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Hi sir, can you explain to me why present value formula works this way? I don’t get it why there’s two way to do it.
Scenario 1: Present value of an annuity year 1 to year 5 at start of each year.
Formula: PV = annuity cash flow x (1+annuity factor for Y4)Scenario 2: Present value of an annuity from Y2 to Y5
Formula: PV = annuity cash flow x (annuity factor Y5 – Y1 annuity factor)Thank you and have a nice day!
The five year annuity factor give the total factor for time 1 to 5.
In scenario 1, since the amounts are at the start of each year, they are from 0 to 4.
(time 0 is the start of the first year, time 1 is the start of the second year, and so on).The PV of an amount at time 0 is the same figure. The PV for flows from 1 to 4 is found by multiplying by the 4 year annuity factor.
In scenario 2, the 5 year annuity factor gives the total for time 1 to 5. Since we only want the total for times 2 to 5, we subtract the discount factor for time 1.
I do suggest that you watch the free Paper F2 lectures on discounting, because this is all revision from Paper F2.
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