percentage sensitivity to estimate of a cost of capital. with indefinite inflow

Although we usually use two guesses to calculate the IRR (which as a result is only an approximation), when it is a perpetuity we can calculate it precisely. Since 150,000 x 1/r = 1,000,000 (for the NPV to be zero), then r = 150,000/1,000,000 = 15%.

thank you sir.. there is one more question related to perpetuity. SCENARIO 1 if a company receives a perpetuity of 20,000 $ per annum in advance, and pays 30% corporation tax 12 months after the end of the year to which the cash flows relate at a cost of capital of 10 % what is after tax value of perpetuity. 1/r+1= 11*20000 . = 220,000 taxation =20,000*.3= 6000*(1/.1-.909) . =(54,546) 165,454 SCENARIO 2 if a company receives a perpetuity of 20,000 $ per annum in arrears, and pays 30% corporation tax 12 months after the end of the year to which the cash flows relate at a cost of capital of 10 % what is after tax value of perpetuity. 1/r= 10*20000 . = 200,000 taxation =20,000*.3= 6000*(1/.1) . =(60,000) 140,000 as per my understanding 1. if tax is paid in arrears following are the rules if cash flows occur at the start of the year then tax will be at time T2 if cash flows occur at the end of the year tax will be at time T1 2. if tax paid in advance should we need to check the cash flows timings as in arrears like at time T1 if it occur at start, tax will be at T0 if at end of T1 , tax will be at T1 2. in case of inflation, we use real rate for perpetuity.

Sorry, but you have not said what your problem is. Also, everything you have written is explained in full in my free lectures :-)

my apologies i forgot to mention at the end please check whether my calculation in scenario 1 and 2 for perpetuity and tax is okay as per understanding. moreover for tax paid in arrears i understand from your lecture. i wanted to know what if tax paid in advance? thank you

Sorry but I do not have time to check your answers - you must surely have answers in the same book in which you found the question. With regard to tax, it will never be the case in the exam that tax is paid in advance. It will either be paid in the same year or there will be a one year delay.

thank you Sir 1. if perpetuity received in arrears that mean cash inflow at the end of year and we are paying tax 12 month after the end of the year to which cash flows relate. (in this case tax will be paid at T1 and for taxation we use factor 1/r-(year one discount factor) please tell me if i am right or not 2 if perpetuity received in advance that mean cash inflow at the start of year and we are paying tax 12 month after the end of the year to which cash flows relate. (in this case tax will be paid at T2 and we use factor 1/r-(period 1 and two discount factor) please tell me if i am right or not thank you so much for being an amazing teacher for millions of students...for me opentution is a blessing. :) May you get the best reward for your efforts..

You are right in both cases :-)