After our Busting the Myth of Discount Rates article was published, it was picked up by the editors on Seeking Alpha and republished there. A Seeking Alpha reader commented that my graph showing the present value of an annuity of $100 for 100 years and discounted at 10% could not be correct because it was showing a value above $1,000.
It was a good catch by that reader who knew the formula PV = CF / r (where PV = Present Value, CF = nominal Cash Flow, and r = discount Rate) and applied it to the numbers used to come up with his answer (PV = $100 / 10% = $1,000).
However, the graph assumed that the first $100 payment was paid at time 0 (today). This extra payment drove the value over the $1,000 mark, for a present value (i.e., “fair value”) of $1,050.79. The present value of the same stream under a discount rate assumption of 12% totals $884.33, 84.2% of the value of the stream discounted at 10%!
I’ve also included similar calculations for the present value of growing annuities (i.e., $100 right now, $105 in 1 year, and so on) under 10% and 12% discount rate assumptions. For valuing companies, whose cash flows (should) grow over time, this is the most important calculation. Those of you who have taken the IOI 102 Course on Intelligently Valuing Companies will recognize the general shape of those curves!
The workbook – with calculations and graphs – is attached below, so take a look and drop me a line if you have questions!
This article has been changed to correct a calculation error in the original spreadsheet for the value of a $100 annuity discounted at 12%. Calculations on the original sheet were mistakenly set to discount a discounted value and generated a present value of $506.38, significantly less than the original value. The calculations for the 10% discount rate were correct.
Many thanks to SA reader SingaporeFred for the catch!