Intro to Finance: Capital Budgeting Capital Rationing and Project Ranking

What This Is

Capital rationing and project ranking are essential concepts in finance that help companies allocate limited funds to the most profitable projects. Imagine Apple, with a market capitalization of $2 trillion, needs to decide whether to invest in a new product line or expand its existing manufacturing capacity. By applying capital rationing and project ranking techniques, Apple can make informed decisions to maximize shareholder value. For example, if Apple has $100 million to invest and two projects with expected returns of 15% and 20%, respectively, it should invest in the 20% return project to maximize its returns.

Key Formulas & Symbols

• IRR = (1 + r)^n - 1 where IRR = internal rate of return, r = periodic interest rate, n = number of periods.
• NPV = ∑(CFt / (1 + r)^t) where NPV = net present value, CFt = cash flow at time t, r = discount rate, t = time period.
• WACC = E/V x Re + D/V x Rd x (1 - T) 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, T = tax rate.
• DCF = FCF / (1 + WACC)^n where DCF = discounted cash flow, FCF = free cash flow, WACC = weighted average cost of capital, n = time period.
• Payback Period = ∑CFt / ∑CFt where Payback Period = payback period, CFt = cash flow at time t.
• Modified Internal Rate of Return (MIRR) = (1 + WACC)^n - 1 where MIRR = modified internal rate of return, WACC = weighted average cost of capital, n = time period.
• Capital Rationing = Maximize NPV subject to EBITDA ≤ Capital Budget where EBITDA = earnings before interest, taxes, depreciation, and amortization, Capital Budget = maximum amount of capital available.
• Project Ranking = Rank projects based on IRR, NPV, or MIRR where IRR = internal rate of return, NPV = net present value, MIRR = modified internal rate of return.

Step-by-Step Calculation

1. Calculate the expected cash flows for each project.
2. Determine the discount rate (WACC) for each project.
3. Calculate the NPV for each project using the formula NPV = ∑(CFt / (1 + r)^t).
4. Rank the projects based on their NPV, IRR, or MIRR.
5. Select the projects with the highest NPV, IRR, or MIRR, subject to the capital budget constraint.

Common Mistakes

• Mistake: Using book value instead of market value for WACC.
• Correction: Use market value of equity and debt to calculate WACC, as book value may not reflect the true market value of the company.
• Mistake: Confusing IRR and NPV ranking.
• Correction: IRR ranking is sensitive to the discount rate, while NPV ranking is not. Use NPV ranking for more accurate results.
• Mistake: Not considering taxes when calculating WACC.
• Correction: Include the tax rate when calculating WACC to reflect the impact of taxes on the company's cost of capital.

Exam / CFA Tips

• Tip: Be careful when using the IRR formula, as it can be sensitive to the discount rate.
• Tip: Use the NPV formula to calculate the net present value of a project, as it is more accurate than IRR.
• Tip: Consider the tax implications when calculating WACC, as it can significantly impact the company's cost of capital.

Quick Practice Problem

Apple is considering two projects: Project A, which requires an initial investment of $10 million and is expected to generate $5 million in cash flows per year for 5 years, and Project B, which requires an initial investment of $15 million and is expected to generate $7 million in cash flows per year for 5 years. If the discount rate is 10%, which project should Apple invest in?

Answer: Project B, with an NPV of $1.5 million compared to Project A's NPV of $1.2 million.

Last-Minute Cram Sheet

• ⚠️ The dividend discount model (DDM) requires g < r – otherwise the model explodes.
• WACC = E/V x Re + D/V x Rd x (1 - T).
• NPV = ∑(CFt / (1 + r)^t).
• IRR = (1 + r)^n - 1.
• MIRR = (1 + WACC)^n - 1.
• Capital Rationing = Maximize NPV subject to EBITDA ≤ Capital Budget.
• Project Ranking = Rank projects based on IRR, NPV, or MIRR.
• ⚠️ The payback period is not a good measure of project profitability.
• ⚠️ The modified internal rate of return (MIRR) is a better measure of project profitability than IRR.
• ⚠️ The weighted average cost of capital (WACC) is a better measure of the company's cost of capital than the cost of equity or debt.