Intro to Finance: Capital Budgeting - Net Present Value, NPV = S CFt / (1 + r)^t - Initial Investment

What This Is

Net Present Value (NPV) is a widely used metric in finance to evaluate investment opportunities. It calculates the present value of expected future cash flows minus the initial investment. A positive NPV indicates an investment is expected to generate returns greater than its cost, making it a good investment. For example, consider Apple's decision to invest $100 million in a new manufacturing facility. If the expected cash flows over the next 5 years are $150 million, $200 million, $250 million, $300 million, and $350 million, and the discount rate is 10%, the NPV would be $1.5 billion, indicating a good investment.

Key Formulas & Symbols

• NPV =-CFt/(1+r)^t – Initial Investment where NPV = net present value, CFt = cash flow at time t, r = discount rate, t = time period.
• CFt = Revenue – Costs where CFt = cash flow at time t, Revenue = total revenue, Costs = total costs.
• Discount Rate (r) = WACC where r = discount rate, WACC = weighted average cost of capital.
• WACC = (E/V x Re) + (D/V x Rd) where WACC = weighted average cost of capital, E = market value of equity, V = total market value, Re = cost of equity, D = market value of debt, Rd = cost of debt.
• Cost of Equity (Re) = Rf +-× (Rm – Rf) where Re = cost of equity, Rf = risk-free rate,-= beta, Rm = market return.
• Cost of Debt (Rd) = Coupon Rate + (Default Risk Premium) where Rd = cost of debt, Coupon Rate = coupon rate of debt, Default Risk Premium = premium for default risk.
• Cash Flow (CF) = Earnings Before Interest and Taxes (EBIT) + Depreciation – Capital Expenditures – Change in Working Capital where CF = cash flow, EBIT = earnings before interest and taxes, Depreciation = depreciation expense, Capital Expenditures = capital expenditures, Change in Working Capital = change in working capital.

Step-by-Step Calculation

1. Estimate the expected cash flows for each time period.
2. Determine the discount rate (WACC) using the weighted average cost of capital formula.
3. Calculate the present value of each cash flow using the NPV formula.
4. Subtract the initial investment from the present value of the cash flows to get the NPV.
5. Compare the NPV to zero to determine if the investment is expected to generate returns greater than its cost.

Common Mistakes

• Mistake: Using the wrong discount rate (e.g., using the cost of equity instead of WACC).
• Correction: Use the weighted average cost of capital (WACC) as the discount rate, which takes into account both the cost of equity and debt.
• Mistake: Forgetting to account for taxes in the cash flow calculation.
• Correction: Include taxes in the cash flow calculation by subtracting taxes from EBIT.
• Mistake: Confusing NPV with IRR.
• Correction: NPV is a present value calculation, while IRR is a rate of return calculation. NPV is used to evaluate the attractiveness of an investment, while IRR is used to determine the rate of return on an investment.

Exam / CFA Tips

• Tip: Be careful with the sign of the NPV. A positive NPV indicates an investment is expected to generate returns greater than its cost, while a negative NPV indicates the opposite.
• Tip: Make sure to use the correct discount rate (WACC) when calculating NPV.
• Tip: Be prepared to calculate NPV using different discount rates (e.g., WACC, cost of equity, cost of debt).

Quick Practice Problem

Apple is considering investing $100 million in a new manufacturing facility. If the expected cash flows over the next 5 years are $150 million, $200 million, $250 million, $300 million, and $350 million, and the discount rate is 10%, what is the NPV of the investment?

Answer: $1.5 billion. Explanation: The NPV is calculated by summing the present value of each cash flow and subtracting the initial investment.

Last-Minute Cram Sheet

• NPV =-CFt/(1+r)^t – Initial Investment
• WACC = (E/V x Re) + (D/V x Rd)
• Cost of Equity (Re) = Rf +-× (Rm – Rf)
• Cost of Debt (Rd) = Coupon Rate + (Default Risk Premium)
• Cash Flow (CF) = EBIT + Depreciation – Capital Expenditures – Change in Working Capital
• The discount rate (WACC) must be used to calculate NPV, not the cost of equity or cost of debt.
• Taxes must be included in the cash flow calculation.
• NPV is a present value calculation, while IRR is a rate of return calculation.
• A positive NPV indicates an investment is expected to generate returns greater than its cost.
• A negative NPV indicates the investment is expected to generate returns less than its cost.