Introductory Corporate Finance: Capital Budgeting - Capital Rationing, Soft vs. Hard Rationing, Ranking Projects by PI

What This Is

Capital rationing occurs when a company faces a constraint on its ability to invest in new projects due to limited funds or resources. This can be a soft rationing, where the company has the funds but chooses not to invest in certain projects, or a hard rationing, where the company lacks the funds to invest in all desired projects. For example, consider a company with a budget of $100 million to invest in new projects. It has two projects to choose from: Project A, which costs $50 million and has a 20% return on investment (ROI), and Project B, which costs $70 million and has a 15% ROI. The company must decide which project to invest in, given its limited budget.

Key Formulas & Models

• PI = (CF0 + CF1 + ... + CFn) / (PV of CF0 + PV of CF1 + ... + PV of CFn) – present value index (PI); measures the present value of a project's cash flows relative to its initial investment.
  • CF0: initial investment
  • CF1: cash flow in year 1
  • CFn: cash flow in year n
  • PV: present value
• IRR = (1 + r)^n - 1 / (1 + r)^n - 1 - (CF0 / (CF0 + CF1 + ... + CFn)) – internal rate of return (IRR); measures the rate of return on a project's cash flows.
  • r: discount rate
  • n: number of years
  • CF0: initial investment
  • CF1: cash flow in year 1
  • CFn: cash flow in year n
• NPV = -CF0 + PV of CF1 + PV of CF2 + ... + PV of CFn – net present value (NPV); measures the present value of a project's cash flows relative to its initial investment.
  • CF0: initial investment
  • PV: present value
  • CF1: cash flow in year 1
  • CF2: cash flow in year 2
  • CFn: cash flow in year n
• WACC = wd × rd(1-T) + wps × rps + we × re – weighted average cost of capital (WACC); used as discount rate.
  • wd: proportion of debt
  • rd: cost of debt
  • T: tax rate
  • wps: proportion of preferred stock
  • rps: cost of preferred stock
  • we: proportion of equity
  • re: cost of equity
• ROI = (EBIT - Interest) / Total Assets – return on investment (ROI); measures a company's profitability.
  • EBIT: earnings before interest and taxes
  • Interest: interest expense
  • Total Assets: total assets

Step-by-Step Calculation

1. Determine the initial investment and cash flows for each project.
2. Calculate the present value of each project's cash flows using the WACC as the discount rate.
3. Calculate the present value index (PI) for each project by dividing the present value of the cash flows by the initial investment.
4. Rank the projects by their PI, with the highest PI indicating the most valuable project.
5. If the company has a limited budget, select the projects with the highest PI until the budget is exhausted.

Common Mistakes

• Mistake: Using the wrong discount rate, such as the cost of debt instead of the WACC.
  • Correction: Use the WACC as the discount rate, as it reflects the company's overall cost of capital.
• Mistake: Ignoring the time value of money when calculating the present value of cash flows.
  • Correction: Use the present value formula to calculate the present value of each cash flow, taking into account the time value of money.
• Mistake: Confusing the internal rate of return (IRR) with the net present value (NPV).
  • Correction: The IRR measures the rate of return on a project's cash flows, while the NPV measures the present value of a project's cash flows relative to its initial investment.

Exam / CFA Tips

• Tip: When ranking projects by their PI, make sure to use the correct discount rate and calculate the present value of each cash flow correctly.
• Tip: Be able to distinguish between the internal rate of return (IRR) and the net present value (NPV), and use the correct formula for each.
• Tip: When faced with a capital rationing problem, make sure to select the projects with the highest PI until the budget is exhausted.

Quick Practice Problem

A company has two projects to choose from: Project A, which costs $50 million and has a 20% ROI, and Project B, which costs $70 million and has a 15% ROI. The company has a budget of $100 million and wants to select the projects with the highest ROI. Which project should the company select?

Answer: Project A, with a ROI of 20%.

Explanation: Project A has a higher ROI than Project B, indicating that it is the more valuable project.

Last-Minute Cram Sheet

• Capital rationing: a constraint on a company's ability to invest in new projects due to limited funds or resources.
• Soft rationing: a company has the funds but chooses not to invest in certain projects.
• Hard rationing: a company lacks the funds to invest in all desired projects.
• Present value index (PI): measures the present value of a project's cash flows relative to its initial investment.
• Internal rate of return (IRR): measures the rate of return on a project's cash flows.
• Net present value (NPV): measures the present value of a project's cash flows relative to its initial investment.
• Weighted average cost of capital (WACC): used as discount rate.
• Return on investment (ROI): measures a company's profitability.
• In M&M Proposition I (no taxes), firm value is independent of capital structure – but with taxes, value increases with debt due to the interest tax shield.
• The IRR is not always the best measure of a project's value, as it can be affected by the timing of cash flows.
• The NPV is a more comprehensive measure of a project's value than the IRR, as it takes into account the present value of all cash flows.