A simple factor that lets you estimate what to pay for a 60-payment cash flow in your head.
By Del Ashby · 4 min read · Lesson 4.11
It’s sometimes handy to estimate what you’ll pay for certain notes, or income streams, without taking out your calculator. Since 5-, 7- and 8-year balloons are a popular loan format, here’s how to derive a simple estimating formula.
Set up a 60-payment cash flow
Let’s use a 5-year, 60-month cash flow as the example. We choose N, the number of payments, as 60. We also choose the yield we require, and I’ll set that at 24% (2% a month). The payment is fixed by the note, here $100 a month. Since we’re buying payments only, FV is zero.
That leaves only PV to calculate: the amount we’ll pay for the privilege of collecting 60 payments.
Worked example: deriving the .03 factor
N
I
PMT
PV
FV
60
2% (24% a year)
$100
$3,476.09
$0
Now divide the payment by the PV: $100 / $3,476.09 = .02877. Round this up (never round down for this calculation) and you get .03 as your factor.
Payment divided by .03 gives a PV with a slightly better than 24% yield.
Using the factor
Any time you have a 60-month cash flow, divide the payment by .03. The answer tells you what you can pay to get a slightly better than 24% yield.
Try it on some examples. What yield does the .03 factor really get you? Remember that .03 works only for 60 payments and a 24%-plus yield.
Why the face rate doesn’t matter here
As far as yield is concerned, this factor says we don’t care about the note’s face interest rate, the face value or anything else. Just tell me the exact payment I’ll receive, and I’ll tell you what I’ll pay to collect 60 of them. Period.
In even simpler terms: divide the payment by three, add two zeros, and that’s your PV. You can do it in your head or on a scrap of paper.
What yield the .03 factor really gets you
The lesson asks you to try the factor and see what yield it actually produces. Here’s the answer for the $100 example. Dividing $100 by .03 gives a price of $3,333.33. Solve for I with that price and you get about 26.1%.
N
I
PMT
PV
FV
60
24.0%
$100
$3,476.09
$0
60
about 26.1%
$100
$3,333.33
$0
So rounding .02877 up to .03 pays you a little over two points of extra yield. That cushion is the reason to always round up: the estimate errs in your favor, never against you.
Building factors for other terms
The .03 factor only works for 60 payments at a 24%-plus yield. You can build your own factor for any other term or yield the same way: find the PV of a $100 payment, then divide $100 by that PV. The table below shows the math for a 24% yield, with each factor rounded up (example figures, worked from the method in this lesson).
Payments (N)
PV of $100 at 24%
Payment / PV
Rounded-up factor
60
$3,476.09
.0288
.03
84
$4,052.55
.0247
.025
96
$4,252.94
.0235
.024
120
$4,535.54
.0220
.023
Notice that the factor gets smaller as the term gets longer. More payments are worth more money, so you divide by a smaller number. Change the yield and the factors change too, which is why each factor fits only one term and one yield.
When to estimate and when to calculate
A quick factor is a screening tool. It helps you decide in seconds whether a cash flow is worth a closer look, or give a rough range when someone asks on the phone. It’s not a price you commit to.
Use the factor for a fast first answer on payments-only purchases.
Don’t use it when there’s a balloon. The factor ignores FV, so it values only the monthly payments.
Don’t use it for a term or yield it wasn’t built for.
Before you make a firm offer, run the exact numbers on a financial calculator or the note calculator.
