2009 Ips - Return Requirement (Q1 Aii)

CFA Level III
#1

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%

WRONG.

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?

#2

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.

http://finexamhelp123.wpengine.com/inflation-in-required-rate-of-return-to-tax-or-not-to-tax/

#3

Thanks!

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.

#4

Good question…I do not know why

#5

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

Your original approach treated them as before-tax expenses.

#6

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

#7

Yup.