Can we capitalize the earnings or cash flow of a declining business? As Curly of Three Stooges fame would say: “Soitenly!”
Two businesses have the same current earnings or cash flow and risk level and a 20% discount rate. One is growing at 5% annually, the other declining at 5% annually. The cap rate for the growing firm is 20% – 5% = 15% and its valuation multiple is 1/15% = 6.7 times. The cap rate for the declining firm is 20% – (-5%) = 25% and its valuation multiple is 1/25% = 4.0 times. This makes perfect sense: a growing business has a higher multiple and is worth more than a declining business with the same risk and current earnings or cash flow.
For the mathematically minded, the discount rate – growth rate = cap rate formula is based on summing an infinite series. It is explained and derived in many valuation books. The key point is that the formula is general – it is derived using algebra with no constraints on the values of the discount rate or growth rate. It does not require the growth rate to be positive or zero; it can be negative.
For the TRULY mathematically minded, there is a restriction after all. The absolute value of the decline rate cannot exceed the discount rate. If our business has a 20% discount rate and a 25% decline rate, the implied capitalization rate is 20% – (-25%) = -5%. This is nonsensical. This is because a business declining that fast will in the long term have no appreciable earnings or cash flow. (In mathematical terms, the infinite series used to compute its discounted earnings or cash flow converges.) At some point, the business will be worth more on a liquidated basis than a going concern, so the general formula cannot be applied (because it does not account for liquidation).