Lecture 14: Capital budgeting, Net present value (NPV), internal rate of return (IRR), profitability index (PI)

What is Net present value (NPV) formula?

The present value of all future cash inflows discounted at the WACC minus the initial investment

• represents the expected change in firm value from taking the project

Rules:

• NPV > 0 → accept project

• NPV < 0 → reject project

What are independent vs. mutually exclusive projects?

• Independent → firm has enough capital to finance both projects, accept all positive NPV projects

• Mutually exclusive → can only accept one project or the other, choose the investment with the highest NPV

What are the strengths of NPV?

• NPV uses cash flows

• NPV uses all relevant project cash flows

• NPV discounts cash flows correctly

• tells you exactly how much value is added to firm

What is the internal rate of return (IRR)?

The discount rate that brings NPV to 0

• the % return of the project

Rules:

• WACC is the benchmark

• IRR > WACC → accept project

• IRR < WACC → reject project

What is an internal rate of return chart?

Y is the NPV when = 0

X is the IRR

What are the 4 issues with the IRR approach?

1. Investing or financing?

2. Multiple IRRS

3. The scale problem

4. The timing problem

What is 1. Investing or financing?

When there is a positive cash flow in the beginning which turns negative later on → Means money is being borrowed!

What is 2. Multiple IRRs?

Multiple IRR’s → means there are multiple changes in sign

• goes from + → - → +

• If there’s only 1 change in sign, there’s 1 solution

What is 3. The scale problem?

Mutually exclusive projects only

Invest in small very profitable vs. Big but not as profitable → which has more value?

• more value is the big project due to higher NPV!

What is 4. The timing problem?

For mutually exclusive projects only

• when the graph lines crossover

Project A has biggest cash flow early on vs. project B has biggest cash flow later

• You accept B until the intersection rate, then accept A after → once it hits the negatives, reject

How do you find the crossover rate?

What is the payback period rule?

• Payback period: amount of time required for an investment to generate cash flow to recover its initial cost

• Payback period rule: a project is accepted if its payback period is less than a cutoff period

What are the strengths & weaknesses of the payback period rule?

Strengths:

• simple & easy to calculate & understand

• useful for firms with limited access to capital

• not very limited in practice

Weaknesses:

• timing of cash flows is ignored

• cash flows after are ignored → may lose out on big cash flow after cutoff period

• arbitrary benchmark

What is the profitability index formula??

Tells us how much each dollar invested in the project generates in present value 

• similar to NPV → divide by initial investment

• how many $ you get relative to initial investment

• PI > 1 → accept project

• PI < 1 → reject project

What is the strength & weakness of the profitability index?

Weakness: Mutually exclusive projects

• PI is a ratio & doesn’t account for $ scale of the project

• more value in bigger project

Strength: Capital rationing

• ratio used to rank projects → useful if a big list of projects