Valuation Β· 2
The DCF, step by step
In the multiples lesson we compared prices. Now we build a full discounted cash flow (DCF) valuation, the method professional analysts use, one formula at a time.
π΄ In one sentence
A business is worth all the cash it will ever produce, with each future year counted a bit less because waiting has a cost.
We value Rat Bakery again (from the three statement lessons), this time the way professional analysts do. Every formula is shown with arrows pointing to what each part means.
πΊοΈ The map
- Forecast the cash the business will produce (free cash flow to the firm).
- Work out the return investors require (cost of equity, cost of debt, combined into the WACC).
- Bring every future cash flow back to today (present value).
- Add the value of all years after the forecast (terminal value, with a perpetuity growth rate).
- Subtract debt, divide by shares: value per share.
Step 1 Β· Present value: why a future dollar is worth less
Money today can be invested and grow. So money received in the future is worth less than the same amount today. Converting it back is called discounting.
β swipe to see the whole formula β
PV =Cash flowthe money you will receive in year tCFtΓ·Discount factorr = required yearly return; t = years until you receive it. The further away, the bigger the divisor(1 + r)t
Example: 110 received in 1 year at r = 10% β 110 Γ· 1.10 = 100 today. In 5 years β 110 Γ· 1.105 = 68.30 today.
Step 2 Β· Free cash flow to the firm (FCFF)
We value the whole business, which belongs to both lenders and shareholders, so we use the cash available to both: before interest is paid.
β swipe to see the whole formula β
FCFF =Operating profit after taxwhat the business earns, taxed as if it had no debt: 100,000 Γ 0.8 = 80,000EBIT Γ (1 β t)+Depreciation & amortisationadded back: a cost with no cash out (30,000)D&AβCapital expenditurecash spent on ovens and equipment (40,000)CapexβChange in working capitalextra cash tied up in receivables and stock, minus extra supplier credit: 5,000 + 3,000 β 4,000 = 4,000ΞNWC
Rat Bakery: 80,000 + 30,000 β 40,000 β 4,000 = 66,000
π Why not the 58,000 from the cash flow lesson?
That free cash flow was after paying the bank's interest. FCFF adds back the after-tax interest (10,000 Γ 0.8 = 8,000): 58,000 + 8,000 = 66,000. Cash for everyone β discounted at the rate that rewards everyone, the WACC.
Step 3 Β· Cost of equity: what shareholders demand (CAPM)
Shareholders take the most risk, so they want the highest return. The standard way to estimate it is the Capital Asset Pricing Model (CAPM):
β swipe to see the whole formula β
Ke =Risk-free ratethe yield on a 10-year government bond in the companyβs currency. We use 4%rf+Betahow much the share moves with the market: 1 = like the market, >1 = more volatile. Small bakery: 1.25Ξ²ΓMarket risk premiumthe extra return stocks have paid over government bonds, commonly 4β6%. We use 5%(Rm β rf)
Ke = 4% + 1.25 Γ 5% = 10.25%
Risk-free rate (rf)
Use a government bond in the
same currency as the cash flows: US Treasuries for dollars, German Bunds for euros, Romanian government bonds for lei (these yield more, because of higher inflation and credit risk).
Beta (Ξ²)
Calculated from how the share price moved against an index over several years. Utilities are often below 1, technology and airlines above 1.
Market risk premium
Estimated from history or from today's prices. Professors such as Aswath Damodaran (NYU) publish yearly estimates for every country, adding a country risk premium for riskier markets.
Step 4 Β· Cost of debt: what lenders demand
β swipe to see the whole formula β
Kd after tax =Pre-tax cost of debtinterest rate on the companyβs borrowing: 10,000 Γ· 100,000 = 10%KdΓTax shieldinterest is a tax-deductible cost, so the state pays part of it. t = 20%(1 β t)
Kd after tax = 10% Γ (1 β 0.20) = 8%
For large companies, Kd is the yield on their bonds, or the risk-free rate plus a credit spread that depends on their rating (bonds lesson).
Step 5 Β· WACC: the blended cost of all the money
The business is financed partly by shareholders and partly by lenders. The weighted average cost of capital mixes their required returns according to how much each provides, using market values: equity at the share price (10,000 shares Γ $90 = $900,000) and debt of $100,000.
β swipe to see the whole formula β
WACC =Equity weight900,000 Γ· 1,000,000 = 90%E/VΓCost of equity10.25% (step 3)Ke+Debt weight100,000 Γ· 1,000,000 = 10%D/VΓAfter-tax cost of debt8% (step 4)Kd(1 β t)
WACC = 0.90 Γ 10.25% + 0.10 Γ 8% = 9.225% + 0.8% = 10.0% (V = E + D = total financing)
π΄ Plain wordsEvery year, the business must earn at least 10% on the money invested in it just to satisfy its owners and lenders. Earning more creates value; earning less destroys it.
Step 6 Β· Forecast and discount five years
Assumption: FCFF grows 5% a year for five years. Each year is discounted at the WACC of 10%.
| Year | FCFF | (1 + 10%)t | Present value |
|---|
| 1 | 69,300 | 1.100 | 63,000 |
| 2 | 72,765 | 1.210 | 60,136 |
| 3 | 76,403 | 1.331 | 57,403 |
| 4 | 80,223 | 1.464 | 54,794 |
| 5 | 84,235 | 1.611 | 52,303 |
| Sum | | | 287,636 |
Step 7 Β· Terminal value and the perpetuity growth rate
The bakery will not close after year 5. Instead of forecasting forever, we assume that after year 5 the cash flow grows at a small, constant rate for ever β the perpetuity growth rate (g). The value of that endless stream at the end of year 5 is the terminal value (Gordon growth formula):
β swipe to see the whole formula β
TV =Cash flow in year 684,235 Γ 1.02 = 85,920FCFF5 Γ (1 + g)Γ·Discount minus growth10% β 2% = 8%. g must be below WACC, or the value becomes infinite(WACC β g)
TV = 85,920 Γ· 0.08 = 1,073,991 at the end of year 5 β today: 1,073,991 Γ· 1.611 = 666,864
Choosing g
No company can grow faster than the whole economy forever, so g is usually set around long-run inflation plus real growth: often 2β3% for developed countries.
The alternative: exit multiple
Value the business in year 5 at a typical EV/EBITDA multiple. EBITDA in year 5 β 165,900 Γ 7 = 1,161,400 β today 721,100. Comparing both methods is a good sanity check.
Warning
Here the terminal value is
70% of the total. Small changes in g or WACC move the result a lot (step 9).
Step 8 Β· From enterprise value to value per share
DCF result Rat Bakery
PV of years 1β5287,636
Step 6.
+ PV of terminal value666,864
Step 7.
= Enterprise value (EV)954,500
The value of the whole business, for lenders and shareholders.
β Net debt (100,000 β 60,000 cash)(40,000)
Belongs to the bank, after using the cash to repay part of it.
= Equity value914,500
What belongs to the shareholders.
Γ· 10,000 shares91.45
Under these assumptions: $91.45 per share, close to the $90 asking price. The price implies roughly these assumptions.
Step 9 Β· Sensitivity: how much the assumptions matter
| WACC β / growth years 1β5 β | 3% | 5% | 7% |
|---|
| 9% | 96.39 | 105.31 | 114.89 |
| 10% | 83.78 | 91.45 | 99.68 |
| 11% | 73.97 | 80.67 | 87.86 |
And the perpetuity growth rate: g = 1% β $83.46; g = 2% β $91.45; g = 3% β $101.72. One percentage point of "forever growth" moves the value by about 10%.
Common mistakes
- Using FCF after interest with the WACC (mixing equity and firm cash flows).
- A perpetuity growth rate above long-run economic growth, or above the WACC.
- A risk-free rate in a different currency from the cash flows.
- Forgetting to subtract debt (and other claims such as minority interests or pension deficits) to get from EV to equity.
- Treating the result as a precise answer instead of a range.
Our company analysis uses this method in simplified form: it starts from each company's own 10-year history and lets you move every assumption.
βοΈ Check yourself: If the risk-free rate rises from 4% to 5%, what happens to the cost of equity, the WACC and the value?
Show the answer
Ke rises to 11.25%, the WACC to about 10.9%, and the value per share falls (to about $81 in this example). This is why share prices often fall when interest rates rise.