A retirement calculator is a financial tool that is used by individuals to simulate a final retirement benefit under different scenarios. This is done in order for an individual to plan for
41 the future and/or to gauge their financial position and readiness for retirement. A deterministic retirement calculator, which calculated the final retirement benefit of a hypothetical member, was modelled in Microsoft Excel. A deterministic retirement calculator can only provide a single outcome for a set of inputs. The retirement calculator has a few inputs that determined the final retirement benefit of the hypothetical member. The inputs used were: contributions, time horizon and rate of return. These inputs were discussed in more detail.
3.4.1.1 Contributions
The contribution variable is the amount of money that the hypothetical member will set aside annually for investing in a specific investment portfolio in the retirement fund. This study assumed that the hypothetical member earned a salary of R197 500 per annum in the first year of contributing. The estimated average monthly salary in February 2015 for the non- agricultural formal sector of South Africa was R16 461 (Statistics South Africa, 2015). The estimated average monthly salary was converted to an annual amount of R197 532, which was rounded to the nearest hundred.
This study assumed that the hypothetical member contributed 12.7% of his/her annual salary towards an institutional defined contribution retirement fund. The contribution rate was based on the average contribution rate after deductions from 2011-2015 mentioned in the 2015 Sanlam Benchmark Survey (Sanlam, 2015). The average contribution rate before deductions from 2011-2015 was 16.34% (Sanlam, 2015). The reason the average contribution rate after deductions was used instead of the average contribution rate before deductions, was for the purposes of making this study more realistic. The retirement fund contributions were capitalised at the end of each year.
The hypothetical member’s annual salary increased by 5.18% annually. The average South African inflation rate was 5.18% over the 112 year period from 1900 to 2011 (Dimson, Marsh & Staunton, 2012). This study assumed that the hypothetical member’s annual salary increased annually by the average inflation rate in South Africa.
3.4.1.2 Time horizon
The time horizon variable is the period that the hypothetical member is invested in a specific investment portfolio in the retirement fund. This study assumed that the hypothetical member worked for a 40-year period. This study assumed that the hypothetical member remained employed and contributed to an institutional defined contribution retirement fund for the entire 40-year period. This study assumed that the hypothetical member preserved his/her full benefit in a preservation retirement fund if and when they left employment to start
42 employment elsewhere. It was also assumed that the preserved benefit was invested in an investment portfolio that was similar to the investment portfolio that the hypothetical member was contributing towards in their new retirement fund.
3.4.1.3 Rate of return
The rate of return variable was the percentage of growth that the hypothetical member received in their retirement funds from a specific investment portfolio. The rate of return variable in the retirement calculator was calculated for each year by weighting each asset class allocation of an investment portfolio. Once each asset class had been weighted, the expected rate of return of each asset class was multiplied by the corresponding asset class weight. The three asset classes expected rates of returns, that were multiplied by the corresponding asset class weights, were then added together to calculate the rate of return for an investment portfolio. The formula below depicts how the rate of return was calculated. 𝒓 = 𝝎𝒆𝑬(𝒓𝒆) + 𝝎𝒃𝑬(𝒓𝒃) + 𝝎𝒄𝑬(𝒓𝒄)
Where:
𝑟 = Expected Rate of Return
𝐸(𝑟𝑒) = Expected Rate of Return of Equity
𝐸(𝑟𝑏) = Expected Rate of Return of Bonds
𝐸(𝑟𝑐) = Expected Rate of Return of Cash
𝜔𝑒 = Portfolio Weight of Equity
𝜔𝑏 = Portfolio Weight of Bonds
𝜔𝑐 = Portfolio Weight of Cash
3.4.1.4 Process of the retirement calculator
Contributions, time horizon and rate of return all worked together in the retirement calculator to calculate the final retirement benefit for the hypothetical member. The process of how the three variables worked together in the retirement calculator was discussed.
In the first year the individual started with an opening balance of nil. The opening balance of the first year then grew by the percentage rate of return earned from the investment portfolio during the first year. The contribution of the first year was capitalised at the end of the year and did not grow by the percentage rate of return earned from the investment portfolio during the first year. Therefore, the closing balance for the first year was equal to the opening
43 balance of the first year plus the rate of return earned by the investment portfolio during the first year, plus the contribution which is capitalised at the end of the first year (which doesn’t grow by the rate of return of the first year). The closing balance of the first year was the opening balance of the second year. The same process discussed above was repeated each year until the fortieth year, when the closing balance was the individual’s final retirement benefit. The calculation of the final retirement benefit could also have been calculated using the following time value of money formula:
𝑭𝑹𝑩 = (𝒑𝒎𝒕(𝟏 + 𝒈𝟎))((𝟏 + 𝒓 𝟐)(𝟏 + 𝒓𝟑)(𝟏 + 𝒓𝟒) … … … (𝟏 + 𝒓𝟒𝟎))+ (𝒑𝒎𝒕(𝟏 + 𝒈𝟏))((𝟏 + 𝒓 𝟑)(𝟏 + 𝒓𝟒)(𝟏 + 𝒓𝟓) … … … (𝟏 + 𝒓𝟒𝟎))+ (𝒑𝒎𝒕(𝟏 + 𝒈𝟐))((𝟏 + 𝒓𝟒)(𝟏 + 𝒓𝟓)(𝟏 + 𝒓𝟔) … … … (𝟏 + 𝒓𝟒𝟎))+……… (𝒑𝒎𝒕(𝟏 + 𝒈𝟑𝟗) Where:
𝐹𝑅𝐵 = Final Retirement Benefit 𝑝𝑚𝑡 = Contribution
𝑔 = Growth in Contributions 𝑟 = Expected Return
The first contribution made by the hypothetical member was only capitalised at the end of the year and did not grow by the rate of return of the first year. The first contribution grew by the rate of return of the second year, as well as the rate of return of the 38 years which followed. The second contribution grew by the rate of return of the third year, as well as the rate of return of the 37 years which followed. The third contribution grew by the rate of return of the fourth year, as well as the rate of return of the 36 years which followed. This procedure continued up until the point where the 40th contribution was capitalised at the end of the year and did grow by the rate of return of the 40th year. The future value of the 40 contributions was then added together to calculate the final retirement benefit of the individual.