Question

a. Eighteen-year-old Linus is thinking about taking a five-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. All these values are stated in real dollars. Assume that Linus lives to be 100 and that real interest rates will stay at 5% per year throughout his life.

i.    Calculate the present value of his lifetime earnings.                                       (1 mark)

ii. Calculate the present value of the cost of his schooling.                                      (1 mark)

iii. Subtract the present value of the schooling cost from his lifetime labour earnings to determine his human capital. Use that value to determine his permanent income, that is, the equal annual consumption Linus could enjoy over the rest of his life.                   (1 mark)

b. 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 each year, in real terms, until he retires at the age of 53. Assume that Linus lives to be 100.

i.    Calculate the present value of Linus’s lifetime earnings, using a spreadsheet or using the growing annuity formula. You can find the formula in the lesson notes, at the end of Note 7 in Lesson 4.                                (1 mark)

ii. Use that value to determine Linus’s permanent income, i.e., how much can Linus spend each year equally over the rest of his life?                                                    (1 mark)

c.       Do you think Linus is better off choosing option a. or option b.? Consider both financial and non-financial measures.

May someone please answer part B of this question.**** No EXCEL calculation

Answer 1

b)

i)

Number of year he works = 53 = 18 = 35 = n

Growth rate = 3%

Interest Rate = 5%

'

Hence the present value of growing annuity is $979,748.15

ii)

We have the present value as when Linus is 18. We need to find the present value of present value factor for the period equal to retirement life of linus and use that to find annual consumption.

The present value factor for the period equal to his life after retirement i.e. 100-53 = 47 years.

= [1 - (1 + r)^-n] /r

= (1-(1.05)^-47)/0.05

= 17.98

Present value today i.e. when Linus is 18 year old of this factor = 17.98*(1+r)^-n, where n = 35 years

= 17.98(1+0.05)^-35 = 17.98*0.18129

= 3.26

Linus's permanent income = 979,748.15/3.26 = $300,556.20

If you have any doubt, ask me in the comment section please.