The problem (or “cool, today I am 36”)

John is the owner of a consulting firm.

At Year 0 he hires 10 recently graduated engineers, aged 26 years old, and places all of them in several body rental projects.The cost of each employee is, say, 1 euro.
In order to ease calculation, let’s spread on each “active” employee the cost of people maintaining a company infrastructure, administration, human resource, furnitures, office rental, PCs, courses and other stuff.
With active employee consider someone whose services can be sold to a client on a time&material contract.
John charges his clients so that the margin ratio on each of these junior consultants is 2,5 ,  thus, he charges 2,5 the client for an engineer whose cost is 1.

So, cost of initial 10 consultants = 10 x 1 = 10

Revenues on body renting all of them = 10 x 2,5 = 25Margin = 25 – 10 = 15.

At year 10, the cost of each of these 10 employees (due to salary increase and company cost raising spread on this factor for simplicity etc…) raises from 1 to 2 each. They are ten years older and much more experienced now, so their rental fee for clients is 4 each now.

Unfortunately only 7 of them have continuosly been on a project.
To ease calculation, the effect on total after 10 years can be summarized as if only 9 of them where sold, while one remained waiting for a chance in the office.

Cost at year 10 of the initial 10 consultants = 10 x 2 = 20
Revenues on body renting 9 of them = 9 x 4 = 36
Margin is 16.
To keep the promised 10% it should be 18.
In order to gain the remaining 2, he should hire 2 young 26ers (revenue would be 2 x 2,5 –  2 x 1 = 3)

Now we are at Year 20, and 1 of the initial pool guys left the company for various reasons, 2 have been hired by the client (who had the chance to try him over a 10 years period).

During the same period, the company have been able to replace them, maintaining the team of 10, but had to pay the new experienced guys a bit more. In fact, while the cost for each of them raised from 2 to 2,5, the new 3 members cost 3,5 each.

Unfortunately, as during these 10 years they passed from being 36 years old to 46 years old, the calculation of revenues must consider as if only 4 of the seven guys worked continuosly on a project, and only 1 of the 3 replacements.

In fact their experience was too high for placing them with lower fees, and as they got married and had babies, they did not accepted contracts too demanding in terms of flexibility. Moreover, as they reached the maximum rental fee, they have been placed with a mean tariff of 4,5 each.

Cost at year 20 of the initial pool (7 original + 3 replaced) = (7 x 2,5) + (3 x 3,5) = 28

Revenues = (4 x 4,5) + (1 x 4,5) = 22,5

The 2 new hired now are 10 year older so they cost now  2 x 2,5 = 5  and bill (only 1,6 of them, remeber the 80% rate of placement) = 1,6 x 4 = 6,4

Margin total = -5,5 + 1,4 = -4,1 In order to reach the promised 18 + 10% = 19,8 still 23,9 should come out!
This means 16 new 26ers to be hired and placed so that you get 24 margin.

John is informed about the following estimation of how Year 30 will look like. Among the 7 initial survivors, 2 are expected to leave the company, and 1 from the pool of 3.  Consider they will be 56 years old, thus only 1 of them will still maintain a project, but the fee will be only 2,5 as experienced on obsolete technologies and not so fast on using future instruments- the cost of them will rise so that they will all cost 3,5 each, but for one, who will become a company manager, costing 5 now to the company.

Calculate:

how many 26 years old guys should he keep hiring every decade (condidering for simplicity rates and fees same as year 0) in order to save his ass maintaining the promise of 10% growth every decade to shareholders?

Consider that for the new hired, the rate of client placing is 80% every decade and that the initial pool, reaches 46 years with no further salary increase.

(solution in grey)

At year 30 we have:

initial pool cost = 5 x 3,5 + 1 x 3,5 + 1 x 5 = 26

hired at year 10 cost = 2 x 2,5 = 5

hired at year 20 cost = 15 x 2 = 30

for a total of 61

Income are:
initial pool = 1 x 2,5  = 5
hired at year 10 = (80% of 1,6) x 4,5 = 5,76
hired at year 20 = (80% of 16) x 4 = 51,2
for a total of 61,96…
You are almost even, with a company of seven 56ers, two 46ers, fifteen 36ers, thus a mean company age of 42,6, which is a miracle
Remeber you should have given about 21,8 margin for shareholders expectations…
Now go find your extra new graduated and place them all.
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