Solving a typical business school NPV problem

I received the following email from a reader:

I’ve been trying to solve this problem for sometime with no success. I have also attempted using your information (How to calculate NPV) on the website, got close but still didnt get the solution.

Can you please help? Here is the question.

A fashion clothing company is considering investing in new machinery to improve its productivity over the next 5 years. You have been given the following information:

Sales are predicted to increase by $1,500,000 in year 1 and continue at this level.

The new machinery costs $10 million payable immediately.

It will be depreciated over 5 years on a straight line basis.

All the old machinery can be sold for $2 million.

The new equipment is more complicated and will cost $160,000 per year every year to maintain, as against the $100,000 for the old machines, but other running costs will be reduced by $120,000.

Finance for the purchase needs to be raised via a loan which requires annual interest payments of $300,000.

Wages will be reduced by $100,000 due to increased automation.

At the end of the five years the machinery will have a scrap value of $2million.

The feasibility study for this project (already completed and paid for) cost $200,000.

The cost of capital on investment appraisal for this level of risk is 7.5%.

Identify which of these items would be included in an NPV calculation and calculate the NPV. You may ignore tax and inflation.

This sounds like a typical NPV problem that you’d find in a business school finance class, and simplifies things by ignoring tax and inflation.

I’m laying out my reasoning and solution here, but I welcome any comments from others, as there may be other interpretations and I might just be plain wrong. (The beauty of a blog, right?)

All the information provided in the problem is relevant to the NPV calculation except for depreciation expense and the feasibility study. The reason the feasibility study is irrelevant is that it’s already done and paid for, making it a sunk cost. Whether or not the fashion company decides to buy equipment and become more productive has no impact on the money already spent on the study. They can’t recover it, it doesn’t increase or decrease because of any decision they make…it’s a sunk cost.

Depreciation expense is a phantom cash flow and impacts cash flows only insofar as taxes are reduced by depreciation expenses, the so-called depreciation tax shield. But, since this problem ignores taxes, depreciation expense isn’t relevant.

Let’s lay out the NPV (click to enlarge)

Normally, you’d probably calculate NPVs by bundling certain things together in a typical process — for example, subtracting operating costs from revenue to arrive at EBITDA, then taking out depreciation to find EBIT, then taking out interest expense, etc. step by step — but for the sake of clarity, I decided to lay out items in the order they were presented in the problem.

We start with revenues. I couldn’t be sure how to interpret the information that the company expected sales to increase to $1.5M and “continue at this level”. I chose to interpret this to mean sales would stay constant at $1.5M a year (but one other interpretation might be that they increase by $1.5M a year).

Next, we know that the machinery costs $10M immediately, so we put that amount down for the column marked “Now”. Again, we ignore depreciation expense for the reasons stated above. It’s a phantom cash flow.

We also gain $2M from selling the old machinery. Again, there’s some room for interpretation here, but I assumed that as soon as we bought the new equipment, we’d decide sell the old stuff. So I put this amount as a gain under “Now”.

We know that some operating costs go up, and some go down, so we net this out and realize that the company will save (gain) $60K a year in the end.

Similarly, we have to pay $300K in interest expense per year, so we put that in as a decrease in cash flows.

Wages will decrease $100K due to automation, so that goes in as a positive cash flow. I chose to interpret this as saying the company would save $100K in wages each year because of the new equipment, but another interpretation might be a one-time savings of $100K.

At the end of 5 years, we can gain $2M from the sale of the new equipment. That figure goes in Year 5.

Now, we just have to present value the future amounts in Years 1-5 back to “now” using the cost of capital of 7.5%. This ends up being around $6.9M.

Finally, we subtract out the capital expenditure of $10M on equipment and add in the $2M from the sale of the old equipment (for a total of -$8M) and end with an negative NPV of about $1.1M.

Assuming I did everything correctly, this would not be a project worth undertaking, since the project’s NPV is negative. On the other hand, if we had kept revenues growing at $1.5M per year, NPV would be positive ($10.2M) and worth doing.

What do you think? Did I make any rookie mistakes? (It’s been 4 years since I went to bschool, so I’m a bit rusty.)

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