# After-tax nominal rate of return

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?

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.

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

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.)

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.

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

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)?

Yup.

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

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%.

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!

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

(0.08+0.03)/0.6=18.3%?

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/

Because next year’s return has two components:

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