Increase in Cap-ex decreases your EV in DCF but increases your EV when moving from Equity value to EV?

Here is a question from 400 question book.

We’re creating a DCF for a company that is planning to buy a factory for $100 in cash (no debt or other financing) in Year 4. Currently the present value of its Enterprise Value according to the DCF is $200. How would we change the DCF to account for the factory purchase, and what would our new Enterprise Value be?

Answer:
In this scenario, you would add CapEx spending of $100 in year 4 of the DCF, which would reduce Free Cash Flow for that year by $100. The Enterprise Value, in turn, would fall by the present value of that $100 decrease in Free Cash Flow.
The actual math here is messy but you would calculate the present value by dividing $100 by ((1 + Discount Rate)^4) – the “4” just represents year 4 here. Then you would subtract this amount from the Enterprise Value.

The explanation makes sense. But if I ask you "But I thought if you buy $100 factory with $100 cash, your EV should increase because you are exchanging $100 non-core asset for $100 asset that is core to your operation." How would you respond to that?

 

Purchasing the factory does increase your EV. It yields the cash flow that generates value in your forecasts. The cost of those cash flows (i.e., the capex), however, will reduce the EV as all expenses do. Expenses generate income. The expenses are accretive If the income to be earned exceeds said costs. If the costs exceed the generated income, then EV will decrease.

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Best Response

You're basically arguing that if the factory purchase is value destructive it will reduce EV. Fair enough, but why would anyone make the purchase...? The year 4 investment will (yes, of course) reduce cash flow in that year, but it will increase cash flow in year 5 and - importantly - in perpetuity. If the DCF captures this and still yields a reduced EV then either the perp value calculation is wrong, or the factory purchase is a bad idea. At some point someone who matters is going to ask "why?" and I for one would recommend having a good answer.

 

The above reasons aren't necessarily true. Think about it in the sense of incremental cash flows. Let's say capex of $500 was originally planned for year 4 and embedded in the DCF and the associated increases in cash flow were also captured. However, then you realize that the asset will cost $100 more than you expected. This incremental $100 you pay will not bring any incremental cash flows and so technically your EV should decrease since Year 4 FCFs decrease and there is no impact on future FCFs. The real reason you are getting two different answers is because in your bridge to equity value in a DCF, you use PRESENT day cash levels (and debt and so on), and these values are not linked to the model (i.e. not impacted by the capex in year 4). As a result, you have capex in year 4, but the associated cash out flow is not reflected in today's cash level (which it is in the second question you proposed).

 

Agree with other commenters that the explanation presented is not complete. If the NPV of the factory purchase is negative (i.e. the year four investment is not offset by future dicounted cash flows), then the EV in year 0 is reduced; if NPV is the factory purchase is $0, EV at year 0 is unchance; otherwise EV is increased by the NPV of the year 4 investment.

"Apparently there is nothing that cannot happen today." -Twain
 

Thanks guys for all good comments. The above question and answer is copy and paste from breaking into wall street questions list.

Based on what you guys posted, here is how I think now.

When you increase Cap-ex -> this will not necessarily decrease your value found by DCF because this will assume that your future cash flow will increase because you are investing in your business. -> If you are simply adding cap-ex without changing future cash flow, of course sum of PV will decrease but then that should mean that your original cash flow was not correct (unless you believe that you are spending cap-ex that is neither necessary or generating future profits)

 

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