In this small letter, I will briefly describe how the valuation of a company is done. I will do this with a very simple toy model and even here, not work out the solution. The aim is to formulate the problem clearly.
So, Let us assume a guy sets up a restaurant in year 0. He buys the land on loan, for which he pays Rs. 100k down and has to pay a fixed installment of Rs. 50k for next 10 years. He builds up the restaurant, purchases cooking apparatus, chairs etc for 100k. He spends Rs. 50k on advertising. He also keeps a cook with Rs.100k annual salary (yeah, low, but let’s keep going with the story). He spends Rs. 200k on materials and earns Rs. 500k from patrons on the first year. We assume the guy doesn’t pay any taxes.
Year 0 : Net Cash flow
It is easy to calculate the net cash flow for year 0. He earned 500k cash and had to pay 600k for all expenses. Therefore, the free cash flow = -100k for the first year, even when he enjoys a 60% gross profit margin.
Year 1 : Net Cash flow
This year, he has 50k loan to pay + 50k on advertising + 100k to cook. Advertisement has an incremental revenue increase of, say 60k and correspondingly input cost increase of, say 24k (proportionally). Thus, net cash flow for year 1 is (560-224 -100 -50 -50)k = 136k.
For arbitrary year - a simple model :
Assume revenue r(t) at year t, advertising cost a(t) at year t, cook’s salary s(t) = 100*(1+n)^t after annual raises of n% for t previous successive years, expenses (loan + furniture + other exigencies) = c(t).
Now, for year t+1,
Revenues r(t+1)= r(t) *(1+ k1(t) a(t)) [ k1= factor driving advertisement to footfall],
Input cost = (1-g)*r(t+1) [ g = gross profit margin, assumed const]
Expenses = c(t+1) = a(t+1) + 50*z(t) + (100*(1+n)^t) + p* r(t) [z(t) = 1 if t<10, 0 otherwise, cook gets an annual raise of n%] p = random number between 0 and \infty distributed according to some distribution, this is to account for some unexpected cost]
Hence, free cash flow can be written down as
f(t+1) = g*r(t+1) -[ a(t+1) + 50*z(t) + (100*(1+n)^t) + p* r(t)]
where z(t) is a known function, p is a random number sampled from a known probability distribution, n is a known raise.
Let us assume further that advertising costs are paid out of the free cash flow last year, i.e. a(t+1) = k2*f(t), where k2 is a known factor.
Now, writing everything down,
f(t+1) = g*[r(t) *(1+ k1(t) *k2*f(t-1)] -[k2*f(t) + 50*z(t) + (100*(1+n)^t) + p* r(t)] …. (1)
while we have used the proviso that a(t+1) = k2*f(t)
This is a set of recursive difference equations with the added subtlety that it is stochastic in nature since p is sampled from a probability distribution. Hence, various simulations will yield various scenarios.
How much is this business worth ?
We shall be using the discounted cash flow model of valuing the company. Worth of the business is the sum of discounted cash flows according to some discounting rate d. For example, if the risk-free rate is 4%, then d = 0.96. Hence the business is worth = f(0) + d*f(1)+ d^2*f(2) + ….. + d^n*f(n) [ n tending to \infty]. One has to run all these simulations for cash flow f(t) to get the intrinsic worth of the company for each scenario. Then some kind of average, expensive, and conservative intrinsic worth can be arrived at by say, allocating a certain confidence interval when you run all simulations.
So, what are the parameters that one can vary ?
Gross profit margin g - more the better, also is it really constant as we scale up ?
Advertising efficiency k1(t) - how sensitive is the intrinsic growth to this function ? If k1(t)*a(t) has a S curve shape (modelled by a tanh function for example) of diminishing returns efficiency, how bad is it vis-a-vis a constant k1 ?
The unexpected cost intensity, is it generally better to have a few huge payouts vs a small but predictable payout ? This determines, e.g., whether an insurance on property makes sense or not.
How much raise can one give a cook (or indeed, a team of cooks) to sustain the business ? Is this raise competitive with businesses nearby ?
Of course, this restaurant model is far too simple to be using/copying exactly for practical valuation of publicly listed companies. However, this eqn. (1) already is a fairly complicated one.