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How does perpetuity formula work?
I just don’t seem to understand it.
For example if X has a choice of receiving $5,000 now or an annual amount forever and assume interest rate is 8%.
When I try to apply the formula cashflow/r I dont get it how to get the answer.
Can anyone tell me how the formula works or how to get the answer.
Have you watched the free lectures on this (together with the free lecture notes)??
If there is a perpetuity of $X per year, then to get the present value you multiply by 1/r where r is the rate of interest.
Here, we know the present value is $5,000.
So if the equal amount per year is $X, then X/0.08 = 5,000
So X = 0.08 x 5,000 = $400
(For an explanation as to why the discount factor is 1/r you should watch the lectures)
I would guess that is because the question says the choice is an annual amount starting immediately. The perpetuity factor assumes that the first receipt is on one years time.
If the first receipt is immediate, then the present value of it is X.
So the total present value is X + X/0.08 = X + 12.5X = 13.5XFor this to be equal to 5,000, then 13.5X = 5,000, or X = 370
If the question does not make it clear that the amount starts immediately then it should have (and in the exam it would).
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