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2009 Ips - Return Requirement (Q1 Aii)

Couple sources confusion, but first the story:

Next year at 60 this couple will have 1.1m in assets. They will also pay off mortgage of 100k. 

Asset base therefore = 1m. 

Now their Cashflows:

They have POST TAX next year a total of 80k from the pension and annual expenses next year of 125k. The Inflation rate is 4%. Tax is 20%.

What is their PRE TAX NOMINAL return?

OK - I am wondering why this solution is not correct:

1. They make 80k post tax, so pre tax its 80k/0.8 = 100K.

2. Therefore pre tax CF = 100k-125k = -25k

3. -25K/1m = 2.5%

4. Plus inflation 4% = 6.5%


Correct = Take the 80k POST TAX -125k = net POST TAX CF = -45k

THEN, we do -45k/0.8 to gross up pre tax = 56,250

THEN we do 56,250/1m = 5.625% + 4% = 9.625%

What gives? Isn’t my method doing the same calculation but I am grossing it up first then calcluating the shortfall return, then adding inflation.  I.E I am taking their combined salaries and working out what it is on a pre tax basis, then using that as a return.

Why are these different and why am i wrong? 


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Rex I just tried this and got it right - here are the steps I followed and what I generally do for pre-tax calcs

  1. Net the inflows and outflows to come to the shortfall. In this case it is $45,000. Before I do this I ensure I am using the post tax income.
  2. Divide this by the investable asset base. In this case $1,000,000, as you pointed out.
  3. Divide this by (1-T) to back out the gross figure…in this case the tax rate is 0.2, so it is the figure from step 2, divided by 0.8. This brings us to 5.63%.
  4. Because it says withdrawals are taxed, we add inflation after not before you back out the tax, as I had done in step three. So, since inflation is 4%, the final return requirement becomes 5.63% + 4% = 9.63%. 
  5. Note - if there were no mentions of withdrawls being taxed I would have added inflation to 5.63% before I went onto step 3, backing out the gross figure.

With regard to when and when not to add inflation, see below handy guide from S2000. 



I am just wondering why the first method does not work -

If we want to know the pre tax return, why cant we jsut take the salary we earn and gross it up first, to get pre-tax then divide by the assets to work out our pretax return requirement?

The example says the shortfall must be post tax THEN grossed up. 


Good question…I do not know why


Their 125,000 in expenses are after-tax, not before-tax.

Your original approach treated them as before-tax expenses.

Simplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams

Thanks S2000, so as a rule of thumb, when expenses are given we assume they are after tax expenses unless otherwise stated?



Simplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams