Question

The Certainty Company (CC) operates in a world of certainty. It has just hired Matt (age 20) who will retire at age 65, draw retirement benefits for 15 years, and die at age 80. Matt's salary is $20,000 per year, but wages are expected to increase at the 5% annual rate of inflation. CC has a defined benefit plan in which workers receive 1% of the final year's wage for each year employed. The retirement benefit, once started, does not have a cost-of-living adjustment. CC earns 10% annually on its pension fund assets. Assume that pension contribution and benefit cash flows occur at year-end. How much will Matt receive in annual retirement benefits? What is CC's required annual contribution to fully fund Matt's retirement benefits? Assume now that CC hires Prof. Condon at the same S20,000 salary as Matt. However, Prof. Condon is 45 years old. Repeat the analysis in parts a and b under the same assumptions used for Matt. What do the results imply about the costs of hiring older versus younger workers? Now assume that CC hires Claire, age 20, at the same time that it hires Prof. Condon. Claire is expected to retire at age 65 and to live to age 90. What is CC's annual pension cost for Claire? If Prof. Condon and Claire are doing the same work, are they truly doing it for the same pay? Would it be "reasonable" for CC to lower Claire's annual retirement benefit to a level that would mean that she received the same present value as Prof. Condon? a. b. c. d. Worker I Worker2 Worker3 Name of Worker Starting salary Age (start) Age (retire) Number of vrs emploved Morbidity age Final year salary Predicted retirement PMT What must fund "accumulate" by the time worker retires? What is the annual PMT necessary every year for retirement fund to be considered fully funded?

Answer 1

Ans (a) For calculating how much Matt will receive in annual retirement benefits, we need to calculate his salary in the last year of service. This can be done using formula A = P(1 + rt).

Where A= total amount (principal +interest)

P=Principal (which is annual salary of Matt) i.e $20,000

r=Rate of interest, inflation in present case- 5%

T= number of years, 45 years as he will work from 20 years and retire at 65

A=20,000(1+5%*45)= 20000*(1+0.05*45)= $65,000

Defined benefit 1% of final year wages, so final year wages as calculated above is $65,000

= 1% of 65,000=650

If retirement benefit received for 15 years = 650*15=9750

If retirement benefit received for 45 years (all completed years of service)= 650*45=29250

Ans(b) CC annual contribution

Total retirement benefit =29250

Number of years of service= 45years

Benefit pear year = 29250/45=650

CC earns 10% interest annually on pension fund. So for giving 650 per year it has to invest =650/110%=591

So CC's annual contribution will be $591.

Ans(c) For calculating how much Prof Condo will receive in annual retirement benefits, we need to calculate his salary in the last year of service. This can be done using formula A = P(1 + rt).

A= 20000*(1+0.05*20) = $40,000

Defined benefit 1% of final year wages, so final year wages as calculated above is $40,000

= 1% of 40,000=400

If retirement benefit received for 20 years (all completed years of service)= 400*20=8,000

CC annual contribution to fund Condon retirement benefit= 8000/20=400

CC earns 10% interest annually on pension fund. So for giving 400 per year it has to invest =400/110%=363.63

So CC's annual contribution will be $363.63.

First 3 questions answered.