Often you are faced with decisions about whether to pay a certain sum up front, or 6 or 12 easy installments – for Auto Insurance, Website hosting, and a myriad of other services. Often you make the decision based on how “flush” you feel with cash. When you are a boot-strapping entrepreneur, that means you almost always take the easy monthly payments. But what is it really costing you? Should you make the effort to pay up front – perhaps borrowing from a credit card or tapping a line of credit?

Of course, the answer is, “It Depends.”

# Discounted Cash Flow (DCF) Analysis

DCF Analysis is a technique that allows you to compute the implied Annual Percentage Rate (APR) of taking the easy payment plan vs. up front lump sum. With DCF Analysis, you apply a discount factor to future cash flows to bring them back to the present so that you can compare them to an amount of money today. Take a simple example of a credit card with an monthly interest rate of 1.5%. If you owe $1,000 today, you can pay it off for $1,000. Or let it ride, and pay $1,015 in a month. DCF analysis is a way of saying that the $1,000 today is the same as $1,015 one month from now – assuming a monthly discount (interest) rate of 1.5%.

The formula for discounting a future payment back to the present is simple:

Present Value = Future Payment * 1 / (1 + i) ^N where “i” is the interest rate per period, “^” means “raised to the power of”, and “N” is the number of time periods in the future that the Future Payment occurs.

# Internal Rate of Return (IRR)

Then Internal Rate of Return is that discount rate that which causes the future “easy payments” to be equivalent to the lump sum payment today. When you model the payment alternatives as a stream of cash flows, the IRR is that rate at which the Discounted Cash Flow is zero.

# Practical Example of DCF/IRR Analysis

I recently joined an entrepereneur peer group and will use their membership fee structure to illustrate. You can either pay $895 up front for annual membership, or $95 per month for 12 months – at the beginning of each month.

Here are the two alternatives:

Pay $895 today

Pay $95 today, and then $95 at one month intervals for the next 11 months

So think of the second alternative as the equivalent of borrowing $800 (the reduction in what you have to pay today: $895 less $95), and paying it back over 11 months. You can state that as a stream of cash flows in Excel:

You get $800 today (cash inflow), resulting in negative $95 per month (cash outflow) for the next 11 months. You can use the IRR function built into Excel to determine the monthly discount rate that would cause the discounted cash flow stream to equal zero, and then multiply by 12 to get an annual rate.

## C4=IRR(C2:N2)

## C5=C4*12

So in this case, making the 12 easy payments is the equivalent of borrowing at an annual percentage rate of 56.88%.

Why would you ever do such a thing? There are at least two or three reasons:

1. There may be some uncertainty about using the service for a full year, so you want to contain your risk by committing to just a month at a time.

2. You could be close to tapping out your credit cards and / or lines of credit, and you don’t want to use up any spare credit capacity.

3. Your cost of capital is above 56.88%, and this is a cheaper form of borrowing.

Filed under: Financial Concepts and KPIs | Tagged: APR, Calculating cost of borrowing, Cost of Capital, DCF, DCF Analysis, INternal Rate of Return, IRR, True Interest Cost |

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