# What are the advantages of a defined contribution plan?

Value of Defined Benefit Plan with Single Employer: Suppose you take your first job with an employer that offers a defined benefit retirement plan and a beginning salary of \$54,000/yr. Suppose also that you average 5.0% raises every year and that you stay with the same employer for all 48 years of your career. Note that during your 48-year career, you will receive 47 raises, the last of which happens on your last working day, which is also your 70th birthday. (No matter your current age, consider that you start working at age 22, and retire at 70). Assume a salary of \$54,000 in the first year and an inflation rate of 2.0%.
a. What is your ending salary in nominal dollars (not adjusted for inflation)?
b. What is your ending salary in real dollars (adjusted for inflation, i.e. in \$2015)?
c. Assuming that the employers defined benefit plan pays 1.25% of ending salary per year of employment, what will your annual retirement income be from this retirement plan (do not adjust for inflation):
Retirement Salary = (.0125)(Ending Salary)(Years employed)
d. On a scale of 1 (very little) to 10 (very much) how much would you like or prefer this particular defined benefit plan?
e. In a defined benefit plan, is your employer required to increase your monthly retirement pay based on the rate of inflation? What does this mean to you?
f. What happens to you if your employer goes out of business and has no money to pay for your (and others) retirement?
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5. Imagine the same situation as above, but now you work for two employers during your career: You work for Employer A for the first 24 years, and Employer B for the second 24 years. Everything else in the problem is the same. Calculate your retirement salary from Employer A, from Employer B, and the total of the two retirement salaries. (Note that throughout your career, you receive a raise of 5.0% every year, even if you change employers, and you never loose salary when you change employers.

6. Value of early career Defined Benefit plan: Assuming the same situation as problem 4 (starting salary of \$54,000; Defined benefit plan which pays 1.25% of your ending salary for each year that you worked for the company) what will your retirement income be if you quit this employer:
a. After 10 years (calculate your salary in the tenth year and then apply the retirement formula of 1.25% of ending salary for every year worked)
1) In nominal \$
2) In “real” or inflation adjusted \$ (assume inflation of 2.0%)
b. After 20 years.
1) In nominal \$
2) In “real” or inflation adjusted \$ (assume inflation of 2.0%)
c. Is a defined benefit a good plan if you do not stay with the company for your whole career?
d. If you work at a company for a whole career, you retire on your defined benefit salary, and the firm goes bankrupt, can the firms obligation to retirees like yourself be lowered, i.e. can retirees be left with a lowered retirement salary by the bankruptcy judge?

7. Value of early career Defined Contribution plan in a mobile career
a. As a point of comparison, assume a starting salary of \$54,000 and 5.0% annual increases each year for the first 10 years of your career. Assume that you are in a defined benefit plan, that you change employers every 2 years and 11 months (total of 4 employers) and that you were never vested in any of the three plans. How much money do you have in total from these three retirement plans at the end of the first 10 years of your career?
b. Assume a starting salary of \$54,000 and 5.0% annual increases each year for the first 10 years of your career. Assume that you are in a defined contribution plan in which your employer contributes 7.0% of your salary each year, that you change employers every 3 years (total of 4 employers) and that you were vested in each of the four plans. How much money do you have in your plan at the end of the 10 years? Pragmatically, you can consider this as one plan for the whole 10 years since you would take the accumulated money with you across firms. Assume an 8% rate-of-return based on an index fund yielding a market average return. (Note that you will have 10 streams of income compounded over 9, 8, 7, …0 years of earnings. This is because we will simplify by assuming that the employer makes only 1 contribution per year and it comes on the last day of the year. In the 10th year, you get the contribution, but there is no interest earned.)
c. Calculate the value of those funds from the first 10 years if you let them stay invested with a return of 8% until you retire at age 70 (for this second part, dont add any principle or employer contribution after the tenth year, just calculate what the compound earnings will yield if left invested at 8% until age 70.
d. What % of your desired retirement portfolio (question #3) does this represent?
e. What are the advantages of a defined contribution plan?

8. Verbally state what you learned from problem 7.

9. Value of Full Career Defined Contribution Plan: Finally, suppose that you again begin your 48 year career at age 22, beginning salary of \$54,000/yr., 5.0% raises every year, and stay with the same employer for your whole career (or are always vested before you move between employers). Assume your employer always contributes 5.0% of your salary each year into your defined contribution plan. Assume that you invest in a mix of stocks and bonds such that you realize an annual average rate of return of 8%. What will the value of your defined contribution retirement fund be at retirement (age 70):
a. In nominal dollars (not adjusted for inflation)?
b. In inflation adjusted (2.0%) dollars?
c. On a scale of 1 (very little) to 10 (very much) how much would you like or prefer this particular defined contribution plan?

10. How can you tell how generous an employer is:
a) In a defined contribution plan?
b) In a defined benefit plan?

11. In the first part of this assignment you estimated the total retirement portfolio you needed for retirement. Why is that an important thing to do? What is likely to happen if you grossly overestimate that amount? What is likely to happen if you grossly underestimate that amount?
12. Usually, a Defined Contribution plan has a number of investment options that the employee may choose to invest in. One of those options will likely be federally insured savings at the then current market rate. That typically would pay less than 0.5% to 3% interest (based on averages over the past 15 years). This is also usually the default choice if you do not tell the plan to invest in stock or bond mutual funds.
a. If you did not choose your investment mutual fund(s) within the plan, but rather just let the plan put you into the default insured savings account, what would be the value of your plan at retirement? (For this problem, you may assume an average rate of return of 2% in the savings plan, and a 2.0% rate of inflation.)
b. Verbally state what you learned from problem 12, a. above.

12. If you change employers during your career, and all of them have defined contribution plans, what can you do with your vested funds once you leave an employer?
a) Leave it in each employers defined contribution program.
b) Move it (sequentially) to each of your next employers plan.
c) Roll it over into your own Individual Retirement Account.
Which of the three options above is most advantageous, and why?