Intro to Finance: Introduction to Finance - What is Finance Definition Finance vs. Accounting, Corporate vs. Personal vs. Public

What This Is

Finance is the study of how individuals, businesses, and governments allocate resources to maximize value. It involves understanding the time value of money, risk, and return on investment. For example, consider Apple's decision to invest $1 billion in a new manufacturing facility. Finance helps Apple's management determine the optimal investment strategy, considering factors like the cost of capital, expected returns, and potential risks.

Key Formulas & Symbols

• NPV = ?(CFt / (1 + r)^t) where NPV = net present value, CFt = cash flow at time t, r = discount rate, t = time period.
• IRR = r where IRR = internal rate of return, r = rate that makes NPV = 0.
• WACC = E/V × Re + D/V × Rd × (1 – Tc) where WACC = weighted average cost of capital, E/V = market value of equity, Re = cost of equity, D/V = market value of debt, Rd = cost of debt, Tc = corporate tax rate.
• FCFF = EBIT × (1 – Tc) + Depreciation – Capital Expenditures where FCFF = free cash flow to the firm, EBIT = earnings before interest and taxes, Tc = corporate tax rate.
• FCFE = FCFF – Net Debt Repayment where FCFE = free cash flow to equity, FCFF = free cash flow to the firm, Net Debt Repayment = net debt repayment.
• D/E = D / E where D/E = debt-to-equity ratio, D = total debt, E = total equity.
• ROE = Net Income / Total Equity where ROE = return on equity, Net Income = net income, Total Equity = total equity.
• ROA = Net Income / Total Assets where ROA = return on assets, Net Income = net income, Total Assets = total assets.
• Beta = Cov(Ri, Rm) / ?m^2 where Beta = beta coefficient, Ri = return on stock i, Rm = return on market, ?m = standard deviation of market return.

Step-by-Step Calculation

1. Calculate the net present value (NPV) of a project using the formula NPV = ?(CFt / (1 + r)^t). For example, if a project has cash flows of $100, $120, and $150 over three years, and a discount rate of 10%, the NPV would be calculated as follows:
2. Year 1: $100 / (1 + 0.10)^1 = $90.91
3. Year 2: $120 / (1 + 0.10)^2 = $109.09
4. Year 3: $150 / (1 + 0.10)^3 = $127.27
5. NPV = $90.91 + $109.09 + $127.27 = $327.27
6. Calculate the internal rate of return (IRR) using the formula IRR = r. For example, if a project has a net present value of $100,000 and a cash flow of $150,000 in year 5, the IRR would be calculated as follows:
7. Set up the equation: $100,000 = -$150,000 / (1 + r)^5
8. Solve for r: r-0.15 or 15%
9. Calculate the weighted average cost of capital (WACC) using the formula WACC = E/V × Re + D/V × Rd × (1 – Tc). For example, if a company has a market value of equity of $100 billion, a market value of debt of $50 billion, a cost of equity of 10%, a cost of debt of 5%, and a corporate tax rate of 20%, the WACC would be calculated as follows:
10. WACC = ($100 billion / $150 billion) × 0.10 + ($50 billion / $150 billion) × 0.05 × (1 – 0.20) = 0.0667 or 6.67%
11. Calculate the free cash flow to the firm (FCFF) using the formula FCFF = EBIT × (1 – Tc) + Depreciation – Capital Expenditures. For example, if a company has earnings before interest and taxes (EBIT) of $100 million, a depreciation of $20 million, and capital expenditures of $30 million, the FCFF would be calculated as follows:
12. FCFF = $100 million × (1 – 0.20) + $20 million – $30 million = $80 million
13. Calculate the free cash flow to equity (FCFE) using the formula FCFE = FCFF – Net Debt Repayment. For example, if a company has a free cash flow to the firm (FCFF) of $80 million and a net debt repayment of $20 million, the FCFE would be calculated as follows:
14. FCFE = $80 million – $20 million = $60 million

Common Mistakes

• Mistake: Using book value instead of market value for WACC.
• Correction: Use market value instead of book value because market value reflects the current market price of the company's securities.
• Mistake: Confusing IRR and NPV ranking.
• Correction: IRR is a rate that makes NPV = 0, while NPV ranking is based on the magnitude of NPV.
• Mistake: Using the wrong discount rate for WACC.
• Correction: Use the cost of equity for equity and the cost of debt for debt, weighted by their respective market values.

Exam / CFA Tips

• Tip: Be careful with the difference between YTM and current yield.
• Tip: When to use arithmetic vs geometric mean.
• Tip: Understand the difference between cash flow and accrual accounting.

Quick Practice Problem

A bond has a face value of $1,000, a coupon rate of 5%, and a yield to maturity of 8%. What is the bond's yield to maturity?

Answer: 8% Explanation: The yield to maturity is the rate that makes the present value of the bond's cash flows equal to its face value.

Last-Minute Cram Sheet

• The dividend discount model (DDM) requires g < r – otherwise the model explodes.
• The weighted average cost of capital (WACC) is a weighted average of the cost of equity and the cost of debt.
• The free cash flow to the firm (FCFF) is calculated as EBIT × (1 – Tc) + Depreciation – Capital Expenditures.
• The internal rate of return (IRR) is a rate that makes NPV = 0.
• The beta coefficient is sensitive to the time period used to calculate it.
• The return on equity (ROE) is calculated as Net Income / Total Equity.
• The return on assets (ROA) is calculated as Net Income / Total Assets.
• The debt-to-equity ratio (D/E) is sensitive to the definition of debt and equity.
• The cost of equity is typically estimated using the capital asset pricing model (CAPM).
• The yield to maturity (YTM) is sensitive to the bond's cash flows and yield.