Using a hypothetical situation, make calculations to assist in retirement planni
ID: 2716699 • Letter: U
Question
Using a hypothetical situation, make calculations to assist in retirement planning (e.g., determine stream of savings necessary for certain standard of retirement).
Make the following assumption about a person:
Age is 40, retirement in 25 years.
Salary is 100,000; growth rate per year is 4%.
Interest rate is 10% (savings grow at 10%).
A constant living standard is desired.
Inflation (CPI rate) is 3%.
Estimated years of retirement is 20.
To maintain standard of living during retirement, one requires 80% of non-retirement expenditure.
With your team: Calculate the stream of expenses possible with the assumed income (Hint: the PV of salary MUST EQUAL the PV of all expenses).
Develop and submit a spreadsheet with clearly labeled material that is formatted to be printable on 1 page (clearly indicate the stream of salary, expenses during working life and expenses during retirement).
Explanation / Answer
Current Age = 40
Time till retirement = 25 years
Current Salary = 100,000
Salary growth rate per annum = 4%
Savings growth rate = 10%
Return on Savings = 11%
Inflation rate = 3%
Estimated years of retirement life = 20 years
He is required to maintain his standard of living at the time of retirement during his retirement years.
After calculations, the results can be summarised as below
The final annual salary of the investor at the time of retirement is $ 266,584
Assuming he saves at least 10% of his annual salary every year from now for 25 years and his annual savings will grow at 10% if invested at a rate of 11% will fetch a balance of 2,750,000 after 25 years
He needs a minimum of 80% his final salary which is 216,267 per annum to maintain his standard of living at the time of retirement.
Assuming the inflation rate will continue at 3% per annum this annuity amount should grow at the rate of 3% per annum to maintain the same standard of living at the time of retirement for next 20 years by removing the effect of inflation.
He should earn a minimum of 7.6% on his retirement investments for next 20 years to maintain his standard of living.
Current Age = 40
Time till retirement = 25 years
Current Salary = 100,000
Salary growth rate per annum = 4%
Savings growth rate = 10%
Return on Savings = 11%
Inflation rate = 3%
Estimated years of retirement life = 20 years
Expected Salary at the time of retirement = 100000*1.04^25 = 100000 * 2.6658
= $ 266,583.63 or $ 266584 (rounded off)
Let us assume that the person can save 10% of his salary every year
Annual savings = 100000 * 10% = 10,000
Total Annual savings by retirement = Initial annual savings * [(1+0.11)^25 –(1+0.10)^25)/0.11-0.10]
= 10000 * [ (1.11^25 – 1.10^25) / 0.11-0.10]
= 10000 * [(13.5855 – 10.8347)/0.01]
= 10000 * 2.7508/0.01 = 10000* 275.08
= 2,750,800
Let us assume 80% of last salary is required to maintain the standard of living at retirement during the retirement years. Annuity should grow at a minimum of 3% every year to account for the inflation. Let us assume that the rate of return on the investment to get this annuity is 10% per annum. The same can be shown below as follows
Amount required to maintain living standards = $ 266584 * 80% = 213,267 (rounded off)
Period of annuity = 20 years
Annual growth rate of annuity = 3%
Return on investment = x%
Let be the initial annuity amount received one year after retirement. Then present value of annuity with above requirements can be calculated as follows
Present Value of Annuity at the time retirement = P/(r-g) * [1- ((1+g)/(1+r))^n]
2,750,800 = 216267/(r-0.03) * [1-((1+0.03)/(1+r))^25]
2,750,000 – 216267/(r-0.03) * [1-((1.03)/(1+r))^25] = 0
Let r = 8%,then LHS of the above equation will be
= 2,750,000 – 216267/(0.08-0.03) * [1 – {1.03/1.08)}^20}]
= 2,750,000 – 4,325,340 * [1- (0.9537)^20]
= 2,750,000 – 4,325,340 * (1-0.3875)
= 2,750,000 – 4,325,340 * 0.6125
= 2,750,000 – 2,649,279.71
= 100,720.2869
Let r = 7%, the LHS of the equation will be
= 2,750,000 – 216267/(0.07-0.03) * [1 – {1.03/1.07)}^20}]
= 2,750,000 – 5,406,675 * (1-(0.9626)^20)
= 2,750,000 – 5,406,675 * (1-0.4667)
= 2,750,000 – 5,406,675 * 0.5333
= 2,750,000 – 2,883,198.8472
= -133,198.8472
r = 0.07 + [(-133198.8472 * (0.07-0.08)/(100720.2869-(-133198.8472)]
r = 0.07 + (1331.988472/233919.1341)
r = 0.07 + 0.005694 = 0.07569 or 7.57% rounded off
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