Module 3 Exercise: Chocolate Factory

Module 3 Exercise: Chocolate Factory—Risks in Groups Purpose & Goal

The purpose of this exercise is to allow you to assist your client, The Chocolate Factory, in the analysis of some of the risks associated with providing The Chocolate Factory‟s employees with a post-retirement income program. Your goal is to provide background research and analysis of the potential approaches that may be used to provide the post-retirement income program. As is almost always the case when working on actuarial problems, you will be part of a team. As a result, you will sometimes be asked to provide an analysis based on a model prepared by another team member. You will also be asked to use data that was prepared by someone else as input to your model. In your memo to file, you will be required to include materials based on your work and the work of your colleagues. You must consider both the underlying risks for the individual employees and the risks for The Chocolate Factory. You must also identify the major risks that should be monitored in the future.

Your Role Your actuarial consulting firm has been hired by The Chocolate Factory, a small manufacturing company that makes, you guessed it, chocolates. The Chocolate Factory has hired your firm to assist them in determining whether the company should establish a pension plan for its employees. You are working with your supervisor as part of a team to prepare a preliminary report for The Chocolate Factory. Your supervisor will review your work and your findings will be incorporated into the report to be delivered to The Chocolate Factory. In this exercise, you will be expected to rely on the materials and results provided by your colleagues unless specifically asked to review their work. You will be provided with tools that were prepared by others in your consulting firm for use on similar projects. You may be required to modify these tools for this assignment.

About Cascadia, the Chocolate Factory and its Employees The Chocolate Factory is a small company located in Cascadia. Cascadia is a small country located in North America that has adopted an interesting blend of the social insurance and tax structures of Canada and the U.S.

All Cascadian citizens who have taxable income are provided a defined benefit retirement pension through the Cascadia Pension Plan (“CPP”). The pension provided under the CPP is equal to 25% of an individual‟s covered earnings in the year prior to retirement. Covered earnings under the CPP are limited to earnings up to twice the average annual income for workers in Cascadia. The average income in Cascadia in 2005 was $50,000; covered earnings under the CPP therefore were limited to $100,000. As a result, the maximum pension under the CPP for a pensioner during 2006 is $25,000. If a citizen had covered earnings of $50,000 during 2005 and retired in 2006, his pension under the CPP would be $12,500; that is, 25% of $50,000.

An individual‟s covered earnings under the CPP may not increase by more than inflation during the final ten years of employment. The CPP is well managed and can be expected to deliver on its promises.

Cascadia provides tax support for private pension plans sponsored by employers or trade associations. The tax-assisted private pension plans must limit pensionable earnings to no more than four times the Cascadian average income. The pensionable earnings limit is therefore $200,000 in 2005. Contributions to a tax-assisted pension plan in Cascadia are deductible for tax purposes and any payment out of the plan, whether to a member or the sponsoring organization, is taxable when received.

© 2003 - 2013 Society of Actuaries - SOA_FAP_Mod3Exercise01-01Assignment.docx - Page 1

About Cascadia, The Chocolate Factory and its Employees (continued) There are two types of tax-assisted private pension plans in Cascadia, defined benefit (“DB”) pension plans and defined contribution (“DC”) pension plans.

Private Cascadian DB pension plans may provide a pension benefit of up to 1.5% of final pensionable earnings per year of service. The formula may be reduced on pensionable earnings up to the CPP covered earnings limit by no more than 0.7%. For example, a formula of 1.3% of final pensionable earnings up to the CPP covered earnings limit and 2.0% of final pensionable earnings in excess of the CPP covered earnings limit is acceptable as long as the resulting pension is also limited to 1.5% of final pensionable earnings.

Post-retirement inflation protection is mandated under DB pension plans and is equal to 100% of actual inflation each year to a maximum of 3.0% per annum. Spousal death benefits are mandated to be equal to 50% of the member‟s benefit after retirement. Members who are not married receive a monthly pension during their lifetime with 120 payments guaranteed. All DB pension plans must have a normal retirement age of 65. Any benefits paid on early retirement or postponed retirement must be paid on an actuarial equivalent basis using mandated methods and assumptions that are determined each month by the Cascadian pension regulators.

Private DC pension plans are popular in Cascadia. Contributions to tax-assisted DC pension plans in Cascadia are limited to 15% of pensionable earnings each year. The formula may be reduced on earnings up to the CPP covered earnings limit by no more than 7%. For example, a formula of 11% of pensionable earnings up to the CPP covered earnings limit and 18% of pensionable earnings in excess of the CPP covered earnings limit is acceptable as long as the resulting contribution is also limited to 15% of pensionable earnings.

Contribution rates may vary between employees under a DC pension plan. A plan‟s minimum contribution rate must be no less than 75% of the maximum contribution rate used in the pension plan. For example, if the maximum contribution rate for an employee is set to 12% of pensionable earnings, then the contribution rate for any other member must be at least 9% of pensionable earnings.

Also, if the maximum contribution formula under a pension plan for any employee is 8% of pensionable earnings up to the CPP covered earnings limit and 12% of pensionable earnings in excess of the CPP covered earnings limit, then the contribution formula for any other employee must be at least 6% of pensionable earnings up to the CPP covered earnings limit and 9% of pensionable earnings in excess of the CPP covered earnings limit.

Personal tax-assisted savings plans similar to IRA and RRSP savings accounts are not available in Cascadia. Employees therefore value private pension plans sponsored by their employers.

Cascadian pension funds must be held in trust. Assets may be invested in North American equities and bonds that meet certain credit risk criteria. In essence, the investments must be made in equities or bonds that are traded on the major North American exchanges. Cascadian pension plans typically invest the trust fund assets using a balanced equity/bond approach.

Private pensions may be purchased at retirement from an insurance company in North America at purchase rates that are heavily regulated and guaranteed by the Cascadian government. It is very common for pensions under tax-assisted private pension plans in Cascadia to be purchased at a member‟s retirement.

© 2003 - 2013 Society of Actuaries - SOA_FAP_Mod3Exercise01-01Assignment.docx - Page 2

About Cascadia, The Chocolate Factory and its Employees (continued) The Chocolate Factory was incorporated in 1985. At January 1, 2006, the company has ten full-time employees. These employees consist of the president, the treasurer, the sales manager, the office manager, the receptionist/office assistant, the plant foreman and four plant workers. Part-time or seasonal employees are hired, as needed, during busy times.

The president, treasurer and sales manager have been employed by The Chocolate Factory since incorporation. They all own part of the company. The plant workers, plant foreman and office staff are more recent hires. Previous workers have left, in part, because The Chocolate Factory did not have a tax-assisted pension plan.

The Chocolate Factory has established a budget of 15% of aggregate employee earnings each year, beginning in 2006, to provide pensions for its employees. Management has indicated that a future contribution rate in excess of 18% in any one year would not be affordable.

In a previous project, The Chocolate Factory considered establishing a final earnings DB pension plan. A split-rate formula equal to 1.30% of pensionable earnings up to the CPP covered earnings limit and 1.75% of pensionable earnings in excess of the CPP covered earnings limit per year of service was proposed by your firm. In the end, management at The Chocolate Factory was very reluctant to establish a final earnings defined benefit pension plan because of the potential risks associated with the funding and accounting for such a plan.

The Chocolate Factory‟s management understands that it could simply establish a 15% DC pension plan for all of its employees and stay on budget. Management believes, however, that such an approach would not provide adequately for their long term employees who have not been covered by a pension plan in the past. The management team would like to consider other options that would allow them to address, at least in part, the issue of income adequacy.

Your team had to make certain assumptions for this project. Specifically, the team has adopted a base expected fund rate of return of 6.5% and a base expected inflation rate of 3.5% for these purposes. Annual increases in earnings will be expected to equal the inflation rate plus 1% per annum up to an employee‟s age 50, the inflation rate plus 0.5% per annum from age 50 to age 60 and the inflation rate from age 60 to 65.

There are many possible combinations of contribution formula rates that may be considered when investigating split-rate contribution formulas. Your team has been agreed that the contribution reduction on pensionable earnings up to the CPP covered earnings limit will be 5% for an employee receiving the maximum contribution.

Your Assignment

TASK 1: CONFIRM A TARGET DEFINED BENEFIT PENSION FOR A CAREER EMPLOYEE OF THE CHOCOLATE FACTORY

Background Your initial goal is to establish a pension target for a career employee under the private Chocolate Factory pension plan. Management at The Chocolate Factory considers a career employee to be an employee who works with them for 35 years. The career employee is typically hired at age 30 and is expected to retire at age 65.

Your team has determined that the total pension target for each career employee from the private Chocolate Factory pension plan and the CPP combined should be 70% of pensionable earnings as defined under the private Chocolate Factory pension plan.

© 2003 - 2013 Society of Actuaries - SOA_FAP_Mod3Exercise01-01Assignment.docx - Page 3

Your Assignment (continued) A split-rate DB pension plan formula equal to 1.30% of pensionable earnings up to the CPP covered earnings limit and 1.75% of pensionable earnings in excess of the CPP covered earnings limit per year of service is proposed for the Chocolate Factory.

Your Task Determine whether the proposed defined benefit formula is appropriate for the following potential Chocolate Factory career employees:  Employees earning $50,000 in 2006 (i.e., the average Cascadia earnings).  Employees earning $100,000 in 2006 (i.e., two times average Cascadia earnings).  And, employees earning $200,000 in 2006 (i.e., four times average Cascadia earnings).

Since the spreadsheet SOA_FAP_Mod3Exercise01-02CareerProjections.xls was developed for a previous project, you should review the spreadsheet to make sure that all calculations are appropriate.

TASK 2: DERIVE A DEFINED CONTRIBUTION FORMULA FOR A CAREER EMPLOYEE OF THE CHOCOLATE FACTORY

Background The team is considering using a DC pension plan that would be designed to meet The Chocolate Factory‟s and its employees‟ goals. Your team‟s total target pension for each career employee from the private Chocolate Factory pension plan and CPP combined is 70% of pensionable earnings. You should consider split-rate defined contribution formulas; that is, one contribution formula to be applied on pensionable earnings to the CPP covered earnings limit and a second contribution formula applied on pensionable earnings above the CPP covered earnings limit.

Your Task Using the spreadsheet SOA_FAP_Mod3Exercise01-02CareerProjections.xls (see “Appendix: Spreadsheets Used in the Chocolate Factory Exercise” for more information about the worksheets contained in this spreadsheet), derive an ideal defined contribution formula for the following potential Chocolate Factory career employees:

Employees earning $50,000 in 2006 (i.e., the average Cascadia earnings). Employees earning $100,000 in 2006 (i.e., two times average Cascadia earnings). And, employees earning $200,000 in 2006 (i.e., four times average Cascadia earnings).

For example, the ideal DC pension plan formula could be a contribution equal to 7% of earnings up to the CPP limit and 12% of earnings above the CPP Limit. All contribution formulas should be rounded to the nearest 0.25%.

TASK 3: ESTIMATE CONTRIBUTION VARIABILITY BASED ON EXPECTED FUND RETURNS

Background The ideal defined contribution formula was calculated using an expected fund rate of return of 6.5% per annum. A change in fund rate of return will result in a change in the member‟s pension under a defined contribution pension plan. The employee is therefore at risk should a 6.5% per annum fund return not be realized.

Your Task Using the spreadsheet SOA_FAP_Mod3Exercise01-02CareerProjections.xls, estimate the effect of a change in the fund rate of return. Estimate the impact of a 2% per annum increase in the return and a 2% per annum decrease in the return.

© 2003 - 2013 Society of Actuaries - SOA_FAP_Mod3Exercise01-01Assignment.docx - Page 4

Your Assignment (continued)

TASK 4: ESTIMATE CONTRIBUTION VARIABILITY WITH PRICE INFLATION

Your team is also concerned with the potential impact of a change in expected inflation which will result in a change in future earnings increases and, potentially, in future fund returns.

Your Task Using the spreadsheet SOA_FAP_Mod3Exercise01-02CareerProjections.xls, estimate the effect of a 1% per annum increase in expected inflation assuming a constant real rate of return and the effect of a 1% per annum decrease in expected inflation assuming a constant real rate of return.

TASK 5: DETERMINE EXPECTED PENSIONS FOR CHOCOLATE FACTORY EMPLOYEES

Background The Chocolate Factory has provided employee data. Your team has asked you to test whether a proposed defined contribution formula of 12 on covered earnings up to the CPP limit and 17 of covered earnings in excess of the CPP limit would produce appropriate target pensions for The Chocolate Factory employees.

Your Task Using the spreadsheet SOA_FAP_Mod3Exercise01-03EmployeeData.xls and the previous spreadsheet, determine whether the proposed defined contribution formula is appropriate. Recommend changes to the proposed defined contribution pension for any employee where the resulting target pension is inappropriate. Determine The Chocolate Factory‟s aggregate contribution should your recommended formula be used. Compare your recommended defined contribution formulas to the team‟s proposed defined benefit formulas.

TASK 6: DETERMINE VARIANCE IN PENSIONS FOR CHOCOLATE FACTORY EMPLOYEES

Background Your recommended pension formula is being considered by the team. The team is concerned, however, with the risk of change and variability in future inflation rates and fund rates of return.

Another member of your team prepared a model to perform a Monte Carlo simulation of future inflation rates and fund rates of return for another project. He has provided you with a summary of the output of this simulation for use on this project.

Your Task Using the spreadsheet SOA_FAP_Mod3Exercise01-04SimulationResults.xls and any of the previous spreadsheets you have at your disposal, determine the target pension members can expect to receive with a 95 probability, assuming the fund returns in the simulation results are reliable. Recommend changes to the proposed defined contribution pension for any employee where the resulting target pension is inadequate.

© 2003 - 2013 Society of Actuaries - SOA_FAP_Mod3Exercise01-01Assignment.docx - Page 5

Your Assignment (continued)

TASK 7: TIE IT ALL TOGETHER

Your Task Prepare a memo that provides background on the matters you have been assigned by your team. You do not have to provide a summary of the Monte Carlo simulation, a summary of the Cascadia Pension Plan or a summary of the background for private tax-assisted pension plans in Cascadia in your memo since these will be handled by another team member. The contents of your memo will be used to supplement a larger report to The Chocolate Factory from your consulting firm. Your memo should clearly answer the following questions:  What is your recommended defined contribution formula for The Chocolate Factory

Pension Plan?  How do the expected defined contribution pension amounts using your recommended

contribution formula compare to the target pensions for career employees under the proposed final earnings defined benefit plan?

 Do you recommend a change to the basic formula for any of The Chocolate Factory employees?

 What is the expected pension (as a percentage of earnings at retirement) for a typical career employee, given your recommended formula? How does this compare to the goals?

 What are the expected pensions for the actual Chocolate Factory employees, given your recommended formula?

 How do the expected defined contribution pensions vary with a change in fund rate or a change in inflation rate?

 What amount of defined contribution pension (as a percentage of earnings at retirement) should a career employee expect to receive with a 95 probability? How does this vary for the oldest and youngest Chocolate Factory employee?

 Does the recommended contribution formula meet The Chocolate Factory‟s budget goals?  What are the risks that should be monitored if this defined contribution pension plan is

adopted?  Will your defined contribution pension plan provide appropriate pensions for all of the

Chocolate Factory employees? Do you recommend a different approach for some of the employees?

 Has the problem been defined completely and the appropriate risks considered for the Chocolate Factory and its employees?

Structure your memorandum into the following sections:  Introduction and Key Findings.  Data and Assumptions.  Model.  Analysis.  Conclusions and Recommendations.

© 2003 - 2013 Society of Actuaries - SOA_FAP_Mod3Exercise01-01Assignment.docx - Page 6

Appendix: Spreadsheets Used in the Chocolate Factory Exercise

The SOA_FAP_Mod3Exercise01-02CareerProjections.xls Spreadsheet The Excel workbook, SOA_FAP_Mod3Exercise01-02CareerProjections.xls, is a model that consists of four worksheets, “Input,” “Results,” “Calcs,” and “Annuity Factors.”

The “Input” worksheet is the input area of the model that you will use. It permits you to enter the necessary details with respect to individual member information, formula rates and assumptions.

The “Results” worksheet provides the replacement ratios (i.e., the ratio of the pension to the member‟s earnings) at age 65 under the defined benefit and the defined contribution plan given your input. This worksheet will allow you to assess the various scenarios for the potential career employees and the actual Chocolate Factory employees. This worksheet is locked and cannot be altered.

The remaining worksheets, “Calcs” and “Annuity Factors,” contain all the formulas for the model as well as the underlying annuity factors that are used to convert the defined contribution pension plan balances to a pension at age 65.

Details for this spreadsheet are described below.

Worksheet 1: “Input”

Input Fields Details Description Member Data Age (enter integral age): Member‟s age (as of 2006), see Member Data

worksheet for employee data Sex (enter "M" or "F"): Member‟s sex Current Year ("YYYY"): Set to 2006 for this exercise, this does not need to

be modified Prior Year Earnings: Earnings during 2005, see Member Data

worksheet for employee data Past Service (enter years): Number of years of service (from 1985 to 2005) –

no partial years are included. Initial Account Balance: This will be zero for all Members in this exercise

Project Parameters Fund Return: Annual expected rate of future investment return assumption

Inflation Rate: Annual expected rate of future inflation assumption External Forces Average W age: Average Annual W age in Cascadia (for 2005) as

determined by the government of Cascadia Defined Benefit Accrual Rate -

up to covered earnings Annual accrual rate for pensionable earnings up to the covered earnings limit under the CPP

in excess of covered earnings Annual accrual rate for pensionable earnings in excess of the covered earnings limit under the CPP

Defined Contribution Rate -

up to covered earnings Annual contribution rate for pensionable earnings up to the covered earnings limit under the CPP

in excess of covered earnings Annual contribution rate for pensionable earnings in excess of covered earnings limit under the CPP

Worksheet Default Fields

All input fields on the „Input‟ worksheet have their default values noted on the worksheet in a separate column.

© 2003 - 2013 Society of Actuaries - SOA_FAP_Mod3Exercise01-01Assignment.docx - Page 7

Worksheet 1: “Input” (cont)

Calculated Fields (calculations are

dependent upon input fields)

Details

Description Annual Increase in: Pensionable Earnings: = Inflation rate (as determined by the government

of Cascadia) plus 1% (The earnings rates from age 50 to age 60 are 0.50% less per annum and from age 60 to age 65 are 1.0% less per annum).

CPP Covered Earnings: = Inflation rate (as determined by the government of Cascadia) plus 0.5% (Individual CPP covered earnings increases are limited to the increase in inflation after age 55)

Maximum Pension Earnings: = Inflation rate (as determined by the government of Cascadia)

External Forces CPP Covered Earnings: = Average W age (as determined by the government of Cascadia) * 2

Maximum Pension Earnings: = Average W age (as determined by the government of Cascadia) * 4

Worksheet 2: “Results” This worksheet contains all of the information on the input worksheet except that the External Forces fields have been replaced with the Replacement Ratios at age 65 that were determined using the input on the previous worksheet.

Results Details Description Replacement Ratios at age 65

Private Defined Benefit Percentage of an individual‟s current earnings that is provided through the private defined benefit pension plan at age 65.

Total Defined Benefit Percentage of an individual‟s current earnings that would be provided through both the private defined benefit pension plan and the Cascadia Pension Plan at age 65.

Private Defined Contribution Percentage of an individual‟s current earnings that is provided through the private defined contribution pension plan at age 65.

Total Defined Contribution Percentage of an individual‟s current earnings that would be provided through both the private defined contribution pension plan and the Cascadia Pension Plan at age 65.

Worksheet 3: “Calcs” This worksheet uses the information from the “Input” worksheet and calculates:

Column Column Heading Description

A Year 1st Year: Calendar Year (from input field on W orksheet 1) Subsequent Years: increased by 1.

B Age 1st Year: Age of Member (from input field on Input Worksheet) Subsequent Years: increased by 1.

C Credited Service (Years)

1st Year: Past Service Years (from input field on Input Worksheet) Subsequent Years: increased by 1.

© 2003 - 2013 Society of Actuaries - SOA_FAP_Mod3Exercise01-01Assignment.docx - Page 8

Worksheet 3: “Calcs” (continued)

E Earnings: Pensionable in Current Year

1st Year: Minimum of Prior Year Earnings (from Input Worksheet) and Maximum Pensionable earnings (indirectly from Input Worksheet) Subsequent Years: Earnings increased by Annual Increase in pensionable earnings increase rate from Input W orksheet subject to the maximum increase allowed for a Cascadian pension plan.

F Earnings: CPP Covered in Current Year

1st Year: CPP covered earnings (from Input W orksheet) Subsequent Years: Earnings increased by Annual Increase in covered earnings increase rate from Input W orksheet subject to the maximum increase allowed under the Cascadian Pension Plan.

G Earnings: Maximum Pensionable Earnings in Current Year

1st Year: Maximum Pensionable Earnings in current year from Input Worksheet. Subsequent Years: equal to the previous year‟s maximum pensionable earnings increased by the annual maximum pensionable earnings increase rate.

I Earnings: Final Pensionable Earnings

1st Year is calculated (estimated) by taking current earnings adjusted by the annual increase in pension earnings increase rate Subsequent years: Use the prior year‟s pensionable earnings.

J Earnings: Final CPP Covered Earnings

1st Year is calculated (estimated) by taking current CPP covered earnings adjusted by the annual increase in pension earnings increase rate Subsequent years: Use the prior year‟s CPP covered earnings.

K Earnings: Final Maximum Earnings

1st Year is calculated (estimated) by taking current maximum earnings adjusted by the annual increase in pension earnings rate Subsequent years: Use the prior year‟s maximum earnings.

M Defined Benefit Projection: Annual Pension Accrual

Amount of pension accrued for one year using the current year‟s earnings levels and using the defined benefit accrual rates from the „Input‟ worksheet (Input:G18 and Input:G19) subject to the maximum accrual for a private Cascadian pension plan.

N Defined Benefit Projection: Total Accrued Pension

Total accrued pension, equals the Annual Pension Accrual multiplied by the years of service.

O Defined Benefit Projection: Private Pension Percent Accrual

Replacement ratio for the private defined benefit pension plan, equals the Total Accrued Pension divided by the member‟s pensionable earnings.

P Defined Benefit Projection: CPP Pension to Age:

CPP Pension payable at age 65 based on the member‟s covered earnings.

Q Defined Benefit Projection: CPP Pension Percent Accrual

Replacement ratio for the CPP pension, equals the CPP Pension to age divided by the member‟s pensionable earnings.

R Defined Benefit Projection: Total Pension Percent Accrual

Replacement ratio for the private defined benefit pension plan and the CPP combined.

T Defined Contribution Pension Projections: Annual Contribution Amount

Amount of pension contributions made during the current year using the defined contribution rates from the „Input‟ worksheet (Input:G22 and Input:G23).

© 2003 - 2013 Society of Actuaries - SOA_FAP_Mod3Exercise01-01Assignment.docx - Page 9

Worksheet 3: “Calcs” (continued)

U Defined Contribution Pension Projections: Accumulated Account Balance

1st Year: The Initial Account Balance (IAB) for all employees of the Chocolate Factory is assumed to be zero. Subsequent Years: Sum of the Account Balance, increased by the input fund rate of return (Input: C18) and the current year‟s contributions increased by ½ of the input fund rate of return (Input: C18). Note: an interest rate of ½ of the input rate has been used to approximate fund returns given contributions are expected to be made throughout the year.

V Defined Contribution Pension Projections: Deferred Annuity Factor

A deferred annuity factor is calculated based on the underlying fund return rounded to the nearest 0.25% and the annuity factors set out on the “Annuity Factors” worksheet. The annuity factors used are based on the blended factor (i.e., based on the assumption that there is an 80% probability that the member is married at retirement). The deferred annuity factor is sex-distinct based on the sex of the member as input.

W Defined Contribution Pension Projections: Estimated Private Pension at 65

A projected pension payable beginning at age 65 is determined equal to the current defined contribution account balance and the deferred annuity factor.

X Defined Contribution Pension Projections: Private Pension Percent Accrual

Replacement ratio for the private defined contribution pension plan, equals the Estimated Private Pension at 65 divided by the member‟s pensionable earnings.

Y Defined Contribution Pension Projections: CPP Pension Accrued

CPP Pension payable at age 65 based on the member‟s covered earnings.

Z Defined Contribution Pension Projections: CPP Pension Percent Accrual

Replacement ratio for the CPP pension, equals the CPP Pension to age divided by the member‟s pensionable earnings.

AA Defined Contribution Pension Projections: Total Pension Percent Accrual

Replacement ratio for the private defined contribution pension plan and the CPP combined.

Worksheet 4: “Annuity Factors“ This worksheet contains annuity factors determined for a member who retires at age 65 based on the UP94 mortality table projected to 2005. The annuity factors contain provision for annual post-retirement increases equal to 100% of the listed inflation rate. Annuity factors for interest rates above 8.0% per annum are based on an assumed interest rare of 8.0% per annum to reflect the fact that annuity purchase rates are not expected to exceed 8.0% per annum.

Column Column Heading Description

A Interest Rate Interest rates from 3.0% to 10.0% per annum in increments of 0.25%. B Inflation Rate Inflation rate is used to determine the annual pension increase built into the

annuity factor. D Male 65: Life Only Annuity factor for a pension payable during a male‟s lifetime only. E Male 65: Life-10 Annuity factor for a pension payable for a male‟s lifetime with 120 monthly

payments guaranteed. F Male 65: J&S (50) Annuity factor for a pension payable to a male annuitant with 50% continuing

to a female joint annuitant upon the annuitant‟s death. G Male 65: Blended Blended annuity factor assuming 80% of the male annuitant‟s are married. I Female 65: Life Only Annuity factor for a pension payable during a female‟s lifetime only.

© 2003 - 2013 Society of Actuaries - SOA_FAP_Mod3Exercise01-01Assignment.docx - Page 10

Worksheet 4: “Annuity Factors” (continued)

J Female 65: Life-10 Annuity factor for a pension payable for a female‟s lifetime with 120 monthly payments guaranteed.

K Female 65: J&S (50) Annuity factor for a pension payable to a female annuitant with 50% continuing to a male joint annuitant upon the annuitant‟s death.

L Female 65: Blended Blended annuity factor assuming 80% of the female annuitant‟s are married.

The SOA_FAP_Mod3Exercise01-03EmployeeData.xls Spreadsheet The SOA_FAP_Mod3Exercise01-03EmployeeData.xls spreadsheet consists of two worksheets. The first worksheet, “Member Data,” contains member data; it was provided by the Chocolate Company effective December 31, 2005. The second worksheet, “Contribution Summary,” provides a summary for 2006 of the aggregate contributions, including the Company‟s budget target. This worksheet may be used to summarize the expected contributions given the defined contribution rates that you recommend. These are described below.

Worksheet 1: “Member Data”

Column Column Heading Description B Member D Age As of December 31, 2005 E Sex F Prior Year Earnings Total earnings for 2005 G Past Service in

Years As of December 31, 2005

Worksheet 2: “Contribution Summary”

Column Column Heading Description

B Member = value on Worksheet 1 („Member Data‟) C Age = value on Worksheet 1 („Member Data‟) D Sex = value on Worksheet 1 („Member Data‟) E Prior Year Earnings = value on Worksheet 1 („Member Data‟) F CPP Covered

Earnings Minimum of Member‟s Prior Year‟s earnings and the Maximum Covered Earnings

G Pensionable Earnings

Minimum of Member‟s Prior Year‟s earnings and the Maximum Pensionable Earnings in Cascadia

H Adjustment to Base Contribution

Input field: an individual member‟s contribution rate may be reduced up to 25% of the contribution rate used for other member‟s of the plan, in accordance with Cascadian law.

I Member Contribution

Actual expected member contribution based on the member‟s pensionable earnings, the contribution formula, the member‟s reduction and the maximum permitted contribution (i.e., 15% of pensionable earnings) under Cascadian law.

J Contribution Rate The actual contribution rate for the member based on the calculated contribution amount for the member and the member‟s pensionable earnings.

© 2003 - 2013 Society of Actuaries - SOA_FAP_Mod3Exercise01-01Assignment.docx - Page 11

The SOA_FAP_Mod3Exercise01-04SimulationResults.xls Spreadsheet The Excel spreadsheet SOA_FAP_Mod3Exercise01-04SimulationResults.xls contains data obtained through a Monte Carlo simulation of equity, bond and inflation annual increases in Cascadia. A total of 1,000 simulations of returns over a 50-year period were performed. Annualized returns for the equity, bond and inflation rates were calculated for each year from year one to year 50. A fund return based on an investment of 60 of the assets in equities and 40 of the assets in bonds was determined based on the equity and bond yields. The investment in this scenario is rebalanced to 60/40 at the end of each year.

A summary of the results is contained in the “Summary” worksheet. The average annualized returns for each year from 1 to 50 is provided for the equity, bond, inflation and fund returns. For example, the average fund return over a 15 year period is estimated to be 7.80% per annum (see cell P11). In other words, a member who enters the defined contribution plan at age 50 could expect to achieve an average fund return of 7.80% per annum over the period from age 50 to retirement at age 65.

A percentile breakdown is provided for the fund return. For example, fund returns are expected to equal or exceed 4.02% over a 15-year period with a 95 probability (see cell P33). In other words, a member who enters the defined contribution plan at age 50 could expect to achieve at least a 4.02% per annum fund return over the period from age 50 to retirement at age 65.

All worksheet in this spreadsheet are locked. For this exercise, you must use the results presented in the spreadsheet without change.

© 2003 - 2013 Society of Actuaries - SOA_FAP_Mod3Exercise01-01Assignment.docx - Page 12

FAP_Mod3Exercise01-03EmployeeData.xlsx