## Wednesday, August 28, 2013

### Financial Mathematics: Flow of Funds Table

A Flow of Funds Table is a simple heuristic that can be useful in understanding assets, especially in more complicated scenarios.

The flow of funds chart has two parties which I call Buyer and Seller. Initially, the Buyer exchanges Capital for an asset; the Seller exchanges an asset for Capital. Eventually at some settlement period (which may be multiple periods), the Seller will make payments back to the buyer.

Here's a simple version of a flow of funds table:

Initial Settlement
Seller + CAPITAL - PAYMENTS

It is easy to note that the columns add to 0:
$$-\text{CAPITAL} + \text{CAPITAL} = 0$$
$$+\text{PAYMENTS} - \text{PAYMENTS} = 0$$
As it turns out, the rows also sum up to zero provided we take into account the Time Value of Money. To state it another way, the present value of those future payments should be equal to the initial capital given today.
$$-\text{CAPITAL} + \text{Present Value(PAYMENTS)} = 0$$
$$+\text{CAPITAL} - \text{Present Value(PAYMENTS)} = 0$$
To give a simple example, suppose that I borrow money to buy a vehicle. The Buyer in this case is the bank. The bank is buying my loan obligation to make a stream of payments.  I'm the Seller since I am selling this stream of future payments because I want the funds to purchase a vehicle.

Initial Settlement
Bank - CAR MONEY + LOAN PAYMENTS
Borrower + CAR MONEY - LOAN PAYMENTS

I'll be using the flow of funds table to aid in understanding what payments are made and when. It can make things easier to see what the value of a particular asset is by analyzing it's components.

As a side note, if you have ever used a financial calculator (such as the tools in Excel) to calculate a present value, the present value is the opposite sign (negative) of the cash payments. The above illustrates why tables illustrate why this is the case. In one instant you're receiving funds which is the opposite of giving funds. So the two have to have opposites signs.

Which one you choose to have the positive or negative side is a matter of convention. I will try to stick to the convention that parting with money amounts to a negative and receiving money is positive. So as in the above example, the bank parted with money for the car (negative) but then later received money in loan payments (positive).