Aston Co-Dec 08

@skybei1987

Hi !

Its a practical question. Default is where a firm will not be able to pay its interest or principal payments as they fall due. First calculate the effective monthly rate because we need to deduct monthly interest payment from monthly avg cash flow.

Monthly Effective Rate = [(1 + r)1/12* – 1] (* raised to power)
Monthly Effective Rate = (1.08)1/12 – 1 = 0.6434 % = 0.006434

The expected monthly cash flow after interest payment is:

= $14,400 – (0.006434 x $1.5 m) = $4,749

To get the annual cash flow = $4,749 x 12 = $56,988

Apart from this, we have $8,500 cash in hand, so the total 8,500 + 56988 = 65,488

Now we need to divide this amount ($65,488) by another amount, which incorporates annualised (annual) volatility (standard deviation).

First, calculate the proportion of fixed interest to monthly cash flow:

(0.006534 x 1.5m)/14,400 = 67.02% = 0.6702

Second calculate the monthly volatility after this fixed interest. Here we use this 0.6702

13% / (1 – 0.6702) = 39.42% = 0.3942 (This is the monthly volatility, we need annualised)

The Annualised Volatility = 0.3942 x ?12 = 136.55%

So the volatility (standard deviation) of annual cash flows = 56,988 x 136.55% = 77,817

Now divide 65,488 by 77,817 = 0.84 (keep it to 2 decimal places to find the relevant value in distribution tables. There in row 0.8 and colum 0.04, you have 0.2995 (or 0.3 if rounded).

But if you take that 0.84 (and round it just 0.8) , that means there is (1-0.8 = 0.2 or 20%) 20% chance of failure within 12 months.

Put another way, the distance to default is 0.8 x 12 = 9.6 months

In part b, you have to justify the rate of 8%, the bank is charging using the elements in he formula. Just follow that and you will get the point.

HTH