Maclins case (Reading 8 problem 13)

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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% ?
 
On your calculator
N=18
PV=1,235,000
FV=-2,000,000
PMT=-26,000
Compute ==> I/Y
In Excel
=RATE(18,-26000,1235000,-2000000)
 
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.
 
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