Reading 9: EOC 11 - The Muellers

Just a quick summary

pension income 100000 (will not increase with inflation)

annual expenses 180000 (will increase with inflation)

inflation 2 %

portfolio 1000000

Mueller’s don’t mind invading their principal.

Time Horizon - 10 years.

How to calculate required rate of return in such a scenario?

Although the question does not ask about required rate (it just asks which portfolio is best for such needs)

I am curious how would we calculate required rate in scenarios like this?


I think the required return is (180,000 – 100,000)/1000,000 = 8% + 2% inflation…ideally geometic. (1.08)(1.02) -1 = 10.16%. You seem to say Part 2 requires picking the best portfolio to invest. I dont think we have all the information here but my guess is that if this is the only information provided, the portfolio to choose will be less than average risk tolerance, low return – more cash, bonds etc….as the income is less than annual expenses and the investor relies on the portfolio to meet personal expenses.

Broadex - Thanks for the calculation.

How will it differ if the pension income also increases with inflation ? and

What’s the significance of this statement “Mueller’s don’t mind invading their principal” - is it just increasing risk tolerance ? but then Muller is also relying on this portfolio to meet his expenses.

It would seem that you need to do a calculation similar to a mortgage payment

Pv 1,000,000

FV 0 (this is the idea of invading the principal… you don’t have to rely on the investment return alone, you can eat up the principal as well)

n 10

PMT= -80,000


The problem I have is:

How do you add inflation? the 2% inflation must be applied to the entire 180,000 of annual income, not just the 80,000 supplement frm the investment.

Furthermore, once you add inflation, the return of Portfolio A , which the CFAI chooses, is insufiicient to meet the return requirement.


^ actually you need -3.86%. the PV is enough to fund the difference for more than10 years. With inflation, add 2%. So RR=(1-0.0386)(1+0.02)-1= -1.94%.

I asked in another post but I think it’s relevant here. Q13 ii of same reading 9 EOC.

Information provided: Income increase fully offset expense increase. Return = net CF / asset base. The solution states ‘no need to adjust for inflation’ for return. It doesn’t say if this return is nominal or real.

So my question is that calculated return 7.38%) is Nominal or Real? I think Nominal. If it’s nominal, does it mean to calulate real return, I’ll need to deduct inflation? Thanks!

I would solve for the required rate with IRR. Using BAII plus:

CF0 = 1,000,000

CF1 = (100,000 - 180,000)

CF2 = (100,000 - 180,000(1.02))

CF10 = (100,000 - 180,000(1.02)^9))

IRR compute.

I got -.503% as the answer.

100k is not inflation adjusted so your CF input is wrong.

He didn’t adjust the 100k for inflation, only the -180k.

I think he is right.

Great point, Audacious

my bad. thanks Barry, too many brackets and it was late night.