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Test 4 2015 Question 4

+1 vote
asked Nov 8, 2016 in BUS 1003H - Introduction to Financial Risk by Njabulo.Dube (2,950 points)

ABC has two pension funds, a Defined Benefit (DB) one and a Defined Contribution (DC) one. New employees may choose between the two funds. 

The DB fund provides a pension with an accrual rate of 2% of final salary. Members contribute 6% to the DB fund and the employer funds the rest of the cost. 

The DC fund has the following characteristics: 

  • employer contributions of 10% of salaries 
  • member contributions of 6% of salaries. 
  • of those contributions, 1% of salaries are used for expenses and the remainder is invested for retirement. 
  • the investment portfolio is expected to earn CPI + 7% p.a. 
  • At retirement, members use their accumulated fund to purchase an annuity using an annuity factor of 17.45

Joanna is 25 and has just joined ABC. She plans to work until 65 and she expects to earn salary increases of CPI + 3% p.a. over her working career. 

Assume salaries are paid annually in arrear. 

(i) Calculate the replacement ratio (RR) Joanna can expect to achieve in the DB fund if she survives to retirement.

(ii) Calculate the RR Joanna can expect to achieve in the DC fund if she survives to retirement. 

(iii) What other factors should Joanna take into account before choosing which fund to join? 

1 Answer

0 votes
answered Nov 8, 2016 by Njabulo.Dube (2,950 points)
selected Mar 1, 2017 by Rowan
Best answer
(i) In order to work out the replacement ratio Jo can expect to achieve in the DB fund, we multiply the accrual rate with the expected years of service:
$$RR = 40 \times 2\% = 80\% $$ 
(ii) We work out the RR in the DC fund as follows:
  • Work out the net contribution 
  • Accumulate the salary for the expected number of working years (taking into account salary increases)
  • Divide the accumulated funds by the annuity factor (the expected price of the annuity (pension) in 40 years time)

Net contributions into fund (after expenses) \( = 15\% \) 
$$ RR = \frac{0.15 \times s_\bar{40|_{4\%}}}{17.45} = 81.68\%$$
The interest rate of \(4\%\) above is the difference between the expected investment return and the expected salary growth. Using this approximation is acceptable when doing pensions questions.

using \( j = \frac{1.07}{1.03} - 1 = 3.88\% \)
Then \(RR = 79.48\%\)

(iii) The factors that you can think about relate to the riskiness of the DC pension and the guaranteed nature of the DB pension. Examples to mention could be:
  • The final pension is unpredictable if the DC fund is chosen. Even though she expects to receive a higher RR of 81.66% (compared to 80% if the DB fund is chosen), she may value the certainty that comes with a DB fund
  • A DC fund can also drop in value right before retirement, which can lead to a lower final pension and lower RR than expected. A DB fund doesn’t have this risk
  • The DB fund benefit is guaranteed, while the DC fund is not. Joanna will take the risk in the DC fund, whilst the employer will take the risk in the DB fund. That means that there is a potential to do better or worse, depending on whether the DC fund does better than expected or worse

Other things to consider:
  • Take into account how those assumptions of interest and salary increases and annuity rates were derived, are they realistic, optimistic, conservative
  • Take into account Joanna’s risk tolerance
  • Her other assets; how financially secure she is?
  • Withdrawal benefits from each fund - how are they calculated?