Question

In: Finance

Let’s consider a retirement planning problem. Suppose you just have had your 55th birthday and you...

Let’s consider a retirement planning problem.

Suppose you just have had your 55th birthday and you plan to retire in five years. As far as your retirement goal is concerned, all you want is to maintain your living standard at the same level as when you start your retirement. You expect to “stick around” until 90 and you plan to leave nothing to “no one”. Therefore, your “sole” concern is maintaining your living standard during your retirement years.

Your current living expense per month is $20,000 (which include everything that you can possibly lay your fingers on) and you expect it to go up in exactly the same pace as the Composite CPI (of Hong Kong). The average yearly rate of increase of the index for the next five years is 3%. You do, however, expect the index to pick up its (yearly) pace afterwards (indeed, throughout your entire retirement period) by 2 percentage points. That is, the expected yearly inflation rate as measured by the CPI is 5% per year during your retirement years.

To facilitate the planning of your retirement, you listed out the following relevant questions which you would like to think over.

(i) State the approximate AND exact relationships between nominal rate of return, real rate of return and (expected) inflation rate. What is the name of this relationship?

(ii) Using the PVA formula, estimate how much money do you need to have in your investment account at the beginning of your retirement to achieve your “sole” retirement goal IF the expected yearly investment return is

- 7%

- 10%

- 4%

[Note: Marks would only be given for using the PVA formula in the calculations. Although some of you may be tempted to use the present value growing annuity formula (which was NOT covered in the Introduction to financial management course) to answer this question, I would strongly urge you NOT to use that formula. Instead, please draw on the insights derived from Part (i) above to construct the relevant equation and carry out the calculations.]

(iii) Based on your answer to Part (ii) above, what conclusion can you draw with respect to the relationships between (a) nominal cash flow, (b) real (inflation-adjusted) cash flow, (c) nominal interest rate and (d) real interest rate when using the PVA formula to answer Part (ii)?

Solutions

Expert Solution

(i) Assume Nominal return =Rn
Real Return=Rr
Inflation Rate =Ri
Approximate relationship:
Rr=Rn-Ri
Exact relationship:
(1+Rr)*(1+Ri)=(1+Rn)
(ii)
Pmt Monthly expense required after 5 years $23,185 (20000*(1.03^5)
Nper Number of months of expenses after retirement 420 (90-55)*12
Inflation Rate during retirement=5% 0.05
Rate1 Inflation adjusted return if nominal return is 7% 1.90% (1.07/1.05)-1
Rate2 Inflation adjusted return if nominal return is 10% 4.76% (1.10/1.05)-1
Rate3 Inflation adjusted return if nominal return is 4% -0.95% (1.04/1.05)-1
PV1 Present Value of expenses at retirement at 7% return $1,216,798 (Using PV function of excel with Rate =1.90%, Nper=420,Pmt=-23185)
PV2 Present Value of expenses at retirement at 10% return $486,895 (Using PV function of excel with Rate =4.76%, Nper=420,Pmt=-23185)
PV3 Present Value of expenses at retirement at 4% return $133,055,924 (Using PV function of excel with Rate =-0.95%, Nper=420,Pmt=-23185)
Money needed in investment account at the beginning of retirement:
Yearly investment return 7% $1,216,798
Yearly investment return 10% $486,895
Yearly investment return 4% $133,055,924
(iii) As the nominal interest rate reduces, the real interest rate will also reduce
Consequently , the amount required at beginning for same cash flow will increase

Related Solutions

Suppose you just have had your 55th birthday and you plan to retire in five years....
Suppose you just have had your 55th birthday and you plan to retire in five years. As far as your retirement goal is concerned, all you want is to maintain your living standard at the same level as when you start your retirement. You expect to “stick around” until 90 and you plan to leave nothing to no one”. Therefore, your “sole” concern is maintaining your living standard during your retirement years. Your current living expense per month is $20,000...
Education Planning: Suppose you have just had your first child and you want to begin saving...
Education Planning: Suppose you have just had your first child and you want to begin saving for their college education. You estimate that with inflation, the cost of four years of college at a top university will cost a total of $225,000 in 18 years when your child graduates from high school. How much do you need to invest at the end of each month (part a) or year (part b) for the next 18 years to accumulate the $225,000...
You are celebrating your 22nd birthday today. You have decided to start investing toward your retirement...
You are celebrating your 22nd birthday today. You have decided to start investing toward your retirement beginning one month from today. For the first twenty years, you will invest $500 every month. During the next ten years, you will increase your contributions to $900 per month. For the remainder of your working life until you retire at age 67, you plan to invest $1,500 every month. If your investments earn a rate of return of 8.4 percent throughout your working...
You are celebrating your 22nd birthday today. You have decided to start investing toward your retirement...
You are celebrating your 22nd birthday today. You have decided to start investing toward your retirement beginning one month from today. For the first twenty years, you will invest $500 every month. During the next ten years, you will increase your contributions to $900 per month. For the remainder of your working life until you retire at age 67, you plan to invest $1,500 every month. If your investments earn a rate of return of 8.4 percent throughout your working...
You are planning your retirement and you come to the conclusion that you need to have...
You are planning your retirement and you come to the conclusion that you need to have saved $3000000million in 30 years. You can invest into an retirement account that guarantees you a 13% annual return. How much do you have to put into your account at the end of each year to reach your retirement goal?
You are planning for your retirement and have decided the following: you will retire in 38...
You are planning for your retirement and have decided the following: you will retire in 38 years and would like to have $7,000 per month as retirement income for 30 years of retirement. You have access to an account that earns a 9% rate of return. 1) How much will you need to have when you retire to be able to withdraw the desired $7,000 per month during your years of retirement? 2) If you plan to save by making...
You are planning for your retirement and have decided the following: you will retire in 40...
You are planning for your retirement and have decided the following: you will retire in 40 years and will make monthly deposits into your retirement account of $300 for the next 15 years and then monthly deposits of $750 for the remaining 25 years until retirement. This account earns a 7% rate of return, compounded monthly. In addition, you will inherit $50,000 7 years from today. The inheritance will be deposited into an account that will earn 10% per year...
You are planning for your retirement and have decided the following: you will retire in 40...
You are planning for your retirement and have decided the following: you will retire in 40 years and will make monthly deposits into your retirement account of $300 for the next 15 years and then monthly deposits of $750 for the remaining 25 years until retirement. This account earns a 7% rate of return, compounded monthly. In addition, you will inherit $50,000 7 years from today. The inheritance will be deposited into an account that will earn 10% per year...
You are planning for your retirement and have decided the following: you will retire in 35...
You are planning for your retirement and have decided the following: you will retire in 35 years and will make monthly deposits into your retirement account of $400 for the next 15 years and then monthly deposits of $800 for the remaining 20 years until retirement. This account earns a 7% rate of return, compounded monthly. In addition, you will inherit $50,000 7 years from today. The inheritance will be deposited into an account that will earn 10% per year...
This is an extension of the Birthday Problem. Suppose you have 500 Facebook friends. Make the...
This is an extension of the Birthday Problem. Suppose you have 500 Facebook friends. Make the same assumptions here as in the Birthday Problem. a) Write a program in R to estimate the probability that, on at least 1 day during the year, Facebooks tells you three (or more) of your friends shat that birthday. Based on your answer, should you be surprised by this occurrence? b) Write a program in R to estimate the probability that, on at least...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT