Question

Linus is 18 years old now, and is thinking about taking a 5-year university degree. The degree will cost him $25,000 each year. After he's finished, he expects to make $50,000 per year for 10 years, $75,000 per year for another 10 years, and $100,000 per year for the final 10 years of his working career. If Linus lives to be 100, and if real interest rates stay at 5% per year throughout his life, what is the equal annual consumption he could enjoy until that date? Linus is also considering another option. If he takes a job at the local grocery store, his starting wage will be $40,000 per year, and he will get a 3% raise, in real terms, each year until he retires at the age of 53. If Linus lives to be 100, what is the equal annual consumption he could enjoy until that date? From strictly a financial point of view, is Linus better off choosing option A or B?

One question I do have about this also: Is the annual consumption from the day he is retired or from now (18 years old) ???

Answer 1

Linus is presently 18 years old. He'll start earning after 5 years that is when he's 23 years old. Thus if he lives till the age of 100, he has 77 years of his life remaining for which equal annual consumption is required to be calculated.

Option A:

Real interest rate = 5%

Initial investment: $25,000 x 5= $125,000

PV of Cash inflows:

(Cash flows x GT of Pv factors @5% every 10 years) = 50,000 x 7.722 x + 75,000 x (12.462-7.722) + 100,000 x (15.372-12.462) = 386,100+355,500+291,000= $1,032,600

NPV= 1,032,600-125,000= $907,600

Equivalent annual consumption= r(NPV)/1-(1+r)^-t

Where,

r = interest rate per year

t= number of years

EAC= 0.05(907,600)/1-(1.05)⁷⁷

= $46,465.31

Option B:

Real interest rate = 5%

Initial investment: $25,000 x 5= $125,000

PV of Cash inflows:

GT of PVF@5% for 30 years= 15.372

Therefore total amount earned over 30 year period = 40,000 x 15.372 x (1.03)³⁰= $1,492,475

NPV= 1,492,475-125,000 = $1,367,475

EAC= r(NPV)/1-(1+r)^-t

=  0.05(1,367,475)/1-(1.05)^-77

= $66,776.72

Therefore, Linus is better choosing option B.