NPV and IRR

Question

Your division is considering two projects with the following cash flows (in millions):
Project X: requires initial investment of $40 million; will bring annual cash flow of $4 million for first 5 years and $14 million for next 5 years. The project will require additional $5 million for machinery overhaul at year 6.
Project Y: also requires initial investment of $40 million; will bring $12 million for first 5 years and $6 million for next 5 years. The project will also require additional $5 million for machinery overhaul at year 6.
a. What are the projects' NPVs assuming the WACC is 5%? Round your answer to two decimal places

b. What are the projects' NPVs assuming the WACC is 10%? Round your answer to two decimal places.

c. What are the projects' IRRs assuming the WACC is 5%? Round your answer to two decimal places.


d. What are the projects' IRRs assuming the WACC is 15%? Round your answer to two decimal places.

Answer 1

Hi Tanner!

Great question! The key to solving this problem is organizing the cash flows correctly and understanding the difference between NPV and IRR.

Step 1: Identify the cash flows

Both projects require an initial investment of $40 million.

Project X:

1. Year 0: −$40 million
2. Years 1–5: +$4 million annually
3. Year 6: +$9 million
4. Years 7–10: +$14 million annually

Project Y:

1. Year 0: −$40 million
2. Years 1–5: +$12 million annually
3. Year 6: +$1 million
4. Years 7–10: +$6 million annually

Notice that we subtract the $5 million machinery overhaul from each project's Year 6 cash flow.

Step 2: Calculate NPV

The formula is:

NPV = Σ [CFₜ / (1 + r)ᵗ]

Here, CF represents the cash flow, r is the discount rate (WACC), and t is the year.

(a) At a 5% WACC:

Project X: NPV = $21.08 million

Project Y: NPV = $28.58 million

(b) At a 10% WACC:

Project X: NPV = $5.29 million

Project Y: NPV = $16.79 million

Both projects have positive NPVs at these discount rates, meaning both are expected to create value.

Step 3: Calculate IRR

IRR is the discount rate that makes a project's NPV equal to zero.

In other words:

0 = Σ [CFₜ / (1 + IRR)ᵗ]

Solving using the cash flows:

(c) IRR assuming a 5% WACC:

Project X: IRR = 12.24%

Project Y: IRR = 21.26%

(d) IRR assuming a 15% WACC:

Project X: IRR = 12.24%

Project Y: IRR = 21.26%

Here's an important distinction: IRR does not change when WACC changes! IRR depends on the project's cash flows, while WACC is used to calculate NPV and evaluate whether the project's return is sufficient.

Which project is better?

Project Y is the stronger investment because it generates more cash earlier, resulting in a higher NPV at both discount rates and a higher IRR.

For perspective, at a 15% WACC, Project X would actually have a negative NPV of $5.42 million, while Project Y would still have a positive NPV of $8.06 million.

My biggest takeaway: NPV tells us how much value a project adds in today's dollars, while IRR tells us the project's percentage return. When comparing mutually exclusive investments, NPV is generally the preferred decision-making tool.

Hope this helps clarify the calculations and, more importantly, the reasoning behind them!

Michael