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 = PV × (1 + r)^n
The 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 = FV / (1 + r)^n
Using 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).
FCFF Formula:
FCFF = EBIT × (1 - Tax Rate) + Depreciation - CapEx - Δ Working Capital
Let'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