IPS Question: Calculating required return--adjusting for tax rate

PV: 1,000,000

FV (desired bequest in today’s $): 800,000

Annual withdraw (100,000)

Time: 10 years

  1. Without regard to inflation and tax rate, calculate the required rate of return:

CPT–>I/Y (required return): 8.66%

  1. Now assume the annual withdraw 100,000 is after tax and the tax rate is 30%.

calculate BEFORE tax required of return:

Shall I gross up the annual withdraw: 100,000/(1-0.3)=

142,857 and enter it into PMT, then CPT for I/Y–>13.21% ?


Shall I gross up the required return already calculated: 8.66%/(1-0.3)=12.37% ?

No 12.37% will leave not 800k at the end of 10 year if you withdraw 142,857 annually. Ending value of the portfolio would only be 6,58,490.

It should grow at 13.211% annually to be able to let u withdraw 142,857 annually & leaving 800 k at the end of 10 years.

Thank you rahuls


rahuls, it is the other method.

solution on page 229, volume 2.

check the paragraph ii

the book adjusts the required return for tax effect, not cashflow.

229 part ii.

it relates to after tax cash flow provided - and they ask for after tax nominal rate.

then they divide that by 1-t to get before tax nominal rate.

then add inflation.

If however the question provides you with an after tax cash flow need, and asks you for before tax nominal rate, your original solution - convert cash flow to “before tax nominal”, use that find before tax rate and then add inflation is the right approach. (You would use the 142,857 number).

Thanks cpk, I am still a bit unclear on this tho. What you mean is if the question asks indirectly:

i) Given after tax cash flow needed, What is the after tax nominal rate?

ii)If the tax rate is 50%, what is the before tax nominal rate?

or the question could directly ask

i) given after tax cash flow needed, What is the before tax nominal rate?

Is this the only way to determine the method of input?

I think the trick is

If you have been given BEFORE TAX Salary & AFTER TAX cash flow requirement to be met from the portfolio with intention of leaving bequest (terminal value), you need to calculate the after tax return & adjust by tax 1/ (1-T) to get the before tax requirement (P. No 229 13 (ii)

However if you have been given AFTER TAX SAL & AFTER Tax Cashflow requirement, you need to adjust AFTER TAX cashflow to before tax 1 / (1-T) then calculate before tax requirement

What do you feel CPK?