Solving a typical business school NPV problem

MBA topics

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 . 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 . 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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8 Feedbacks on "Solving a typical business school NPV problem"

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Mike Phillips

Your analysis is terrific, although I have one question. The problem states: 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.

If I read this correctly, you have calcultated these items as a “decrease in operating costs” of $60,000 (+), but I think it should be considered an “increase in operating costs of $40,000 (160,000-120,000 resulting in an additional $40,000 expenditure). If correct, this would result in a PV of CFs= $6,491. The NPV then being (1,509), a result even less favorable than what you calculated. Please let me know your thoughts.


I would like the simplest explanation. I think people must understand that current NPV and depreciation explanation doesnt allow easy translation to the practical calculations.

All I would like to know is, if in an NPV scenario there is a yearly decpreciation on an asset do I:-

i) Add or subtract its value to net cash flows?
ii) where do I add or subtract its value, yearly? or in year 0 or at terminal yeary as lump sum
iii) do i discount depreciation?

If I do add deprecation why is this?


your a nuggat

Capital Gain Tax Rate

Home Appreciation and Capital Gains…

The last seven years has seen tremendous appreciation in home prices. This brings up the issue of home capital gains tax issues for people when they sell….

Chalwe mpundu

hi.i stubled upon this in my research for a new assignment.its been helfpul but not in totality. my assignment(at the office for budgeting purposes goes like this)
option 1- purchase an office building for $15m.

option 2- operating lease
-lease period of 10 & 15yrs
-option to buy in Yr10 price to be determined by a Market value
price determination isa capitlization rate of 8.5% of the lease charges applicable for the twelve months prior to exercise of the offer
-lease charges of $20/square meter escalating by 5%per annum.phase of 6000square meters to be occupied in june2010. phase two of 4000square meters to be occupied in june 2012.
optin 3-finance lease
-property valued at $15m
-capital yield of 10% for the developer
-IRR required by the developer of 13.65%
-if it were rented, the developer would ordinarily requre a 5%escalation on the rental
-create an SPV (SPECIAL PURPOSE VEHICLE) to own the property
-cost of funding of around LIBOR+3.5%
-Lease period is 10 & 15 years

* factor in the tax implications as well

AS Naidu

Your analysis is terrific, I am working in Private Organisation. I need help from you. the question is i ahve some Estimated data to establishing a new project. They are giving data of Estimating Costs, Revenues, interest rate, O&M Costs & Time period. with this data how can I calculate cash in & outflows, profitability Statements, NPV, Capex Calculations, Risk Analysis, Consolidated statements. Can you tell simple methods. we have to forecast all for further 10 or 20 years.

Smarter Finances

This is one of the difficult problems that I’ve known,but thanks for this article which gives relevant ideas and information that would truly help a lot.

Great thanks!