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Hi
There is one question in the current F9 Kaplan text book that related to a new way of working out the discount factor. I am not understanding the way. Here is the question. May I seek you help? Thanks!
Facts:
lease of the asset will be $36000 pa, payable at the start of each year;
the project will be running for 4 years;
tax payable is 30%, one year in arrears;
the post-tax cost of borrowing is 10%Answer:
They used the annuity discount factor, which I feel fine.
step 1: discount the annuity based on T1 ~ T3, then add the T0 sum: (-36000)*2.487+(-36000)=(-36000)*(2.487+1)
step 2: discount the tax relief as full T0 ~ T5, then less the tax relief of T0 ~T1: 10800*3.791-10800*0.909=10800*(3.791-0.909)=10800*2.882
step3: subtract the value in step2 from step 1.However, the DF in step 2, which is 2.882, they provided a new way, which is like this:
3.170*0.909=2.882
I checked the annuity table, and found that 3.170 is the 4yr annuity factor, while 0.909 is the 1yr annuity factor.
Why the factor can be worked out as above new way?
Kindly please help me. Thanks!It is not a ‘new’ way – the discount factor can always be worked out in two ways in that sort of situation.
What is happening in step 2 is that the flows are from time 2 to time 5.
The annuity factors give the total from time 1 to time anything (not time 0 to time anything as you have written).So….the first way (which is the easiest for most people) is to take the discount factor from time 1 to time 5 and then subtract the discount factor for time 1.
The other way is to say that there are 4 years of flows. If they were time 1 to time 4 then there would be no problem – simply use the 4 year annuity factor and it would give a present value at time 0.
However, instead of being 1 to 4, they are 2 to 5 – it is all 1 year later. So using the 4 year annuity factor gives a present value one year later as well – i.e. time 1. So to get back to time 0 you need to discount by 1 year using the ordinary discount factor for 1 year.Here is another example:
Suppose you had flows from time 3 to time 8, and the interest rate is 10%
Method 1: Take the 8 year annuity factor and subtract the 2 year annuity factor.
5.335 – 1.736 = 3.599Method 2: since the first flow is at time 3 and the last flow at time 8, there are 6 years of flows. However instead of being 1 to 6, it is 3 to 8 – everything is 2 years later.
Take the 6 year annuity factor and multiply by the ordinary factor for 2 year.
4.355 x 0.826 = 3.597(The difference is purely due to rounding because the tables given are only to 3 decimal places)
Again, for most people the first method is the more obvious. However either method will always work.
In F9 it is very rare that annuity tables are needed.
If you want more examples then look at my lectures and notes on this for Paper F2.
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Thank you so much! I get it now.
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