow and discount rate should be used to estimate firm value and equity value?

FCFF. What is FCFF? Free cash flow to the firm is cash available to debt and equity investors after operations and reinvestment. FCFE. What is FCFE? Free cash flow to equity is cash left for common shareholders after reinvestment and net debt financing. WACC. What is WACC? The weighted average cost of capital is the required return demanded by all capital providers.

1. Match each cash stream to its owner

\[ \boxed{\text{Firm value}=PV(FCFF\text{ discounted at WACC})} \]

Carry that checkpoint into the next step.

\[ \boxed{\text{Equity value}=PV(FCFE\text{ discounted at }r)} \]

Here, \(r\) is the required return on common equity. The discount rate must belong to the same people who receive the cash.

Note

FCFF → WACC → firm value. FCFE → equity return → equity value. Mixing the lanes breaks the valuation.

Variant: Discount a Finite FCFF Stream

Abstract: Discount each FCFF to today, add the pieces, then subtract debt. Do not subtract debt before valuing the operating business.

A firm will produce FCFF of $100 million, $110 million, and $120 million over the next three years. WACC is 10%, debt is worth $50 million, and 10 million shares are outstanding. Ignore cash flows after Year 3. Find value per share.

Present value. What is present value? It is future cash translated into today’s money: \(PV=CF_t/(1+k)^t\), where \(CF_t\) is the Year-\(t\) cash flow, \(k\) is the discount rate, and \(t\) is years away.

1. Discount the operating cash flows

\[ V_{firm}=\frac{100}{1.10}+\frac{110}{1.10^2}+\frac{120}{1.10^3}=\boxed{\$271.98\text{m}} \]

2. Move from the whole firm to common equity

\[ V_{share}=\frac{271.98-50}{10}=\boxed{\$22.20} \]

Note

FCFF first gives operating firm value. Debt gets paid before common shareholders, so subtract debt afterward.

Variant: Discount a Finite FCFE Stream

Abstract: FCFE already belongs to common shareholders, so discount it at the equity return and divide by shares—no second debt subtraction.

Forecast FCFE is $50 million, $55 million, and $60 million in Years 1–3. The required return on equity is 12%, 10 million shares exist, and there is no terminal value. Find value per share.

Required return on equity. What is it? It is the return common shareholders demand for bearing the stock’s risk. FCFE valuation. What is it? \(V_{equity}=\sum FCFE_t/(1+r)^t\), where \(r\) is that required equity return.

1. Bring each FCFE home to today

\[ V_{equity}=\frac{50}{1.12}+\frac{55}{1.12^2}+\frac{60}{1.12^3}=\boxed{\$131.20\text{m}} \]

Carry that checkpoint into the next step.

\[ V_{share}=\frac{131.20}{10}=\boxed{\$13.12} \]

Debt is already reflected through interest and net borrowing inside FCFE.

Note

Do not subtract debt again from an FCFE valuation. That would charge shareholders for the same debt twice.

Variant: Calculate WACC with Market-Value Weights

Abstract: Weight debt and equity by market value, tax-adjust only debt, and add the pieces.

A company is financed with 40% debt and 60% equity. Its before-tax cost of debt is 6%, required equity return is 10%, and tax rate is 25%. Calculate WACC.

Market-value weight. What is it? It is each funding source’s current market-value share. Tax shield. What is it? Interest reduces taxable income, so after-tax debt cost is \(r_d(1-T)\), where \(r_d\) is debt cost and \(T\) is the tax rate. WACC. What is WACC? \(WACC=w_dr_d(1-T)+w_er_e\).

1. Tax-adjust debt, then weight both sources

\[ WACC=0.40(0.06)(1-0.25)+0.60(0.10)=\boxed{7.80\%} \]

The weights add to 100%, which is our quick debugger.

Note

Use market or target weights—not book weights—and never tax-adjust the common-equity return.

Variant: Value Equity with the Constant-Growth FCFF Model

Abstract: Grow FCFF once to Year 1, divide by WACC minus growth, then remove debt and divide by shares.

FCFF just ended at $100 million. It will grow forever at 4%. WACC is 9%, debt is $500 million, and 100 million shares exist. Estimate value per share.

Constant growth. What does it mean? Cash flow grows forever at one sustainable rate \(g\). FCFF model. What is the formula? \(V_{firm}=FCFF_1/(WACC-g)=FCFF_0(1+g)/(WACC-g)\).

1. Value the operating firm

\[ V_{firm}=\frac{100(1.04)}{0.09-0.04}=\boxed{\$2{,}080\text{m}} \]

2. Pay debt, then spread equity across shares

\[ V_{share}=\frac{2{,}080-500}{100}=\boxed{\$15.80} \]

Note

The numerator is next year’s \(FCFF_1\), not the cash flow that just ended at Time 0.

Variant: Value a Share with the Constant-Growth FCFE Model

Abstract: FCFE is already shareholder cash. Grow it once, divide by equity return minus growth, and stop.

FCFE per share just ended at $3.20. It should grow forever at 5%, and shareholders require 11%. Estimate intrinsic value per share.

Intrinsic value. What is it? It is the model’s estimate of what the share is worth. Constant-growth FCFE model. What is it? \(V_0=FCFE_1/(r-g)=FCFE_0(1+g)/(r-g)\), where \(r\) is the equity return and \(g\) is growth.

1. Grow once and capitalize forever

\[ V_0=\frac{3.20(1.05)}{0.11-0.05}=\boxed{\$56.00} \]

The model says the entire future stream is worth $56 today.

Note

FCFE per share goes straight to value per share. Do not subtract debt or divide by shares again.

Variant: Solve Backward for the Implied Growth Rate

Abstract: When price, cash flow, and return are known, rearrange the constant-growth model to discover the growth rate baked into price.

A stock sells for $50. FCFE per share just ended at $3, and the required return is 10%. What perpetual FCFE growth rate does the price imply?

Implied growth. What is it? It is the growth assumption hidden inside the market price. Starting from \(V_0=FCFE_0(1+g)/(r-g)\), solve for \(g\) rather than value.

1. Rearrange without guessing

\[ 50=\frac{3(1+g)}{0.10-g} \]

Carry that checkpoint into the next step.

\[ 5-50g=3+3g\quad\Rightarrow\quad g=\frac{2}{53}=\boxed{3.77\%} \]

The answer is below 10%, so the denominator stays positive.

Note

Back-solving exposes the market’s assumption; it does not prove that assumption is sensible.

Variant: Reject an Impossible Perpetual-Growth Input

Abstract: A perpetuity only works when the discount rate beats growth. If growth catches or passes it, the denominator hits zero or turns negative.

An analyst uses \(FCFE_1=5\), required return \(r=9\%\), and perpetual growth \(g=10\%\). Calculate value and assess the model.

Perpetuity. What is it? A cash-flow stream assumed to continue forever. No-growth boundary. What is the rule? The constant-growth formula \(V_0=FCFE_1/(r-g)\) requires \(r>g\).

1. Check the denominator before touching the calculator

\[ r-g=0.09-0.10=-0.01 \]

A negative denominator produces \(-500\), which is not a valid equity value here.

\[ \boxed{\text{Model invalid because }g\ge r} \]

Note

Always run the \(r>g\) check first. A calculator can print a number even when the economics are broken.

Variant: Calculate FCFF from Net Income

Abstract: Start with shareholder earnings, add back noncash charges and after-tax interest, then subtract money reinvested in fixed and working capital.

Net income is $120 million, noncash charges are $20 million, interest is $30 million, tax is 25%, fixed-capital investment is $80 million, and working-capital investment is $10 million. Calculate FCFF.

Noncash charges, or NCC. What are they? Expenses that lowered profit without using cash. FCInv and WCInv. What are they? Investment in long-lived operating assets and net operating working capital. FCFF formula. What is it? \(FCFF=NI+NCC+Int(1-T)-FCInv-WCInv\).

1. Rebuild cash available to every investor

\[ FCFF=120+20+30(1-0.25)-80-10=\boxed{\$72.50\text{m}} \]

Note

Add after-tax interest because net income removed a lender cash flow, while FCFF belongs to lenders and shareholders together.

Variant: Build Net Noncash Charges with Gains and Losses

Abstract: Add back noncash expenses and losses; subtract noncash gains. The sign follows what each item did to net income.

Net income includes $20 million depreciation, an $8 million gain on an asset sale, and a $5 million noncash impairment loss. Calculate net noncash charges.

Depreciation. What is it? A noncash expense spreading an asset’s cost across years. Gain. What is it? Income already included in net income but not an operating cash inflow. Impairment. What is it? A write-down that reduces profit without current cash leaving.

1. Reverse the accounting effects

\[ NCC=20-8+5=\boxed{\$17\text{m}} \]

Depreciation and the loss reduced profit, so add them back. The gain raised profit, so subtract it.

Note

Debug the sign by asking: “Did this noncash item push net income up or down?” Then reverse that push.

Variant: Calculate FCFF from CFO

Abstract: CFO already contains net income, noncash adjustments, and working-capital changes. Add after-tax interest and subtract fixed-capital investment.

CFO is $150 million, interest expense is $30 million, tax is 25%, and fixed-capital investment is $70 million. Interest was classified inside CFO. Calculate FCFF.

CFO. What is CFO? Cash flow from operations is operating cash reported on the cash-flow statement. FCFF from CFO. What is the formula? \(FCFF=CFO+Int(1-T)-FCInv\) when CFO already deducts interest paid.

1. Restore lender cash, then pay for fixed assets

\[ FCFF=150+30(1-0.25)-70=\boxed{\$102.50\text{m}} \]

There is no separate \(WCInv\) subtraction because CFO already captured it.

Note

Starting from CFO and subtracting working-capital investment again is a classic double-count.

Variant: Handle IFRS Interest Classified as Financing

Abstract: The usual CFO formula assumes interest was deducted inside CFO. Under IFRS, if interest paid sits in financing cash flow, do not add it back again.

An IFRS company reports CFO of $120 million, classifies $20 million interest paid as financing, and invests $50 million in fixed capital. Calculate FCFF.

IFRS classification. What does it mean? IFRS may place interest paid in operating or financing cash flow. Classification check. Why does it matter? \(FCFF=CFO+Int(1-T)-FCInv\) adds interest back only when CFO first deducted it.

1. Follow what is already inside CFO

Because this CFO never lost the financing-classified interest, adding it would count the same cash twice.

\[ FCFF=120-50=\boxed{\$70\text{m}} \]

Note

Read the cash-flow classification before using a memorized formula. The statement’s plumbing controls the adjustment.

Variant: Derive Fixed-Capital Investment from Net PPE

Abstract: Ending net PPE equals beginning net PPE plus purchases minus depreciation, so solve backward for purchases.

Net property, plant, and equipment rose from $550 million to $620 million. Depreciation was $50 million, and there were no disposals or acquisitions. Calculate fixed-capital investment.

Net PPE. What is it? Long-lived operating assets after accumulated depreciation. FCInv. What is it? Cash invested in those fixed operating assets. With no disposals, \(FCInv=Ending\ net\ PPE-Beginning\ net\ PPE+Depreciation\).

1. Reconstruct the asset roll-forward

\[ FCInv=620-550+50=\boxed{\$120\text{m}} \]

The company needed $50 million just to replace the accounting wear plus $70 million to grow net PPE.

Note

A $70 million rise in net PPE is not the capex answer; depreciation hid another $50 million of purchases.

Variant: Calculate Investment in Operating Working Capital

Abstract: Use noncash operating current assets minus non-debt operating current liabilities. Cash and borrowings stay outside the pipe.

Noncash operating current assets rise from $180 million to $220 million. Operating current liabilities rise from $110 million to $130 million. Calculate working-capital investment.

Operating working capital. What is it? Short-term operating assets financed after short-term operating liabilities: \(OWC=Operating\ CA-Operating\ CL\). WCInv. What is it? The period’s increase, \(WCInv=\Delta OWC\).

1. Find how much extra cash got tied up

\[ WCInv=(220-130)-(180-110)=90-70=\boxed{\$20\text{m}} \]

An increase uses cash, so it will be subtracted in FCFF and FCFE.

Note

Exclude cash, marketable securities, notes payable, and short-term debt unless the question explicitly treats them as operating.

Variant: Convert FCFF into FCFE

Abstract: Move from all-investor cash to shareholder cash by removing after-tax interest and adding net new borrowing.

FCFF is $150 million, interest is $30 million, tax is 25%, and net borrowing is $10 million. Calculate FCFE.

Net borrowing. What is it? New debt issued minus debt repaid. FCFF-to-FCFE bridge. What is it? \(FCFE=FCFF-Int(1-T)+Net\ borrowing\).

1. Remove the lender’s after-tax slice

\[ FCFE=150-30(1-0.25)+10=\boxed{\$137.50\text{m}} \]

Interest belongs to lenders, not common shareholders; new debt supplies fresh cash that can support shareholder cash flow.

Note

New borrowing raises current FCFE; debt repayment lowers it. Use net borrowing, not gross issuance.

Variant: Calculate FCFE from Net Income

Abstract: Net income is the shareholder starting point: reverse noncash charges, pay for reinvestment, and add net debt financing.

Net income is $100 million, noncash charges are $20 million, fixed-capital investment is $70 million, working-capital investment is $15 million, and net borrowing is $25 million. Calculate FCFE.

FCFE from net income. What is the formula? \(FCFE=NI+NCC-FCInv-WCInv+Net\ borrowing\). Each symbol is a cash adjustment needed to move from accounting profit to shareholder cash.

1. Run the cash pipeline

\[ FCFE=100+20-70-15+25=\boxed{\$60\text{m}} \]

The $25 million borrowing funds part of the $85 million investment burden.

Note

Common dividends are not subtracted. FCFE is cash available for distribution, whether or not the board distributes it.

Variant: Calculate FCFE from CFO

Abstract: CFO has already absorbed operating working capital. Subtract fixed investment and add net borrowing.

CFO is $130 million, fixed-capital investment is $60 million, and net borrowing is $15 million. Calculate FCFE.

FCFE from CFO. What is the formula? \(FCFE=CFO-FCInv+Net\ borrowing\). Why no interest adjustment? CFO begins after the interest treatment relevant to common-equity cash, while FCFE keeps debt financing through net borrowing.

1. Pay for long-lived assets and add fresh debt cash

\[ FCFE=130-60+15=\boxed{\$85\text{m}} \]

The units remain millions of currency per year.

Note

From CFO to FCFE: subtract fixed investment, add net borrowing, and do not subtract working capital twice.

Variant: Calculate FCFF from EBIT

Abstract: Turn operating profit into after-tax operating profit, restore depreciation, then subtract fixed and working-capital investment.

EBIT is $200 million, tax is 25%, depreciation is $40 million, fixed-capital investment is $90 million, and working-capital investment is $15 million. Calculate FCFF.

EBIT. What is EBIT? Earnings before interest and taxes is operating profit before lender financing. FCFF from EBIT. What is the formula? \(FCFF=EBIT(1-T)+Dep-FCInv-WCInv\).

1. Convert operating profit into operating cash

\[ FCFF=200(1-0.25)+40-90-15=\boxed{\$85\text{m}} \]

Depreciation reduced EBIT but did not spend current cash, so it comes back.

Note

EBIT is before interest already. Do not add interest again when starting from EBIT.

Variant: Calculate FCFF from EBITDA

Abstract: Tax EBITDA, restore the depreciation tax shield, then subtract both kinds of reinvestment.

EBITDA is $250 million, depreciation is $40 million, tax is 25%, fixed-capital investment is $90 million, and working-capital investment is $15 million. Calculate FCFF.

EBITDA. What is EBITDA? Earnings before interest, taxes, depreciation, and amortization. Depreciation tax shield. What is it? Depreciation saves taxes even though it uses no cash: \(Dep\times T\). FCFF formula. What is it? \(FCFF=EBITDA(1-T)+Dep(T)-FCInv-WCInv\).

1. Build after-tax operating cash

\[ FCFF=250(0.75)+40(0.25)-90-15=\boxed{\$92.50\text{m}} \]

Note

Do not simply use \(EBITDA(1-T)\). Depreciation still created a real tax saving.

Variant: Reconcile FCFF and FCFE by Two Routes

Abstract: Equivalent formulas should land on the same number. Use the bridge as a checksum, not as another fact to memorize blindly.

Net income is $100 million, depreciation is $20 million, interest is $20 million, tax is 25%, fixed investment is $50 million, working-capital investment is $10 million, and net borrowing is $5 million. Calculate FCFF and FCFE, then verify the bridge.

Reconciliation. What is it? An independent route used to check the same answer. Bridge. What is it? \(FCFE=FCFF-Int(1-T)+Net\ borrowing\).

1. Calculate both cash flows

\[ FCFF=100+20+20(0.75)-50-10=\boxed{\$75\text{m}} \]

Carry that checkpoint into the next step.

\[ FCFE=100+20-50-10+5=\boxed{\$65\text{m}} \]

2. Check the bridge

\[ 75-20(0.75)+5=65 \]

Note

If the direct FCFE and bridged FCFE disagree, a sign or tax adjustment is wrong.

Variant: Use the Target Debt-Ratio Shortcut

Abstract: If debt finances a fixed fraction of reinvestment, shareholders fund only the leftover fraction.

Net income is $120 million. Net fixed-capital investment plus working-capital investment is $50 million, and debt finances 40% of that investment. Calculate FCFE.

Debt ratio, or DR. What is it? The fraction of new operating investment financed with debt. Net investment. What is it? \(FCInv-Dep+WCInv\). Shortcut. What is it? \(FCFE=NI-(1-DR)(FCInv-Dep)-(1-DR)WCInv\).

1. Charge equity only for its 60% share

\[ FCFE=120-(1-0.40)(50)=\boxed{\$90\text{m}} \]

Debt supplies $20 million and equity absorbs $30 million.

Note

Apply the target debt ratio to net fixed investment plus working-capital investment, not to gross capex blindly.

Variant: Solve Backward for Net Borrowing

Abstract: When FCFE is given, rearrange the net-income formula and let net borrowing be the balancing cash source.

FCFE is $95 million, net income is $110 million, noncash charges are $10 million, fixed investment is $40 million, and working-capital investment is $5 million. Find net borrowing.

Net borrowing. What is it? Debt issued minus debt repaid. From \(FCFE=NI+NCC-FCInv-WCInv+Net\ borrowing\), isolate the unknown.

1. See what cash exists before financing

\[ 110+10-40-5=75 \]

2. Fill the gap to the reported FCFE

\[ Net\ borrowing=95-75=\boxed{\$20\text{m}} \]

Note

A positive answer means net debt issuance; a negative answer means the company repaid more debt than it issued.

Variant: Forecast FCFE from Sales Growth

Abstract: Forecast profit from next year’s sales, forecast reinvestment from the sales increase, then leave equity only its share of that bill.

Sales rise from $1,000 million to $1,100 million. Net margin is 8%. Net fixed investment equals 30% of the sales increase, working-capital investment equals 10%, and debt finances 40% of total investment. Forecast FCFE.

Net margin. What is it? Net income divided by sales: \(NI=Sales\times margin\). Incremental investment. What is it? New investment tied to the change in sales, not total sales.

1. Forecast income and reinvestment

\[ NI_1=1{,}100(0.08)=88 \]

Carry that checkpoint into the next step.

\[ Investment=(0.30+0.10)(1{,}100-1{,}000)=40 \]

Carry that checkpoint into the next step.

\[ FCFE_1=88-(1-0.40)(40)=\boxed{\$64\text{m}} \]

Note

Margin uses total forecast sales; incremental investment ratios use the increase in sales.

Variant: Forecast FCFF Component by Component

Abstract: Forecasting from sales means each operating component gets its own driver. This is safer than pretending one historical cash-flow number grows forever.

Next-year sales are $1,080 million, EBIT margin is 15%, depreciation is 4% of sales, fixed investment is 6% of sales, working-capital investment is 10% of the $80 million sales increase, and tax is 25%. Forecast FCFF.

Component forecast. What is it? Each FCFF input is forecast separately from its economic driver. EBIT margin. What is it? \(EBIT/Sales\).

1. Build the pieces

\[ FCFF=1{,}080(0.15)(0.75)+1{,}080(0.04)-1{,}080(0.06)-80(0.10) \]

Carry that checkpoint into the next step.

\[ FCFF=121.50+43.20-64.80-8.00=\boxed{\$91.90\text{m}} \]

Note

State what each percentage applies to. “10% working capital” is useless unless you know whether the base is sales or the sales change.

Variant: Separate FCFE from Dividends and Repurchases

Abstract: FCFE measures cash available to shareholders; dividends and buybacks describe how management uses it afterward.

A company generates FCFE of $100 million, pays $40 million of dividends, and repurchases $30 million of shares. What happens to FCFE, and how much remains undistributed?

Dividend. What is it? Cash paid directly to shareholders. Share repurchase. What is it? Company cash used to buy back its own shares. Distribution. What is it? A use of FCFE, not an ingredient in the FCFE formula.

1. Keep generation separate from payout

\[ FCFE=\boxed{\$100\text{m}} \]

Carry that checkpoint into the next step.

\[ Undistributed\ FCFE=100-40-30=\boxed{\$30\text{m}} \]

Note

Dividends, repurchases, and common-share issuance do not directly change current FCFF or FCFE; they allocate or raise equity cash afterward.

Variant: Measure the Current FCFE Effect of More Debt Financing

Abstract: For the same investment bill, more debt financing means shareholders supply less cash now, so current FCFE rises by the extra borrowing.

A $100 million operating investment was going to be financed with 30% debt. Management changes the plan to 60% debt. Holding everything else fixed, how does current FCFE change?

Leverage. What is leverage? The use of debt financing. Net borrowing. What is it? New debt minus repayments, and it enters FCFE with a plus sign.

1. Compare the debt cash supplied

\[ Net\ borrowing_{old}=100(0.30)=30 \]

Carry that checkpoint into the next step.

\[ Net\ borrowing_{new}=100(0.60)=60 \]

Carry that checkpoint into the next step.

\[ \Delta FCFE=60-30=\boxed{+\$30\text{m}} \]

Note

More borrowing boosts current FCFE but also changes future interest, risk, and required return. It is financing, not free wealth.

Variant: Identify When Net Income Equals FCFE

Abstract: Net income becomes a valid FCFE shortcut only when reinvestment after depreciation is exactly financed and working-capital and debt effects net to zero.

Net income is $80 million, depreciation is $50 million, fixed investment is $70 million, working-capital investment is $10 million, and net borrowing is $30 million. Calculate FCFE and assess net income as a proxy.

Proxy. What is a proxy? A shortcut used in place of the actual measure. FCFE formula. What is it? \(FCFE=NI+Dep-FCInv-WCInv+Net\ borrowing\) here.

1. Test the shortcut instead of assuming it

\[ FCFE=80+50-70-10+30=\boxed{\$80\text{m}} \]

Net investment is \(70-50+10=30\), exactly matched by net borrowing.

Note

Net income equals FCFE only in a special balancing case. It is not the general definition of shareholder cash flow.

Variant: Quantify Why EBITDA Is a Bad FCFF Proxy

Abstract: EBITDA skips taxes and reinvestment. Convert it properly, then measure how badly the shortcut overstates cash.

EBITDA is $200 million, depreciation is $30 million, tax is 25%, fixed investment is $60 million, and working-capital investment is $10 million. Calculate FCFF and EBITDA’s overstatement.

EBITDA proxy. What does that mean? Treating EBITDA as if it were distributable firm cash. Correct conversion. What is it? \(FCFF=EBITDA(1-T)+Dep(T)-FCInv-WCInv\).

1. Calculate actual firm cash

\[ FCFF=200(0.75)+30(0.25)-60-10=\boxed{\$87.50\text{m}} \]

Carry that checkpoint into the next step.

\[ Overstatement=200-87.50=\boxed{\$112.50\text{m}} \]

Note

EBITDA ignores the tax bill, the depreciation tax shield, fixed investment, and working-capital investment.

Variant: Include Preferred Stock in WACC and FCFF

Abstract: Preferred stock is a third capital provider: weight its required return in WACC and add preferred dividends back when FCFF starts from common net income.

Debt, preferred stock, and common equity have market values of $400 million, $100 million, and $500 million. Their required returns are 8%, 8%, and 12%; tax is 30%. Common net income is $110 million, interest $32 million, preferred dividends $8 million, depreciation $40 million, fixed investment $70 million, and working-capital investment $20 million. Find WACC and FCFF.

Preferred stock. What is it? Equity with a stated dividend paid before common shareholders. Preferred cost. What is it? Its required return, not tax-deductible.

\[ WACC=0.40(0.08)(0.70)+0.10(0.08)+0.50(0.12)=\boxed{9.04\%} \]

Carry that checkpoint into the next step.

\[ FCFF=110+40+32(0.70)+8-70-20=\boxed{\$90.40\text{m}} \]

Note

Add preferred dividends to common net income for FCFF because that cash belongs to another firm capital provider.

Variant: Add Preferred Issuance to Common FCFE

Abstract: Preferred dividends are already removed from common net income, but net preferred issuance is another financing cash source for common holders.

Common net income is $60 million, depreciation is $10 million, fixed investment is $20 million, working-capital investment is $5 million, net debt borrowing is zero, and net preferred issuance is $15 million. Calculate FCFE to common shareholders.

Net preferred issuance. What is it? Preferred shares issued minus preferred shares redeemed. Like new debt, positive issuance supplies financing cash.

1. Start from income already after preferred dividends

\[ FCFE=60+10-20-5+0+15=\boxed{\$60\text{m}} \]

Without the preferred issuance, FCFE would have been $45 million.

Note

Do not add preferred dividends back to FCFE when starting from net income available to common shareholders.

Variant: Complete a Constant-Growth FCFF Valuation with Preferred Stock

Abstract: Value operating assets with FCFF, then remove every senior capital claim before common equity gets the remainder.

FCFF just ended at £28 million and grows forever at 4%. WACC is 8.435%. Debt is £145 million, preferred stock is £65 million, 8 million common shares exist, and market price is £32.50. Estimate value per share and classify the stock.

Senior claims. What are they? Debt and preferred stock claims paid before common equity. Classification. What is it? Compare intrinsic value with market price.

\[ V_{firm}=\frac{28(1.04)}{0.08435-0.04}=\boxed{£656.60\text{m}} \]

Carry that checkpoint into the next step.

\[ V_{share}=\frac{656.60-145-65}{8}=\boxed{£55.82} \]

Because £55.82 exceeds £32.50, the shares are undervalued by the model.

Note

In an FCFF bridge, subtract both debt and preferred stock before dividing common equity by common shares.

Variant: Value a Two-Stage FCFE Stream with Fixed Growth Rates

Abstract: Forecast the high-growth cash flows, calculate terminal value at the handoff date, then discount every piece to today.

FCFE per share is $2.00 now, grows 15% for three years, then 5% forever. The required equity return is 11%. Estimate value per share.

Two-stage model. What is it? A high-growth period followed by perpetual stable growth. Terminal value. What is it? All cash flows after Year 3 compressed into \(TV_3=FCFE_4/(r-g)\).

\[ FCFE_1=2.30,\quad FCFE_2=2.645,\quad FCFE_3=3.04175 \]

Carry that checkpoint into the next step.

\[ TV_3=\frac{3.04175(1.05)}{0.11-0.05}=53.2306 \]

Carry that checkpoint into the next step.

\[ V_0=\frac{2.30}{1.11}+\frac{2.645}{1.11^2}+\frac{3.04175+53.2306}{1.11^3}=\boxed{\$45.36} \]

Note

Terminal value sits at the end of Year 3, so discount it three periods—not four.

Variant: Value a Two-Stage FCFF Stream

Abstract: Discount high-growth FCFF plus terminal firm value, then bridge from firm value to equity value.

FCFF is $100 million now, grows 12% for two years, then 4% forever. WACC is 9%, debt is $400 million, and 50 million shares exist. Find value per share.

Terminal firm value. What is it? \(TV_2=FCFF_3/(WACC-g)\). Equity bridge. What is it? \(V_{equity}=V_{firm}-Debt\).

\[ FCFF_1=112,\quad FCFF_2=125.44,\quad FCFF_3=130.4576 \]

Carry that checkpoint into the next step.

\[ V_{firm}=\frac{112}{1.09}+\frac{125.44+130.4576/(0.09-0.04)}{1.09^2}=\boxed{\$2{,}404.40\text{m}} \]

Carry that checkpoint into the next step.

\[ V_{share}=\frac{2{,}404.40-400}{50}=\boxed{\$40.09} \]

Note

The stable-growth numerator is \(FCFF_3\), the first cash flow after the explicit forecast period.

Variant: Value a Declining-Growth FCFE Stream

Abstract: When growth fades gradually, forecast each year separately. A two-stage jump shortcut would erase the transition the question gave you.

FCFE per share is $1.50 now. Growth declines through 20%, 15%, 10%, and 5% over Years 1–4, then remains 5%. The required return is 12%. Estimate value.

Declining growth. What is it? A transition in which each year has a different growth rate. Stable stage. What is it? The perpetual phase beginning after Year 4.

\[ FCFE_1=1.80,\ FCFE_2=2.07,\ FCFE_3=2.277,\ FCFE_4=2.39085 \]

Carry that checkpoint into the next step.

\[ TV_4=\frac{2.39085(1.05)}{0.12-0.05}=35.86275 \]

Carry that checkpoint into the next step.

\[ V_0=\sum_{t=1}^{4}\frac{FCFE_t}{1.12^t}+\frac{TV_4}{1.12^4}=\boxed{\$29.19} \]

Note

Apply each year’s growth to the previous year’s cash flow; do not apply all rates to \(FCFE_0\).

Variant: Value a Three-Stage FCFE Stream

Abstract: Three-stage means three growth regimes. Build the timeline first, then discount; otherwise it is easy to apply the right rate in the wrong year.

FCFE per share is $0.75 now. It grows 10% in Year 1, 26% in Years 2–4, and 6% from Year 5 onward. Beta is 2.0, the risk-free rate is 4.5%, and the equity risk premium is 5%. Estimate value per share.

CAPM. What is CAPM? It estimates the equity return as \(r=R_f+\beta ERP\), where \(R_f\) is the risk-free rate, \(\beta\) is market sensitivity, and \(ERP\) is the equity risk premium. Three-stage model. What is it? Three distinct growth phases before the last phase continues forever.

\[ r=4.5\%+2.0(5\%)=14.5\% \]

Carry that checkpoint into the next step.

\[ FCFE_1=0.825,\ FCFE_2=1.0395,\ FCFE_3=1.30977,\ FCFE_4=1.65031 \]

Carry that checkpoint into the next step.

\[ TV_4=\frac{1.65031(1.06)}{0.145-0.06}=20.5804 \]

Carry that checkpoint into the next step.

\[ V_0=\sum_{t=1}^{4}\frac{FCFE_t}{1.145^t}+\frac{TV_4}{1.145^4}=\boxed{\$15.32} \]

Note

Growth changes when moving into a year. Mark the rate above each timeline arrow before multiplying.

Variant: Use a Price Multiple for Terminal Value

Abstract: A terminal multiple prices the company at the end of the forecast period. Discount that future sale price back along with the interim cash flows.

A company is expected to earn $4.00 per share in Year 5. A justified terminal P/E is 18, and the required return is 12%. Ignoring interim FCFE, find the present value of the terminal stock price.

P/E. What is P/E? Price divided by earnings per share. Terminal multiple. What is it? A valuation multiple applied to a forecast fundamental at the horizon: \(P_5=(P/E)_5\times EPS_5\).

\[ P_5=18(4.00)=\boxed{\$72.00} \]

Carry that checkpoint into the next step.

\[ PV(P_5)=\frac{72}{1.12^5}=\boxed{\$40.86} \]

Note

A terminal multiple creates a future price. It is not today’s value until it has been discounted back.

Variant: Place Gordon Terminal Value on the Correct Date

Abstract: Terminal value at Year 5 begins with Year 6 cash flow. Grow the Year 5 cash once, capitalize it, then discount five years.

FCFE per share is $4.00 in Year 5. Stable growth from Year 6 onward is 5%, and the required return is 10%. Find terminal value at Year 5 and its present value.

Gordon terminal value. What is it? \(TV_n=FCFE_{n+1}/(r-g)\), where \(n\) is the last explicit forecast year.

\[ TV_5=\frac{4.00(1.05)}{0.10-0.05}=\boxed{\$84.00} \]

Carry that checkpoint into the next step.

\[ PV(TV_5)=\frac{84}{1.10^5}=\boxed{\$52.16} \]

Note

The most common timing bug is using \(FCFE_5\) in the numerator instead of \(FCFE_6\).

Variant: Measure How Much Value Comes from Terminal Value

Abstract: Terminal value often carries most of the model. Measure its present-value share so you know where fragile assumptions are hiding.

A model gives present value of explicit FCFE of $18 million and present value of terminal value of $72 million. What percentage of equity value comes from terminal value?

Terminal-value weight. What is it? The fraction of total estimated value coming from cash flows beyond the explicit forecast: \(Weight=PV(TV)/(PV(Explicit)+PV(TV))\).

1. Divide the long-tail value by total value

\[ Weight=\frac{72}{18+72}=\boxed{80\%} \]

Only 20% comes from individually forecast years.

Note

A high terminal-value weight is not automatically wrong, but it makes \(r\), \(g\), and the terminal multiple the model’s pressure points.

Variant: Run a Single-Variable Sensitivity Analysis

Abstract: Change one input while freezing the rest. That isolates which assumption is moving the valuation.

FCFE per share is $2.00, required return is 10%, and perpetual growth is 4%. Find base value, then change growth alone to 5%.

Sensitivity analysis. What is it? Recalculating value after changing one assumption. Base case. What is it? The central set of assumptions used for comparison.

\[ V_{base}=\frac{2(1.04)}{0.10-0.04}=\boxed{\$34.67} \]

Carry that checkpoint into the next step.

\[ V_{g=5\%}=\frac{2(1.05)}{0.10-0.05}=\boxed{\$42.00} \]

Carry that checkpoint into the next step.

\[ \Delta V=42.00-34.67=\boxed{+\$7.33} \]

Note

Change one input at a time for sensitivity analysis; changing several inputs creates a scenario, not a clean sensitivity test.

Variant: Rank Inputs by Valuation Sensitivity

Abstract: Compare each input’s low-to-high price range. The widest range marks the assumption that deserves the most scrutiny.

A one-variable sensitivity table gives price ranges of £18.50 for FCFE, £2.89 for the risk-free rate, £22.18 for the equity risk premium, £16.89 for beta, and £30.23 for growth. Rank the inputs from most to least sensitive.

Sensitivity range. What is it? \(Range=Highest\ value-Lowest\ value\) while other inputs remain at base case.

1. Sort the ranges, biggest first

\[ 30.23>22.18>18.50>16.89>2.89 \]

Carry that checkpoint into the next step.

\[ \boxed{Growth>ERP>FCFE_0>Beta>Risk\!\!-free\ rate} \]

Note

Rank the resulting price ranges, not the numerical sizes of the input changes.

Variant: Value a Stock with Real Cash Flows and Real Rates

Abstract: Real cash flows must travel with real discount and growth rates. Add justified real-risk adjustments, then use the familiar stable-growth model.

Normalized real FCFE per share is KRW1,300. The real country return is 6.50%, with industry +0.60%, size −0.10%, and leverage +0.25% adjustments. Real growth is 3.50%. Estimate value.

Real rate. What is it? A rate with inflation stripped out. Build-up return. What is it? \(r_{real}=Country+Industry+Size+Leverage\).

\[ r_{real}=6.50\%+0.60\%-0.10\%+0.25\%=\boxed{7.25\%} \]

Carry that checkpoint into the next step.

\[ V_0=\frac{1{,}300(1.035)}{0.0725-0.035}=\boxed{KRW35{,}880} \]

Note

Real FCFE goes with real \(r\) and real \(g\). Nominal FCFE goes with nominal rates. Never cross the wires.

Variant: Convert a Nominal Return to a Real Return

Abstract: Use the Fisher relation when cash flows are stated in real purchasing power but the discount rate includes inflation.

The nominal required return is 12% and expected inflation is 5%. Calculate the exact real required return.

Nominal return. What is it? A return including inflation. Real return. What is it? Growth in purchasing power. Fisher relation. What is it? \(1+r_{nominal}=(1+r_{real})(1+\pi)\), where \(\pi\) is inflation.

\[ r_{real}=\frac{1.12}{1.05}-1=\boxed{6.67\%} \]

The quick subtraction \(12\%-5\%=7\%\) is only an approximation.

Note

Use the exact Fisher relation when precision matters; the subtraction shortcut is rough.

Variant: Classify a Stock from Model Value and Market Price

Abstract: The model supplies intrinsic value; the market supplies price. Their direction tells you under- or overvaluation.

A free-cash-flow model estimates value at $45 per share while the stock trades at $52. Classify it and calculate the percentage overvaluation relative to intrinsic value.

Overvalued. What does it mean? Market price is above model value. Percentage gap. What is it? \((Market-Intrinsic)/Intrinsic\).

\[ Gap=52-45=\boxed{\$7} \]

Carry that checkpoint into the next step.

\[ Percentage\ overvaluation=\frac{52-45}{45}=\boxed{15.56\%} \]

Note

“Overvalued” is conditional on the model and assumptions; it is not a guaranteed trading profit.

Variant: Add Non-Operating Assets before Finding Equity Value

Abstract: FCFF values operating assets. Add assets outside operations at market value, subtract debt, then divide by shares.

Operating assets are worth SEK720 million. Excess cash is SEK60 million, noncurrent investments have market value SEK45 million, a pension surplus is SEK40 million, debt is SEK215 million, and 100 million shares exist. Find value per share.

Non-operating asset. What is it? An asset not required to produce forecast operating FCFF. Pension surplus. What is it? Plan assets above pension liabilities.

\[ Total\ firm\ value=720+60+45+40=\boxed{SEK865\text{m}} \]

Carry that checkpoint into the next step.

\[ Equity\ value=865-215=650 \]

Carry that checkpoint into the next step.

\[ V_{share}=\frac{650}{100}=\boxed{SEK6.50} \]

Note

Use market value for separately valued assets. Do not add operating cash already needed to generate FCFF.

Variant: Choose FCFF When FCFE Is Negative

Abstract: Negative FCFE can be noisy when debt financing is heavy. FCFF may expose the operating business more cleanly.

A levered company has FCFF of $40 million, after-tax interest of $18 million, and net debt repayment of $30 million. Calculate FCFE and choose the cleaner valuation approach.

Levered company. What is it? A company using debt. Negative FCFE. What is it? Shareholder cash is below zero after investment and debt financing effects.

\[ FCFE=FCFF-After\!\!-tax\ interest+Net\ borrowing \]

Debt repayment means net borrowing is \(-30\) million:

\[ FCFE=40-18-30=\boxed{-\$8\text{m}} \]

FCFF is the cleaner starting point because it separates operations from the large financing swing.

Note

Negative FCFE does not automatically mean a worthless firm; debt repayment can drag FCFE below zero.

Variant: Choose FCFF When Capital Structure Is Changing

Abstract: When leverage moves sharply, FCFE and the equity discount rate move with it. FCFF is usually the steadier lane.

A firm’s debt ratio will fall from 70% to 30% over five years. Operating forecasts are reliable, but annual net borrowing and equity risk will swing. Which model is more defensible?

Capital structure. What is it? The mix of debt and equity financing. Changing leverage. What does it mean? That mix is moving, altering net borrowing and common-equity risk.

1. Identify which cash stream is less contaminated by financing changes

\[ \boxed{\text{Prefer FCFF discounted with a consistent forecast of WACC}} \]

FCFE would require forecasting volatile net borrowing and a changing required equity return.

Note

FCFE is usually simplest with stable leverage; FCFF is often cleaner with negative FCFE or major capital-structure change.

Variant: Compare FCFE and Dividend Values for a Control Investor

Abstract: Dividends are what the board chooses to pay; FCFE is what could be paid without damaging operations. Control makes that distinction matter.

Dividends per share are $2 and FCFE per share is $5. Both grow at 4%, and the required return is 10%. Compare the two stable-growth values and choose the relevant measure for an acquirer.

Control investor. What is it? An owner able to influence payout and operating decisions. Dividend capacity. What is it? FCFE available for distribution, whether paid or retained.

\[ V_{DDM}=\frac{2(1.04)}{0.10-0.04}=\boxed{\$34.67} \]

Carry that checkpoint into the next step.

\[ V_{FCFE}=\frac{5(1.04)}{0.10-0.04}=\boxed{\$86.67} \]

The control investor focuses on FCFE because payout policy can be changed.

Note

Low dividends do not prove low capacity to pay. For control valuation, FCFE usually exposes that hidden capacity.

Variant: Cap a Working-Capital Release at Its Economic Floor

Abstract: A forecast cannot release more inventory cash than the inventory balance available to unwind.

A forecast assumes a $30 million cash inflow from reducing inventory, but only $10 million of inventory exists. What is the maximum inventory-related reduction in working-capital investment?

Working-capital release. What is it? A decrease in operating working capital, recorded as negative \(WCInv\), which increases free cash flow. Economic floor. What is it? Inventory cannot fall below zero.

\[ Minimum\ inventory\ WCInv=-\$10\text{m} \]

Carry that checkpoint into the next step.

\[ \boxed{\text{Maximum cash release from inventory}=\$10\text{m}} \]

The extra $20 million assumed release is impossible unless another working-capital account supplies it.

Note

Negative \(WCInv\) can boost cash, but balance-sheet accounts have real floors. Check the available stock before forecasting a release.

Variant: Remove Acquisition Inventory from Operating WCInv

Abstract: A balance-sheet change may include inventory bought inside an acquisition. Only the operating part belongs in operating working-capital investment.

Inventory rises by $30 million during the year, but $12 million arrived with an acquired subsidiary rather than through ordinary purchases. Holding other working-capital accounts constant, estimate operating WCInv.

Non-articulation. What is it? Balance-sheet changes do not match cash-flow-statement changes because acquisitions, disposals, or currency translation moved the accounts. Operating WCInv. What is it? The cash tied up through normal operations.

\[ Operating\ WCInv=30-12=\boxed{\$18\text{m}} \]

The acquisition amount belongs to the investing transaction, not ordinary operating cash flow.

Note

Do not blindly use balance-sheet differences when acquisitions, divestitures, or foreign-currency translation break articulation.

Variant: Compare Gordon and Multiple-Based Terminal Values

Abstract: Two terminal methods can disagree because they encode different assumptions. Compute both and investigate the gap instead of averaging blindly.

At Year 5, FCFE per share is $4.00 and EPS is $5.00. Required return is 10%, stable growth is 5%, and a justified terminal P/E is 18. Calculate both terminal values.

Fundamental terminal value. What is it? \(TV_5=FCFE_6/(r-g)\). Multiple terminal value. What is it? \(P_5=(P/E)_5EPS_5\).

\[ TV_{Gordon}=\frac{4(1.05)}{0.10-0.05}=\boxed{\$84} \]

Carry that checkpoint into the next step.

\[ TV_{multiple}=18(5)=\boxed{\$90} \]

The $6 difference comes from the multiple’s embedded profitability and growth assumptions.

Note

A terminal multiple is a cross-check, not magic. Make sure it is consistent with the stable-stage fundamentals.

Variant: Solve for the Required Return Implied by Price

Abstract: Rearrange the stable-growth FCFE model to find the return that makes the model equal the observed price.

FCFE per share just ended at $3.00, perpetual growth is 4%, and market price is $39.00. What required return is implied?

Implied required return. What is it? The discount rate consistent with price. From \(V_0=FCFE_0(1+g)/(r-g)\), rearrange to \(r=FCFE_1/V_0+g\).

\[ r=\frac{3(1.04)}{39}+0.04=0.08+0.04=\boxed{12.00\%} \]

The 8% cash-flow yield plus 4% growth produces the 12% required return.

Note

In a stable-growth model, expected return decomposes into next-period FCFE yield plus growth.

Variant: Reject a Vendor’s Mislabelled Free Cash Flow

Abstract: A number called “free cash flow” is not automatically valuation FCFF or FCFE. Reconcile its definition before discounting it.

A data vendor defines FCF as \(NI+Dep-Dividends-FCInv\). Given net income $100 million, depreciation $20 million, dividends $30 million, fixed investment $50 million, working-capital investment $10 million, interest $12 million, tax 25%, and no net borrowing, calculate the vendor FCF, FCFF, and FCFE.

Vendor FCF. What is it? A provider-specific label that may omit required items. Reconciliation. What is it? Comparing the definition line by line.

\[ FCF_{vendor}=100+20-30-50=\boxed{40} \]

Carry that checkpoint into the next step.

\[ FCFF=100+20+12(0.75)-50-10=\boxed{69} \]

Carry that checkpoint into the next step.

\[ FCFE=100+20-50-10=\boxed{60} \]

Note

Never discount a database field until you know exactly which cash flows it adds and subtracts.

Variant: Revalue FCFF under an ESG Cost Scenario

Abstract: An ESG issue matters numerically only through forecast cash flows, growth, or risk. Put the effect into the model rather than adding a vague premium by feel.

A mine’s next-year FCFF is $120 million before a recurring $15 million environmental-compliance cost. WACC is 9% and stable growth is 3%. Calculate firm value before and after the cost.

ESG scenario. What is it? A forecast translating environmental, social, or governance effects into financial inputs. Recurring cost. What is it? A cost expected every year and therefore embedded in sustainable FCFF.

\[ V_{before}=\frac{120}{0.09-0.03}=\boxed{\$2{,}000\text{m}} \]

Carry that checkpoint into the next step.

\[ V_{after}=\frac{120-15}{0.09-0.03}=\boxed{\$1{,}750\text{m}} \]

Carry that checkpoint into the next step.

\[ Value\ impact=\boxed{-\$250\text{m}} \]

Note

Avoid double-counting an ESG risk in both cash flow and WACC unless the source assumptions genuinely require both effects.

Variant: Trace a $100 Change through FCFF and FCFE

Abstract: Shock one input, hold everything else fixed, and follow the cash-flow formula. Taxes soften income-statement shocks; financing and payout items split FCFF from FCFE.

With a 40% tax rate, show the isolated change in FCFF and FCFE caused by a $100 increase in each listed item.

Isolated change. What is it? One input moves while every other input is frozen. After-tax effect. What is it? A deductible $100 expense changes after-tax income by \(100(1-0.40)=\$60\).

1. Trace each shock

$100 increase in \(\Delta FCFF\) \(\Delta FCFE\) Why?
Net income +$100 +$100 starting cash proxy rises
Cash operating expense −$60 −$60 after-tax operating cash falls
Depreciation +$40 +$40 $100 add-back minus $60 income loss
Interest expense $0 −$60 FCFF adds after-tax interest back
EBIT +$60 +$60 after-tax operating income rises
Accounts receivable −$100 −$100 more cash is tied up
Accounts payable +$100 +$100 suppliers fund more operations
PP&E purchases −$100 −$100 fixed investment uses cash
Notes payable $0 +$100 debt financing affects FCFE only
Dividends, common issuance, or buybacks $0 $0 distributions or equity financing

The row that most cleanly separates the two cash flows is the debt-financing shock:

\[ \boxed{+\$100\text{ notes payable}\Rightarrow\Delta FCFF=0,\quad\Delta FCFE=+\$100} \]

Note

Operations and investment hit both measures; debt financing separates FCFE from FCFF; shareholder distributions hit neither current measure.

Variant: Build Multistage FCFE from Earnings and Reinvestment

Abstract: When earnings and investment follow different paths, forecast them separately. FCFE growth cannot be hard-coded from EPS growth.

EPS is $3.00 now and grows 20%, 15%, and 10% in Years 1–3. Net capital expenditure per share is $4, $3, and $2; working-capital investment is 25% of net capex; debt finances 40% of both. In Year 4, EPS grows 5%, net capex is $1.50, and all components then grow 5% forever. Required return is 12%. Estimate value per share.

Net capex. What is it? Capital expenditure minus depreciation. Reinvestment charge to equity. What is it? Equity funds \(1-DR=60\%\) of net capex plus working-capital investment. Thus \(FCFE=EPS-(1-DR)(Net\ capex+WCInv)\).

\[ FCFE_1=3.60-0.60(4+1)=0.60 \]

Carry that checkpoint into the next step.

\[ FCFE_2=4.14-0.60(3+0.75)=1.89,\quad FCFE_3=4.554-0.60(2+0.50)=3.054 \]

Carry that checkpoint into the next step.

\[ FCFE_4=4.7817-0.60(1.50+0.375)=3.6567 \]

Carry that checkpoint into the next step.

\[ V_0=\frac{0.60}{1.12}+\frac{1.89}{1.12^2}+\frac{3.054+3.6567/(0.12-0.05)}{1.12^3}=\boxed{\$41.40} \]

Note

Falling reinvestment can make FCFE grow much faster than EPS. Forecast the ingredients before valuing the stream.

Variant: Finish a Multi-Stage FCFF Scenario from Operations to Share Price

Abstract: A scenario is not finished at operating value. Add separate non-operating assets, remove senior claims, divide by shares, then compare with the market.

FCFF just ended at €100 million, grows 2% for three years, then 1% forever. WACC is 8%. Non-operating land is worth €50 million, debt is €400 million, preferred stock is €50 million, and 50 million common shares exist. The market price is €18. Estimate intrinsic value and classify the shares.

Scenario valuation. What is it? A complete valuation under one coherent set of assumptions. Operating value. What is it? Present value of FCFF generated by operations; separately valued assets are added later.

\[ FCFF_1=102,\quad FCFF_2=104.04,\quad FCFF_3=106.1208,\quad FCFF_4=107.1820 \]

Carry that checkpoint into the next step.

\[ V_{operations}=\frac{102}{1.08}+\frac{104.04}{1.08^2}+\frac{106.1208+107.1820/(0.08-0.01)}{1.08^3}=\boxed{€1{,}483.38\text{m}} \]

Carry that checkpoint into the next step.

\[ V_{share}=\frac{1{,}483.38+50-400-50}{50}=\boxed{€21.67} \]

Because €21.67 exceeds €18, the shares are undervalued under this scenario.

Note

Compare market price only after completing the full operating-assets-to-common-equity bridge.

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