IRR return calculation - Nominal or Real??

CFA Level III
#1

When you have to calculate a IRR return over a specified period in a IPS question is the result nominal or real return requirement?

Ex. PV of portfolio is 100,000 and need 120,000 in 3 years to fund MBA program. Inflation is assumed to be 2%. What is the required nominal after tax investment return to meet objective?

PV = -100,000

N = 3

PMT = 0

FV = 120,000

I/Y = 6.27%

This would be considered the after tax nominal return right? You wouldn’t add the 2% the get nominal of 8.27% as you do in non IRR calculations. But if you subtract the 2% you would be left with the after tax real return of 4.27% right?

#2

It would be helpful if you referred to the specific question. With the facts given above, I would have done:

PV = -100k

FV = 115k

N = 3

CPT I = 4.76 % (Real)

  • Inflation 2% = 6.76% (Nominal)
#3

Depends on whether your inputs is real or nominal. That will determine your IRR.

Based on your example, it seems like the 115,000 required is in nominal terms, thus your IRR generated will be nominal.

#4

Agree with Jmachine that 4.77% (4.7689) is the real, after-tax return that you’d need. It’s the bare minimum return that will get you to your goal. Other factors (inflation & taxes) have to be paid by way of earning a higher return, so they’re in addition to this 4.77%.

But I would actually multiply to get the nominal rate instead of add. (1.0477)(1.02) = 1.0686%, or 6.86%.

Then divide either of these by (1-T) if they ask for pre-tax returns.

#5

Yeah all values were nominal. Makes sense that result would be nominal. Subtract assumed inflation to get real return. Thanks

#6

If you were doing it geometrically wouldn’t the equation be (1 + real return)(1.02) = .0627

Solving the equation gives a real return of 4.19% not 4.77% since (1.0419)(1.02) = .0627

Additive would be just to subtract 2% from 6.27% to get 4.27%

Edit: He was using 115 while I used 120

#7

From my understanding, the required $115,000 in 3 years is not a nominal figure. Cash flows can be nominal as can interest rates, but generally if they give you a target funding number out in the future, it’s a real number. $115,000 is $115,000 after taxes and inflation. And you’ve gotta grow your portfolio to that minimum number in real terms.

If you grew your investment by only 4.27% after inflation, you’d only end up with just over $113,000 in real terms, which won’t pay the tuition bill. Only a real $115,000 will settle up with the MBA office, so a real rate has to be calculated to get you there, then adjust for inflation.

No?