after tax real return -----> before tax nominal return

CFA Level III
#1

Hi, if after tax real term required rate of return = 6% tax rate is 30% inflation rate is 4% how do I convert to before tax nominal return? adjust inflation first? or adjust tax rate first? I just found they produce different result. Adjust inflation first: (1+6%)(1+4%)-1=10.24%, 10.24%/(1-30%)=14.63% Adjust tax first: 6%/(1-30%)=8.57%, (1+8.57%)(1+4%)=12.91% which one is correct? thx

#2

Adjust for inflation 1st I think. The sequence goes like this: before tax real return (backed out from spending needs) >>> before tax nominal return (add in inflation) >>> after tax nominal return (times 1-t).

#3

Adjust inflation first. You are always taxed on your nominal income.

#4

If the entire account is taxed on a yearly basis inflation must be multiplicative then taxed. If just the withdrawal is taxed, i.e. realized capital gains for the payment, realized interest income only that part that is withdrawn is compounded at the inflation rate. Inflation must be taken to the extent that the account is taxable. If taxed every year. [(1.05)(1.03) -1]/.8 = 10.1875 If taxed only on withdrawals. 1 + (.05/.8) = 9.4375 Again, inflation is still added in both circumstances, one to the extent that both principal and payment need to grow (taxed on both each year) and one that only payment needs to grow as principal continues to grow tax deferred (inflation is still added, just inflation is not added to the extent of the tax). Either principal continues to grow at (RR)(Inflation) and I am only taxed on withdrawals or everything is taxed and I am taxed to the extent of all gains and the entire portfolio must grow at the rate of inflation. 2009 essay was the perfect example of that as the participant was only taxed on withdrawals from the account. So CFA used (.045/.8 + 1)(1.04) = 9.86% as opposed to multiplying it first.

#5

So why on the 2009 exam do they take tax out first? AT Req real return = 4.5% Tax: 20% PT Req real return = 4.5/.8 -> 5.625% Inflation: 4% PT Nominal req return = 9.85% (using geo)

#6

CFABLACKBELT Wrote: ------------------------------------------------------- > So why on the 2009 exam do they take tax out > first? > > > AT Req real return = 4.5% > Tax: 20% > PT Req real return = 4.5/.8 -> 5.625% > Inflation: 4% > > PT Nominal req return = 9.85% (using geo) They are only taxed on withdrawals. Making this example two. Have to read how the account is structured. This was a “tax-deferred” account.

#7

Paraguay Wrote: ------------------------------------------------------- > CFABLACKBELT Wrote: > -------------------------------------------------- > ----- > > So why on the 2009 exam do they take tax out > > first? > > > > > > AT Req real return = 4.5% > > Tax: 20% > > PT Req real return = 4.5/.8 -> 5.625% > > Inflation: 4% > > > > PT Nominal req return = 9.85% (using geo) > > > They are only taxed on withdrawals. Making this > example two. Have to read how the account is > structured. This was a “tax-deferred” account. Thanks.

#8

Thanks for clearing up the above. One more question then: Would there be any different handling of the aftertax return? Ie. If found the after tax return for both situations (with annual tax and deferred tax), do you simply add inflation to both? Thus total return required (for annual tax AND deferred tax treatment) = R(after tax) + inflation ? Surely there must be a difference?