Question

20. You are an investment advisor who has been approached by a client for help on his financial strategy. He has $250,000 in savings in the bank. He is 55 years old and expects to work for 10 more years, making $100,000 a year. (He expects to make a return of 5% on his investments for the foreseeable future. You can ignore taxes) a. Once he retires 10 years from now, he would like to be able to withdraw $80,000 a year for the following 25 years (his actuary tells him he will live to be ninety years old.). How much would he need in the bank 10 years from now to be able to do this? to afford these planned withdrawals ($80,000 a year) after the tenth year? you client have to lower his annual withdrawal by, assuming that he still plans to b. How much of his income would he need to save each year for the next 10 years to be able C. Assume that interest rates decline to 4% 10 years fronm now. How much, if any, would withdraw cash each year for the next 25 years?

Answer 1

After 10 years the client will be 65 years old. Hence, he will withdraw for 25 years.

As taxes are not considered, the client is expected to make 5% return on the portfolio.

a. As client would like to withdraw $80,000 a year, hence, after retirement, Present Value of the withdrawal, (discounted by the expected reture i.e. 5%) should be the amount he should have.

let he should have x amount after retirement.

Hence,

$x = \frac{80000}{1+r}+\frac{80000}{(1+r)^{2}}+...+\frac{80000}{(1+r)^{25}}$

Here r is the discount rate.

Now,

$PV=PMT\times (\frac{1-\frac{1}{(1+r)^{25}}}{r})$

Here, PMT = 80000

Hence,

$x=80000\times (\frac{1-\frac{1}{(1+0.05)^{25}}}{0.05})$

Hence, x = 1,127,515.56. Hence, the client would require 1.127 million in the bank 10 years from now.

b. Now, he has 250000 as a saving.

Hence, the value of saving at the time of retirement is;

$savings at the time of retirement = 250000\times 1.05^{10}=407223.66$

Hence, his savings should be 1,127,515.56 - 407223.66 = 720291.90

I.e. Future value of his savings should be 720291.90 after 10 years. Let he saves s per year, then we have

$FV=s\times \frac{(1+r)^{10}-1}{r} \therefore s=720291.90\times \frac{0.05}{1.05^{10}-1}$

Hence, s = 57266.50

Hence, client should save $57,266.50 per year

c. The client have 1,127,515.56 in the bank account at the time of retirement.

Lets assume he can withdraw y amount per year. Hence, as per the above formula, we have

$1127515.56=y\times (\frac{1-\frac{1}{(1+0.04)^{25}}}{0.04})$

Hence, y = $72,174.5

Hence, client can withdraw $72,174.5 per year if interest rate drops to 4%.