aston 2008dec q3

This is an awful question – it was set by the previous examiner, and it is because of questions like this that he is no longer the examiner. (The current examiner took over in 2010 and you are best concentrating more on the current examiners questions 🙂 )

With regard to the effective monthly rate, you should be happy that if we had been given the monthly rate (for example, say 1% per month), then to get the effective annual rate we would say 1+R = 1.01^12 (where R is the annual rate).
Here we are just doing it the other way round, we know the annual rate (8%) so it is the same formula but the monthly rate is what we are after.

We regard to the monthly volatility, we know that the volatility of the operating cash flows is 13% from the question. However, some of that is being paid out as fixed interest, so we need the volatility of the amount after the interest. It is this bit that really is not fair – he uses a formula from nowhere, and although I will explain it to you, I really think that there is no chance at all of the current examiner expecting this.

I will explain with a simple example.

Suppose the average operating flow was $100. Then 67% of this is being paid as fixed interest – i.e. $67. Leaving $33.

However the operating flow is uncertain. Just suppose it fell by 10%. It would fall to $90. However, we would still be paying $67 as fixed interest which would then leave only $23.
The amount left has fallen by $10, which is a percentage fall of 10/33 = 30.3% – even though the operating profits only fell by 10%.
So the change in the amount left is 3.03 times as much as the change in the operating profits (30.3%/10%)

Try any figures you want – whether the operating profit rises or falls – and you will find that the change in what is left (in percentage terms) is always 3.03 time the change in operating profits.

This means it is 3.03 times a volatile, and since the volatility of the operating flows is 13%, the volatility of the after fixed interest flows is 3.03 x 13% = 39.4%

I hope that helps a bit 🙂