Question

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’
a) To achieve your “sole” retirement goal, how much money do you need at the beginning of the first
year, 10th year and the last year of your retirement period [Note that as the expected inflation rate
provided in the question is assumed to be yearly, simply assume the overall price level remains unchanged throughout each year BUT jumps at the end of the year (i.e., at the beginning of the coming year],

b) 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) Given the inflation figures provided in the question, what is the average yearly investment rate of return (based on the exact relationship in part (i)) that you need to achieve to maintain your living standard during the retirement years? (3 mans)

c) Using the PVA formula. estimate how much money do you need to have in your investment account at the beginnlng of youf retirement to achieve your “sole” retirement goal lF the expected yearly investment return is
- 7%
- 10%
- 40%

[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 lFM course) to answer this question, I would strongly urge you NOT to use that formula Instead, please draw on the insights derived from Part (bi) above to construct the relevant equation and carry out the calculations ]

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

Answer 1

a)

Amount needed at the beginning of first year retirement

$23,185.48

(20000*((1+0.03)^5)

Amount needed at the beginning of 10th year retirement

$5,914,021.98

(23185.48*(1+0.05)^9)

Amount needed at the beginning of Last year retirement

$95,434.59

(23185.48*(1.05^29)

b.i)

Assume Nominal return =Rn

Real Return=Rr

Inflation Rate =Ri

Approximate relationship:

Rr=Rn-Ri

Exact relationship:

(1+Rr)*(1+Ri)=(1+Rn)

b(ii)

Average Yearly Investment Return Required

5%

c

Pmt

Monthly expense required after 5 years

$23,185

(20000*(1.03^5)

Nper

Number of months of expenses after retirement

360

(90-60)*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 40%

33.33%

(1.40/1.05)-1

PV1

Present Value of expenses at retirement at 7% return

$1,242,029

(Using PV function of excel with Rate =1.90%, Nper=360,Pmt=-23185, Type=1)

PV2

Present Value of expenses at retirement at 10% return

$510,265

(Using PV function of excel with Rate =4.76%, Nper=360,Pmt=-23185, Type=1)

PV3

Present Value of expenses at retirement at 4% return

$92,740

(Using PV function of excel with Rate =33.33%, Nper=3600,Pmt=-23185, Type=1)

Note: Type=1, because withdrawals are at beginning of months

Money needed in investment account at the beginning of retirement:

Yearly investment return 7%

$1,242,029

Yearly investment return 10%

$510,265

Yearly investment return 40%

$92,740

(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