AFMInteresting topic

Suppose market is rising, then you can borrow at risk free rate and invest in market portfolio (suppose no tax):
1)No borrowing. You have $100 that will bring income 100*Rf + 100*ERP in a year.
2)You have $100 and borrow $100 at risk free rate, then you will have 200*(Rf+ERP)-100*Rf =Rf*100 + 2*100*ERP. Due to financing sensitivity of your investment to market risk increased (beta increased from 1 to 2, gearing from 0% to 50%).
Unsystematic risks associated with increased risk of bancrupcy, costs of bancrupcy are ignored.

from 200*(Rf+ERP)-100*Rf =Rf*100 + 2*100*ERP
I understood how you arrived 200*(Rf+ERP)-100*Rf but by splitting it into Rf*100 + 2*100*ERP how could you say 2 is beta...$200 is our investment in stock market..what is logic of splitting it into 2*100 and saying 2 is beta..if it is true then i would like to split this into 4*50 to say 4 is beta...ha ha funny..never mind
its just i didn't get any sense in it....i may b wrong please clarify
anyway my question is if shareholders are only concerned about systematic risk..why we use equity beta instead of asset beta in CAPM..as equity beta includes firms specific risk(finance risk) which is unsystematic risk..isn't it?

Assume no tax. Suppose your business has asset beta 1.7 and that is all equity financed. Then you expect to receive Rf+1.7*ERP. Then you borrow the same amount of money (so that gearing becomes 50%), at risk free rate, you will then expect to receive 2*(Rf+1.7*ERP)-Rf=Rf+2*1,7*ERP. Your busines became more sensitive to systematic market risk, due to leverage. You can try different leverages, the result will be according to the M&M formula.

Beta represent how sensitive the return as compared to average market. Leverage increases exposure to systematic market risk (the higher leverage the higher profits when market rises, and vice versa).

hey thanx for giving your time to answering my question...but i m still confused about finance risk...is it systematic risk or company specific risk(unsystematic risk)..
if it unsystematic why CAPM use equity beta(combination of business risk and finance risk) when actually well-diversified shareholders in perfect market should only concern about purely systematic risk...

I think you are confused with the concept of unsystematic risk.
Unsystematic risk is risk that has no correlation with the market portfolio. Let Rs be a random variable representing return on a given share within a year. Decompose it this way: Rs=Rf+beta*(Rm-Rf)+epsilon (proof that it is possible is simple, but requires some background in probability theory), where Rm - is market portfolio and epsilon is residual unsystematic company specific risk (both random variables) and Rf - is risk free return (constant). Epsilon and Rm do not correlate (!), and expected value of epsilon equals zero. Change in gearing affects both beta (sensitivity to market risk) and epsilon (e.g. increased gearing means higher credit risk), however, CAPM ignores residual risk, assuming that rational investors will diversify it away.

So, taking into account all the above said, the answer to your initial question is the following: I will use equity beta because gearing affects the sensitivity of shares in my well-diversified portfolio to market risk (i.e. volatility of market portfolio).

P.S. ACCA syllabus contains some math stuff like Black-Scholes model, linear programming, portfolio theory. I have never seen any non-math book, that could rigorously explain those topics :), so you just have to believe it or study math :).

so i should learn that finance risk cannot be diversified by shareholders no matter how many different types of shares it invest in?
i wonder what would happen if business risk is zero at generating 15% return(unrealistic assumption but just for illustration)..will shareholders be still affected if business uses cheap debt (say 10%)..and hence increase its gearing? I think in this situation shareholders would increase demand of shares increasing share price..(because they would get more return than previously and in long term due to increase in share price their required return would be same as 15%)

so i guess there is relation between business risk and finance risk...for low business risk(stable cash flows) shareholders would be less concerned about finance risk compared to high business risk (relatively less stable cash flows)..

Finance risk in question is increased sensitivity to systematic market risk due to gearing. By definition, investor cannot diversfy it, however, taking this risk is rewarded by higher returns.
Low business risk (asset beta 0.05), with gearing of 50% (no tax), will give equity beta 0.1 - also low. Therefore, your explanation is correct, with stable cashflows it is easier to cope with higher interest payments.