00:01
What is the present value of the loan at the end for part a? to find your present value, we're given a lot of information.
00:11
We need to assume a few spreads.
00:19
Let's assume for year one, we have a treasury rate of 3 % and a spread of 1%.
00:31
And we're going to go up by 0 .2 % all the way up to year five where we have 3 .8 % and 1 .8%.
00:43
Then the discount rates would be the treasury rate plus the spread.
00:48
So for example, rate one one is 4 % that's our discount rate rate two is 4 .4 % rate three is 4 .8 % rate four is 5 .2 % every five is 5 .6 % to find our present value we discount the annual interest payments so our annual payment is going to be equal to our 100 million times 7 % or 7 million.
01:24
Now let's go ahead and do our present value calculation.
01:28
Our present value is the sum over all of our years so we have our annual payment divided by 1 plus our interest rate so we have 1 .04 plus let's say we have 7 over 1 .04 squared plus 7 over 1 .048 cubed plus 7 over 1 .054 to the fourth power plus 7 plus 100 over 1 .056 to the fifth power.
02:11
Adding these up we find our present value to be 104 .9 million.
02:20
Now we want the expected value of the loan at the end of year one.
02:26
So this is our part fee.
02:29
To find our expected value, our expected value here is equal to our upgrade percentage.
02:38
So let's say it's 0 .10 % times our value, 104 .9 million, plus our remaining percentage, percentage 0 .70 times 100.
02:49
That's our value at 100 million plus 0 .15 our downgrade times 95 million plus zero.
03:00
So we get 94 .7 million.
03:05
Now let's find the volatility at the end of year one...