# Maclins case (Reading 8 problem 13)

In Maclins case, the answer states that the after-tax return required to accumulate £2 million in 18 years beginning with an investable asset base of £1,235,000 (calculated below) and with annual outflows of £26,000 is 4.427 percent.

Without the annual outflows, i use time value of money formula to calculate, and get the return required of 2.7%. If including the annual outflows, how do we find out the return required of 4.427% ?

N=18

PV=1,235,000

FV=-2,000,000

PMT=-26,000

Compute ==> I/Y

In Excel

=RATE(18,-26000,1235000,-2000000)

Thank you. Ah, it is annuity formula with negative payment value.

You can reverse the signs and it will still give you a correct answer, i.e.

=RATE(18,-26000,1235000,-2000000) and =RATE(18,26000,-1235000,2000000) yield the same.

The logic has to be correct. PMT and FV must have the same sign in this case. In another annuity you may have PMT and PV the same (when you are making periodic payments as opposed to periodic withdrawals).

Watch out if you have non equal cash flows (withdrawals) mostly compounded by growth (inflation rate) in case method of above will not work. Use IRR option instead after calculating each period cash withdrawal.

This is question 13 in the practice problems in Reading 8 - Managing Individual Investor Portfolios

N = 18 years

PV = 1,235,000 portfolio in hand today thus a positive value

Pmt = (26,000) as an outflow to cover income shortfall, its coming out of the portfolio thus negative

FV = (2,000,000) has a negative value because Maclin will USE this portfolio in retirement, depleting it over time

IRR = 4.427% after tax

Pre tax 4.427%/(1 - 0.40) = 7.38% pretax rate of return

nicely written.

Ah shucks, thanks… Its what I do

^Are you actually Marc LeFebvre!?

Yes HE IS!!!

Yes…but its not like I’m Kobe Bryant or Jimmy Fallon or anything more exciting!

Hey CP, thanks for the shoot out! You do great work here on AF…keep it up!

I totally agree with unequal CF’s being a weakness of the IRR method, that topic comes up in Level I material frequently especially in Alt Inv when they discuss real estate. On the Level III exam, the two methods of determining the IPS return calculation include the IRR method (Maclin) and the spending need (Inger case in the reading). Because the time is so limited on the exam and the minutes/points allocated to the IPS calc have become so short the questions usually include a statement that makes the CF’s constant and that is why we simply add inflation to the end of the calculation to make it nominal. Notice in the Maclin case they say “After-tax salary increases will offset any future increases in their living expenses.”

-Marc LeFebvre, CFA

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