The Time Value of Money & Free Cash Flow
Master the foundational concept behind all valuation: why a dollar today is worth more than a dollar tomorrow, and why we focus on cash flow rather than accounting profits.
Learning Objectives
- Understand why money has time value and how to quantify it
- Calculate present and future values using discounting and compounding
- Explain why Free Cash Flow matters more than Net Income for valuation
- Distinguish between FCFF (Firm) and FCFE (Equity) and when to use each
The Time Value of Money & Free Cash Flow#
Imagine you win a lottery and are offered a choice: $1 million today, or $1 million in ten years. Which would you choose?
Almost everyone picks "today"—and for good reason. That choice captures one of the most fundamental concepts in finance: the Time Value of Money (TVM).
Why Money Has Time Value#
A dollar today is worth more than a dollar in the future for three powerful reasons:
1. Opportunity Cost#
Money in your hand today can be invested and grown. If you invest $1,000 at 8% annual return, you'll have $1,080 next year. Waiting to receive that same $1,000 next year means you've lost the opportunity to earn $80.
2. Inflation Erodes Purchasing Power#
At 3% annual inflation, today's $100 cup of premium coffee might cost $134 in ten years. The same $1 million buys less in the future than it does today.
3. Uncertainty and Risk#
A dollar promised today is certain. A dollar promised in ten years depends on the promisor still being around and able to pay. The further into the future, the more can go wrong.
The Core Insight: Future money must be "discounted" to reflect what it's actually worth in today's terms. This is the foundation of the Discounted Cash Flow (DCF) model.
The Mathematics: Discounting and Compounding#
Compounding: Growing Money Forward#
If you invest $1,000 today at 10% annually:
| Year | Calculation | Value |
|---|---|---|
| 0 | Starting amount | $1,000 |
| 1 | $1,000 × 1.10 | $1,100 |
| 2 | $1,100 × 1.10 | $1,210 |
| 5 | $1,000 × (1.10)^5 | $1,611 |
| 10 | $1,000 × (1.10)^10 | $2,594 |
| 30 | $1,000 × (1.10)^30 | $17,449 |
Future Value Formula
FV=Future ValuePV=Present Value (starting amount)r=Interest rate (decimal)n=Number of periodsThe power of compounding is remarkable—your $1,000 becomes $17,449 over 30 years at 10%. This is why starting early matters so much for retirement savings.
Discounting: Bringing Future Money to Today#
Discounting is compounding in reverse. If someone promises you $1,000 in five years, what's that worth today?
Present Value Formula
PV=Present Value (today's worth)FV=Future Valuer=Discount raten=Number of periodsUsing a 10% discount rate:
- PV = $1,000 / (1.10)^5 = $620.92
This means you should be indifferent between receiving $620.92 today versus $1,000 in five years (assuming a 10% required return).
The Lottery Example#
A lottery offers two options:
- Option A: $10 million paid as $1 million per year for 10 years
- Option B: $6 million lump sum today
Which is better? Let's discount Option A at 8%:
| Year | Payment | Discount Factor | Present Value |
|---|---|---|---|
| 1 | $1,000,000 | 1/(1.08)^1 = 0.926 | $925,926 |
| 2 | $1,000,000 | 1/(1.08)^2 = 0.857 | $857,339 |
| 3 | $1,000,000 | 1/(1.08)^3 = 0.794 | $793,832 |
| ... | ... | ... | ... |
| 10 | $1,000,000 | 1/(1.08)^10 = 0.463 | $463,193 |
| Total | $10,000,000 | $6,710,081 |
The present value of $10 million over 10 years is only $6.7 million! Option A is still slightly better, but nowhere near the "$4 million more" it appears to be.
The Discount Rate is Everything
Notice how sensitive this calculation is to the discount rate. At 12%, Option A's present value drops to $5.65 million—making Option B the better choice. This sensitivity is why choosing the right discount rate is crucial in DCF valuation.
Why Free Cash Flow, Not Net Income?#
When valuing a company, we don't discount net income—we discount Free Cash Flow. Here's why:
Net Income Can Be Misleading#
Net Income is an accounting concept that includes:
- Non-cash expenses (depreciation, amortization) that don't actually use money
- Accruals (revenue recognized before cash is collected)
- Management discretion in accounting choices
A company can report positive net income while actually burning cash—and vice versa.
Free Cash Flow is Real#
Free Cash Flow represents the actual cash a business generates that could be:
- Paid out to shareholders as dividends
- Used to buy back shares
- Reinvested in growth
- Used to pay down debt
Think of it this way: if you owned 100% of a business, Free Cash Flow is the money you could take home each year without harming the business.
Calculating Free Cash Flow#
Unlevered Free Cash Flow (FCFF)#
FCFF is the cash available to all capital providers—both debt holders and equity holders. It's independent of capital structure (how much debt vs. equity the company uses).
Free Cash Flow to Firm (FCFF)
EBIT=Earnings Before Interest & TaxesT=Tax RateD&A=Depreciation & AmortizationCapEx=Capital ExpendituresΔWC=Change in Working CapitalLet's break this down:
| Component | What It Means | Example |
|---|---|---|
| EBIT × (1-Tax) | Operating profit after tax (NOPAT) | $100M × 0.75 = $75M |
| + Depreciation | Add back non-cash expense | +$20M |
| - CapEx | Subtract cash spent on equipment/facilities | -$30M |
| - Δ Working Capital | Subtract cash tied up in inventory/receivables | -$5M |
| = FCFF | Cash available to all investors | $60M |
Levered Free Cash Flow (FCFE)#
FCFE is the cash available to equity holders only, after paying debt obligations.
FCFE Formula:
FCFE = FCFF - Interest Expense × (1 - Tax Rate) - Net Debt Repayment
When to Use Each#
| Situation | Use | Discount Rate |
|---|---|---|
| Valuing the entire enterprise | FCFF | WACC |
| Valuing equity directly | FCFE | Cost of Equity |
| Company has stable debt levels | Either works | Corresponding rate |
| Company is deleveraging rapidly | FCFF preferred | WACC |
Don't Mix and Match
A common mistake is discounting FCFF at the Cost of Equity, or FCFE at WACC. This produces meaningless results. Always match your cash flow type with the corresponding discount rate.
A Simple Example: Coffee Shop Valuation#
You're considering buying a coffee shop. The owner claims it generates $50,000 in annual "profit." But what's the true Free Cash Flow?
| Item | Amount | Notes |
|---|---|---|
| Net Income | $50,000 | Owner's claim |
| + Depreciation | $10,000 | Non-cash expense for equipment |
| - Maintenance CapEx | $15,000 | New espresso machine, repairs |
| - Working Capital Increase | $5,000 | More inventory for expansion |
| = Free Cash Flow | $40,000 | What you could actually take home |
If you require a 15% return on your investment (your discount rate), the present value of $40,000 per year in perpetuity is:
PV = $40,000 / 0.15 = $266,667
That's the maximum you should pay for this coffee shop—not the price based on "$50,000 profit."
Key Takeaways
- Money today is worth more than money tomorrow due to opportunity cost, inflation, and risk - Compounding grows money forward: FV = PV × (1 + r)^n
- Discounting brings future money to present value: PV = FV / (1 + r)^n - The discount rate reflects your required return—higher for riskier investments
- Free Cash Flow represents actual distributable cash, unlike accounting profit - FCFF (unlevered) is for valuing the whole enterprise; discount at WACC - FCFE (levered) is for valuing equity directly; discount at Cost of Equity - Always match your cash flow type to the appropriate discount rate