BUSINESS APPRAISAL: THE RIGHT FORMULA WHEN NET CASH FLOWS ARE VARIABLE (PART 1)

It has been long ago since our last gathering. I am writing the following notes to clear up a misunderstanding arising when the common student is pricing or appraising a business -either a company or a financial asset- with variable net cash flows and a well-known end.

We have to blend the classical formula for both -present value and future value- with the Gordon Growth Model. The conventional formula states that the installments will always be the same during the life of the venture, this is, they are always a constant numerical value

PV =PMT*[1-(1+r)^-t/(r)] or FV = PMT*[(1+r)^t-1/(r)] Hey! But what happens if PMT IS NOT CONSTANT??

Well, we will have to overhaul and to reprise the theories, formulas and laws by William Baumol, Stephen Ross and Myron Gordon. What you are about to read is merely a patchwork!

PV=PMT*[1-(1+r/1+g)^-t / (r-g)] or FV = PMT*[(1+r)^t-(1+g)^t / (r-g)]

Where: PV is an unknown present value, FV is an uncertain future value, r is a chosen discount rate, t is Time or a number of payments set up on purpose, PMT is the first installment/payment as an income or outcome and g is a rate at which PMT changes all accross the lifetime of the net cash flow.

So thus, the only new argument added was "g" and among its attributes: is not constant, has to be calculated over and over because g is often referred as a geometric historical average and finally, has to be related to r in terms of accrued periods.

An easy example: SELF CENTERED SOCIETY is hired to carry out a due dilligence process for ICU, Inc. After several researches the following information is found out. The net cash flow for the next year is expected to be 500k, the historical rate of change in percentage is 5% per year, with the current assets and forthcoming market conditions ICU is expected to last 20 years and the discount rate applied to ICU operations is fixed at 10%

Question: PV of ICU with and without g? Answers as follow:

PV=500*[1-(1.1)^-20/(0.1)]=4256.78186k or PV=500*[1-(1.1/1.05)^-20/(0.1-0.05)]=6056.042028k

On a regular basis, the agents work under uncertainty about the net cash flow collected by the shareholder. The formula involving a change factor is the right one. The original formula only works on a fixed scheme where all of the payments -from first to last- are already well known like in a "treasury", bank note or government bond.

Thank you very much for your patience!