Economic capital - TopDown - Return on capital

[bdeyal89]

This section (C13-2.3) ends with
Required Capital = (Net Profits)/(Required Rate of Return)

I know i am making a mistake in my logic somewhere but this seems to say for a given amount of net profit, A riskier activity would have a higher beta and have a higher required rate of retrun and thus have a lower required capital.

where have I gone wrong with this?

 

[Colin McKee]

Good point! It does seem odd. But I think your logic is ignoring the "net profit" part. I am happy with the idea that
(capital * required return ) = net profit. So a riskier activity would have a higher required rate of return, and hence generate a higher net profit. When you flick the equation round you get
capital = (net profit)/(required return) meaning that a riskier activity would have a higher required rate f return on the bottom line, but would also generate a higher net profit on the top. So its the interaction between these two issues that determines the required capital for the business.

 

[bdeyal89]

I agree with the first form you wrote where return x capital = net profit but its the second form that is giving some trouble. That 'interaction' you are referring to is what I dont think i understand, if you dont mind indulging me perhaps you can just correct where I am going wrong in the example I am thinking of.

Lets say a project has $100 allocated to it with net profits of $10 and required rate of return of 10% so 100 = 10/0.1

If expected losses were to increase by z,
) net profit = Revenue - cost - expected losses
) project is more risky as a result and required return increases by y

New capital Aloocated = (10-z)/(0.1+y) which would certainly be less than $100 since both z and y are positive. So increased risk is implying that less capital should be allocated.

Where have I gone wrong?

 

[Colin McKee]

Hmmm - convincing set of numbers here.

Lets say a project has $100 allocated to it with net profits of $10 and required rate of return of 10% so 100 = 10/0.1

OK.



If expected losses were to increase by z,

This is where I have trouble. If expected losses increase, its not a riskier project, just a worse project. Similarly if costs or tax increase, the project is just worse, and the sponsor would pay a lower price for that project and those cashflows.
A riskier project is a project that gives a HIGHER return, but has associated risks and volatility.


) net profit = Revenue - cost - expected losses
) project is more risky as a result and required return increases by y

New capital Aloocated = (10-z)/(0.1+y) which would certainly be less than $100 since both z and y are positive. So increased risk is implying that less capital should be allocated.

Where have I gone wrong?


My numbers would be that the new project has higher risk, but will generate 12 of profits on average. If the higher risk, means that the required rate of return according to CAPM is 12%, rather than 10%, then the capital required is 12/0.12 = 100m as before.

the other method is to model one standard deviation of profits, and call that the EAR. Then the capital required is EAR / WACC or EAR / Risk-free (different companies choose different things. So long as they are applied equally across th institution, they add something to the process). Then a riskier project would result in an increased EAR and hence more capital.

 

[Mesut]

@Bdeyal89
A few thoughts...
1. When you say riskier activity I would imagine a greater spread of returns hence higher risk and an attendant HIGHER EXPECTED RETURN. Consequently, in your example above, I would expect an expected return greater than 10 for a RISKIER avtivity. To compensate for the greater volatility of return, investors would demand a higher RoC. So numerator gies up and denominator also goes up.

2. When you are working with EBIT/net profits you are essentially looking at an expected value, so should it also be the case that the denominator should reflect this aspect? In your example you have picked one value out of a distribution of returns while your denominator seems to be looking at the attributes of the expected result?

3. Collin please correct me if I am off base.

 

[Colin McKee]

Your comment on point 1 is consistnt with my thoughts above.

On your point 2, I think of the numerator as the "best estimate" or "average expected" profit after interest and tax. Ie the profit that is likely to fall to equity shareholders from the activity. So although its one number, it feels like an average of many expectations. The denominator is a rate of return that reflects that activity and its risk.