Answer To: Task: See attached file 3000 words max (excluding annexes and references) Pedagogical aim and...
David answered on Dec 23 2021
For the first part the first assumption that is made is I have 20 more years to live, currently
retired at 60. I expect my pension amount will be given to me each month for the next 20
years. The total amount I have is US $700,000. After due consideration of my requirements,
the amount that I expect would suffice for my requirements is $2500. This would include the
following expenses:
Rent amount = $700
Car insurance per month = $500
Food and utilities = $600
Travel and entertainment = $400
Miscellaneous expenses = $300
Total amount required per year = $2,500*12 = $30,000
Total amount required for 20 years = $30,000* 20 = $600,000
Since I have a saving of $700,000 I would like to keep a fixed amount separately for urgent
needs. Whatever be my investment plan, in either of the investment scenario, I would keep
some amount for unforeseen contingencies. I fixed this amount to approximately 15% of my
savings which comes out to be $100,000. This will be kept in a savings bank account which
retrieves an interest rate of approximately 5-6%.
Now we analyse our investment and returns thereof in the two given scenarios.
In the first case we are asked to establish a yearly pension a life insurance will pay me back
for the rest of your life.
In the second case, on the other hand, I am managing my wealth on my own. Here, I set an
amount that I wish to withdraw each year, and estimate the returns that can be generated
on the outstanding balance.
Before discussing each case separately, I would like to explain the assumptions taken
commonly for both cases. The first one is assumption for inflation rate. We assume the
inflation rate to be constant for the coming twenty years at 2%. While we assume a monthly
amount of $30,000 in year zero, every subsequent year, we increase this amount by the
degree of inflation. So every subsequent year we calculate the yearly amount required by
multiplying the previous year’s amount by 2%.
Second assumption comes with the return on investment. The risk-free rate of investment is
assumed to be 4%. Generally, the risk-free rate of return is the interest that one can expect
from government bonds or treasury bonds. The rate of interest on these instruments varies
with the duration of investments. In addition, these are liquid investments. They come as
short term bonds with a maturity period of 3 months, 6 months and 12 months. Since we
have taken all calculations on a yearly basis, we assume, for short-term we use 12 month
treasury bonds as investment vehicles which have a coupon rate of 4%.
Third assumption we have taken is that we have ignored the actuarial assumptions related
to mortality rate etc. Because we have assumed the person is at his/her retirement age i.e.
is sixty years old, there is no further wage growth. The only assumption, as stated above is
with respect to preserving the value of money in real terms should be maintained, therefore
only inflation rate is considered.
Fourth assumption is regarding the interest rate that banks offer. The banks in US are
assumed to offer an interest rate of 5% which is compounded yearly. This value of interest
rate is considered to remain constant for the span of twenty years. This investment option is
used for the fixed amount that is put in bank.
We assume we have a total of $6, 00,000. This amount is the maximum we have for
investment of use over a span of next 20 years.
Option I: When the amount is withdrawn by the individual himself/herself. The following
table gives the amount of cash flows. Starting from year zero, we begin by withdrawing
$30,000 and invest the remaining amount in 12 month treasury bills which generate a
return of 4%. The next year, we increase the amount we withdraw by 2%. Therefore, the
amount becomes 30,000*1.02= 30,600. In addition, we reinvest the 5, 70,000 we had left
from the previous year as well as the interest 22,800 received from our investment. This
generates an income of 4%*5, 70,000 plus 4%* 22,800. And the amount we have retained is
5, 70,000+22,800-30,600 = 5, 62,200. This way at the end of 20 years we generate a total of
$3, 64,667.
Our calculations are as follows:
Year
Withdrawal
(inflation
adjustment) Balance
Investment
income @
4%
Total
amount
0
30,000
5,70,000
22,800
1
30,600
5,62,200
23,400
2
31,212
5,54,388
23,112
3
31,836
5,45,663
22,751
4
32,473
5,35,941
22,348
5
33,122
5,25,167
21,901
6
33,785
5,13,282
21,407
7
34,461
5,00,229
20,865
8
35,150
4,85,945
20,272
9
35,853
4,70,364
19,625
10
36,570
4,53,420
18,922
11
37,301
4,35,041
18,158
12
38,047
4,15,152
17,332
13
38,808
3,93,676
16,440
14
39,584
3,70,532
15,479
15
40,376
3,45,635
14,445
16
41,184
3,18,896
13,334
17
42,007
2,90,222
12,142
18
42,847
2,59,517
10,866
19
43,704
2,26,679
9,067
3,64,667
Option II: In the second case, we make a lump sum investment in a pension fund, which will
enable us to withdraw a fixed amount of $2,500 per month...