After-tax nominal rate of return

CFA Level III
#1

Hi,

Lets say we are asked to find the after tax nominal rate of return for next yr.

Next yr’s net cash flows after taxes and inflation is $200000

Investible asset base is $2.5M

Thus required rate of return for next yr = 8% .

Inflation is 3%

Now do we add inflation to this rate of return to find the nominal rate of return?

Remember the cash flows required next yr are already accounted for inflation?

#2

Inflation’s already in there; don’t include it twice.

You need to cover the increased cash flow, plus increase the asset base for the following year. Include inflation.

#3

That’s what I thought but 2011 mock has it done differently.

#4

They’re absolutely right, and I was way, way to hasty in my reply: I didn’t think.

(It’s early in the morning here; forgive me.)

I’ve corrected my reply.

#5

But the question says to find the nominal rate of return for next yr and inflation is already factored into the cash flows for next yr.

#6

True. But the return has two components:

  • 8% return to cover the (current year, including inflation) cash flow
  • 3% growth in the asset base, so that next year’s 8% return covers that year’s cash flow
#7

So even if inflation has been accounted for in cash flows or the investable assets, when calculating nominal return, we still add inflation to the real return (o nominal = real + inflation)?

#8

Yup.

#9

Thanks magician. Are you able to please elaborate on why, conceptually? I didn’t quite get your previous response

#10

Suppose, for simplicity, that the required cash flow increases with inflation, so that the following year (the year after next), it will be $206,000.

Next year we need our return to cover $200,000, plus we need our asset base to grow by 3%. Thus, our return is $200,000 / $2,500,000 + 3% = 8% + 3% = 11%. Of that, $200,000 is spent, and $75,000 is added to our asset base, bringing it to $2,575,000.

The following year, the return is $206,000 / $2,575,000 + 3% = 8% + 3% = 11%. Note how the extra 3% return next year increased the asset base so that the return to cover the cash flow was still 8%.

#11

Makes sense. But my confusion has been that they asked the return for next yr only.

Why on earth would you ask inflation for next yr’s return computation?

Thanks!

#12

so, assuming tax rate of 40 %, what would be the pre-tax nominal required return?

(0.08+0.03)/0.6=18.3%?

#13

That depends on whether the inflation is taxable or not. I wrote an article on this: http://financialexamhelp123.com/inflation-in-required-rate-of-return-to-tax-or-not-to-tax/

#14

Because next year’s return has two components:

  • Meeting the cash flow need (8%)
  • Maintaining the real value of the portfolio (3%)