PV of Perpetuity

If they receive 20,000 per year, then their profits will increase by 20,000 a year and therefore they will have to pay extra tax (an outflow) of 30% x 20,000 = 6,000 a year. So.....they want the PV of the flows which are: 1 - infinity 20,000 p.a. 2 - infinity (6,000) p.a.

Thank you very much sir! Ur explaintaion is very clear! Normally perpetuies are calcutated by 1/discount factor into the relvant cashflows, so for this example it would be for tax part = 6000 into 1/0.10= 60 000 But in the BPP revision kit it is done as= 1/0.10-0.909( 1yr DF) so that is 10-0.909=9.901 and that into 6000 which is then 54 546! But for the inflow of 20 000 it is done by 20 000 into 1/0.10= 20 000 Why is there two ways ? And how do we know to apply which way ?

Multiplying by 1/r assumes that the perpetuity starts in 1 years time. If it starts in 2 years time, then you need to subtract from 1/r the discount factor for 1 year so that you are left with the factor for 2 to infinity. I suggest that you watch my free Paper F2 lectures on discounting where I explain this (this is revision of F2).

Thank you sir! It's very clear! :) But if the perpetuity starts in 3 years we need to do the same as for 2 years right ? Example : BPP Revision Kit 96, Take $90 000 per annum indefinitely starting in 3 years' time (and bequeath this right to their children) . Cost of capital 11% Should it not be : 1/0.10=10-0.826(2 year DF) = 9.174 multiplied by 90 000= 825 660 ?

No. To get 3 to infinity, you take 1 to infinity (1/0.10 = 10) and subtract the 2 year annuity factor at 10% (you have subtracted the discount factor just for year 2). For the benefit of anyone else reading this, you typed that the cost of capital is 11% whereas in fact it is 10%.

Hello Sir Sir I have a doubt: An annuity of $3000 per annum for eight years start at the end of third year and finishes at the end of tenth year? Sir in the answer in the Bpp workbook, they are taking a annuity factor of only two years but as it starts at the end of three years, an annuity of 3 years should be taken.??

Annuity factors give the PV 'now' of an annuity that starts in 1 years time. Here, the annuity starts in 3 years time which is 2 years later than in 1 years time. Therefore using the 8 year annuity factor gives a PV two years later and we therefore need to then discount for 2 years using the normal PV factor to get the PV 'now'. If you are still unsure than do watch the free Paper MA lectures on investment appraisal because this is revision from Paper MA.