Enterprise Value - House Analogy with Excess Cash

Another common question that comes up is related to enterprise value, particularly as it relates to excess cash. Recall that enterprise value is the value of the entire company and should be capital structure neutral.

EV = Equity + Debt - Excess Cash
or
EV = DCF Value + Excess Cash

The initial reaction is: "Wait, how can that be?" How is it that in one formula excess cash detracts from EV whereas in the other it increases? Does that make sense? In explaining, I find that a house analogy is helpful for understanding how to calculate EV.

Scenario 1:
Imagine Steve ownes a house worth $100k. Over the years, Steve has paid down his mortgage to $50k. Therefore, Steve's house's capital structure is $50k debt and $50k equity.

Dave is interested in buying Steve's house. For simplicity, let's say the house hasn't appreciated in value and is still worth $100k. Dave doesn't care what Steve's mortgage is, how much he's paid down etc. After all, that is Steve's capital structure. Dave is a new home buyer and is starting with a $20k downpayment and $80k mortgage.

The main point is that it doesn't matter who is buying the house (over simplified assumption), the house is worth $100k. It is an attempt to understand an unbiased (unlevered) way of looking at value of the company.

Scenario 2:

Let's assume a few changes:

• The $100k price of the house includes $10k in cash which is sitting on the floor of a room
• The house is being rented out as an investment property for $4k per year forever and the appropriate discount rate is 5%

Using the following formula:

EV = Equity + Debt - Cash = $100k - $10k = $90k

Does this make sense? Dave buys the house with $80k of debt, $20k of equity for a total price of $100k. However, immediately upon buying the house, Dave takes the $10k sitting on the floor and pays down his mortgage. Effectively, Dave has only paid $90k for the house.

Using the alternate formula (using a perpetuity formula for DCF):

EV = DCF Value + Excess Cash = $4,000 / 5% + $10k = $80k + $10k = $90k

That is to say, forgetting the cash, the house is worth $80k only from the income it generates. However, because the cash sitting on the floor is not integral to operating the house, it can be taken out of the house without affecting the income stream.

While it isn't an entire conicidence that the end numbers are the same (I've deliberately selected convenient numbers), it should hopefully demonstrate how excess cash in one formula decreases EV whereas in another in increases EV.