Question

Ashley is 30 years old when graduating from the University of Utah. At the time of graduation, she is offered employment in both Utah and California. Sally will work until she is 65 years old regardless of her employment choice. Compensation is distinct for each employment option according to the following criteria:

Utah: Starting salary of $52,000. Annual wage growth of 2.5% through age 52 and then no wage growth through retirement. Discount rate of 3.5%.

California: Starting salary of $57,000. Annual wage growth of 3.0% through age 54 and then no wage growth through retirement. Discount rate of 4.5%. Costs of moving to California total $23,500 – incurred in the first period.

Which job should Ashley take in order to maximize real lifetime earnings? Show all calculations.

Answer 1

Case of Utah

Total number of working years=65-30=35 years

Initial salary=P=$52000

Growth rate=g=2.5%

Discount rate=i=3.5%

First we estimate the PV of income for first 22 years in which salary growth is there

We know that PV of growing annuity is given by

Let us calculate the salary at the end of year 22 (Age 52 years)

Salary=R=P*(1+2.5%)^21=52000*(1+2.5%)^21=$87338.26

There will be an annuity of income with uniform payments for 65-52=13 years, So,

PVu=87338.26*(P/F,0.035,22)(P/A,0.035,13)

(P/F,0.035,22)=1/(1+0.035)^22=0.4691506

PVu=87338.26*0.4691506*10.3027385=422152.62

Total PV=PVg+PVu=1000083.20+422152.62=1422235.82

Case of California

Initial shifting cost=Co=$23500

Initial salary=P=$57000

Growth rate=g=3%

Discount rate=i=4.5%

First we estimate the PV of income for first 24 years in which salary growth is there

We know that PV of growing annuity is given by

Let us calculate the salary at the end of year 24 (Age 54 years)

Salary=R=57000*(1+3%)^23=$112494.43

There will be an annuity of income with uniform payments for 65-54=11 years, So,

PVu=87338.26*(P/F,0.045,24)(P/A,0.045,11)

(P/F,0.045,24)=1/(1+0.045)^24=0.3477035

PVu=112494.43*0.3477035*8.5289169 =333606.09

Total PV=-Co+PVg+PVu=-(23500/(1+4.5%))+1114123.63+333606.09=1425241.68

Total lifetime earnings are maximized in case of california