Capital Cash Flow (CCF), NPV, IRR and Valuation Metrics
Capital Cash Flow (CCF) and Components
Capital Cash Flow (CCF)
Cash flow available to all holders — debt and equity.
CCF = Cash Flow to Shares (CFAC) + Cash Flow to Debt (CFD)
Cash Flow to Debt (CFD) = interest paid on debt + change in debt (growth of debt).
Example notation: CFD = D * k_d + ΔD
Therefore: CCF = CFAC + CFD
Cost of Equity and Market Rates
Ke = Required return on equity (cost of equity)
Rf = Risk-free rate
Ke = Rf + equity risk premium
E(Rm) = Rf + market risk premium
Firm Value, WACC and Tax Shields
VL = D + E
VL = VU + PV(tax shields)
WACC: Weighted average cost of capital — the discount rate used to discount operating cash flows to value a company using discounted cash flows.
EVA and Economic Profit
EVA (Economic Value Added): Net operating profit after taxes (NOPAT) less the book value of invested capital multiplied by the average cost of capital:
EVA = NOPAT − (Invested Capital × WACC)
Economic profit (EP): Accounting profit less the book value of equity multiplied by the required return on equity.
Relationship example: AN × EVA = (RONA − WACC) × AN (where AN is invested assets; RONA is return on net assets)
RONA and Improving EVA
RONA: Can be decomposed as (Operating income / Sales) × (Sales / Net assets).
How to improve EVA:
- Decrease invested assets
- Increase operating income (sales or margins)
- Increase returns on investments
Optimal Capital Structure
Optimal capital structure: The mix of debt and equity that minimizes the weighted average cost of capital (WACC) and thereby maximizes firm value.
To analyze optimal structure, it is necessary to consider how the total value of the firm (debt + equity + present value of tax shields) changes with leverage.
NPV (Net Present Value) and IRR (Internal Rate of Return)
NPV: Net Present Value represents the value of all discounted future cash flows from an investment today. If, after deducting the initial investment, the result is positive, the project is viable.
To find the NPV you need:
- Investment size
- Projected net cash flows
- Discount rate
Example
An investment project with an initial investment of 12,000 and a discount rate (TD) of 14%.
| Year 0 | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 |
| Investment | 4,000 | 4,000 | 4,000 | 4,000 | 5,000 |
NPV Calculation
The NPV is calculated as the discounted sum of future cash flows minus the initial investment. In this example:
NPV = −12,000 + 4,000 / (1 + 0.14)1 + 4,000 / (1 + 0.14)2 + 4,000 / (1 + 0.14)3 + 4,000 / (1 + 0.14)4 + 5,000 / (1 + 0.14)5
IRR Calculation
To find the IRR we use the same NPV formula but set NPV = 0 and solve for the discount rate i (the IRR):
0 = −12,000 + 4,000 / (1 + i)1 + 4,000 / (1 + i)2 + 4,000 / (1 + i)3 + 4,000 / (1 + i)4 + 5,000 / (1 + i)5
In practice, IRR is found using numerical methods or financial calculators.
NPV Formula Reminder
NPV = Present value of benefits − Initial investment
Notes
- Keep consistent units and timing (e.g., flows at year-ends).
- Be explicit about whether cash flows are before or after financing effects; CCF is cash available to all providers.
- Tax shields from debt affect the value of a leveraged firm.