Question

A person invested 2,000,000 SR in an account that pays 10% compounded annually.
The first withdraw happens at the end of year 3. The payments increase at
5% every year until the end of 6th year. Thereafter, the payments decrease
by 5,000 SR every year. The planning horizon is 15 years. Calculate the value
of the first withdraw such that this investment is attractive (Use PW
analysis)

Answer 1

Let the first withdrawal be x

So PW of withdrawals = x/1.1^3 + x*1.05/1.1^4 + x*1.05^2/1.1^5 + x*1.05^3/1.1^6 + (x*1.05^3-5000)/1.1^7 + (x*1.05^3-5000*2)/1.1^8 + (x*1.05^3-5000*3)/1.1^9 + ... + (x*1.05^3-5000*9)/1.1^15

Now if this PW of withdrawals is more than 2,000,000SR, then the investment will be profitable

So x/1.1^3 + x*1.05/1.1^4 + x*1.05^2/1.1^5 + x*1.05^3/1.1^6 + (x*1.05^3-5000)/1.1^7 + (x*1.05^3-5000*2)/1.1^8 + (x*1.05^3-5000*3)/1.1^9 + ... + (x*1.05^3-5000*9)/1.1^15 > 2,000,000

Solving for x we get

x>315244.44

So if the first withdrawal is more than 315,244.44 SR, then the investment will be profitable.

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