A corporate finance conundrum (Part 2)
Posted by Arun Uday on October 1, 2007
The valuation question posed in my last post had three responses. Two readers suggested that the cash needs to be added back and one said that it needs to be left alone. And now for the right answer - neither is correct. It in fact needs to be subtracted. Let me “prove” that to you.
One of the mistakes that people typically make is in understanding the difference between enterprise and equity values. One way of articulating what enterprise value actually stands for is - it is the full net amount that a buyer pays to buy a business or the net amount that a seller gets when he sells a business. Let me explain that. Suppose you own a golden box that is worth 1000. Further, suppose the box has another 100 of cash in it. Say you decide to sell the box with the cash. How much would you expect? 1100 right? So, suppose a buyer is buying the box for 1100, how much is he paying in reality - 1000 (because he is getting 100 back immediately). So, thats the difference between enterprise and equity value. The equity value holders will always expect what the business is intrinsically worth and over & above that, they will expect the extra cash that the business has. Looking at it from the buyer’s stand point, what he ends up effectively paying is the equity value of the business minus the extra cash that the business has.
So, thats the first step: Enterprise Value = Equity Value - cash.
Now, apart from cash, when someone buys a business, he also assumes the various liabilities that the business has. In other words, debt is the opposite of cash (i.e cash which the business owes to the debtors). Therefore the above relation needs to be modified to: Enterprise value = Equity value + debt - cash.
Which brings us to the answer to the query posed last time. We indeed have to subtract the cash from the enterprise value and not add it or leave it alone.
Let me illustrate that with an example. Consider two companies - CoA and CoB, which are exact clones in all respects, except one. CoA has a surplus cash of 10, while CoB has a surplus cash of 0. Lets assume that both also have a debt of 20. The NPV of FCFF for both of them net of this extra cash is (say) 100. What we mean by this is we remove the surplus cash from CoA and then do a cash flow starting from EBIT(1-tax rate) for both of them. Since they are operational clones of each other and also have the same leverage, both will have the same NPV for FCFF, which is (say) 100. So, if our above analysis of reducing cash from EV is right, then both have to also give the same value for FCFE (again since both are operational clones). Lets see if that actually happens.
So, as explained above, we have Enterprise Value = (FCFE + debt) - cash
where FCFF = FCFE + debt (again note that FCFF has to be calculated neglecting the interest income of surplus cash)
Lets see what the FCFEs for the two cases will be. If they are same, our reasoning is correct. If they are different, we are wrong.
CoA:
Enterprise value = FCFF - cash = 100 - 10 = 90
Now, FCFE = Enterprise value - debt + cash = 90 - 20 + 10 = 80
CoB:
Enterprise Value = FCFF - cash = 100 - 0 = 100
Now, FCFE = Enterprise value - debt + cash = 100 - 20 + 0 = 80
Therefore, we see that the FCFEs for both the above cases is 80, which validates the reasoning that the surplus cash needs to be subtracted while computing Enterprise Value.
Comments, queries welcome.
October 1, 2007 at 12:22 pm
Hi Arun,
I see you are using the Enterprise value and Equity value loosely here.
In your Part 2 posting, you reveal the master equation “Enterprise value = Equity value + debt - cash”. In the very subsequent line, you mention “We indeed have to subtract the cash from the enterprise value and not add it or leave it alone.” Both these lines are mutually contradictory.
Can you pls clarify?
Finance Pro
October 1, 2007 at 12:46 pm
OK, sorry that should read, “subtract the cash from FCFE” and not “subtract the cash from the enterprise value”. Similarly, by equity value in that line, I mean FCFE (and not FCFE + cash) Thats actually one issue with the way all of us use these terms Equity Value and Enterprise Value. The best way of minimizing this confusion is to use the relations :
Enterprise Value = (FCFE + debt) - cash
and FCFF = FCFE + debt
The numericals for CoA and CoB should make the nomenclature clear.
October 16, 2007 at 1:33 pm
Hi Arun
I m a MBA student at SDM-IMD Mysore. I am doing a project on Venture Capital in India. I just wanted to know that how venture capital is helpful in economic development of a country.
Thank You
Kunal Borana
November 11, 2007 at 6:20 am
Hi Arun,
I think your concept is a little flawed - Lets assume the balance sheet of CoA & CoB consist of Debt (20 each), Equity (50 each), Cash (10 and 0) and Fixed Assets (60 and 70) for simplicity. Then, per your example the only difference in the two BSs is Cash and FA. My question for you is given the situation would you pay the same amount to buy equity in both the firms?
Per my methodology you should be paying 90 for CoA’s equity and 80 for CoB’s equity. However, the value of the operating enterprise of both the firms will be the same - 100.