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.   

ii. Calculate the present value of the cost of his schooling.       

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.   

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.    

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?                                                          

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

NO EXCEL, SHOW CALCULATIONS PLEASE

Answer 1

You have asked a question with two parts. Further each part has multiple sub parts. I have addressed all the sub parts of the first part. Please post the second part separately.

i. Calculate the present value of his lifetime earnings.   

Present value of earnings in the first 10 year at the end of five years from now = A / r x [1 - (1 + r)^-n]

= 50,000 / 5% x [1 - (1 + 5%)^-10] = 386,087

PV of this today = 386,087 x (1 + r)^-m = 386,087 x (1 + 5%)^-5 = 302,509

Present value of earnings in the next 10 year at the end of fifteen years from now = A / r x [1 - (1 + r)^-n]

= 75,000 / 5% x [1 - (1 + 5%)^-10] = 579,130

PV of this today = 579,130 x (1 + r)^-m = 579,130 x (1 + 5%)^-15 = 278,571

Present value of earnings in the final 10 year at the end of twenty five years from now = A / r x [1 - (1 + r)^-n]

= 100,000 / 5% x [1 - (1 + 5%)^-10] = 772,173

PV of this today = 772,173 x (1 + r)^-m = 772,173 x (1 + 5%)^-25 = 228,025

Hence, the present value of his life time earnings = Sum of the three PVs calculated above = 302,509 + 278,571 + 228,025 = $ 809,106

ii. Calculate the present value of the cost of his schooling.  

the present value of the cost of his schooling = A / r x [1 - (1 + r)^-n] = 25,000 / 5% x [1 - (1 + 5%)^-5] = $ 108,237

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.

Human capital = 809,106 - 108,237 = $ 700,869

Let A be his permanent income. When he stops working it will be 5 + 10 + 10 + 10 = 35 years from now and his age will then be 18 + 35 = 53. Balance years till he lives on = 100 - 53 = 47

PV of his permanent income when he stops working i.e. at the end of 35 years from now = A / r x [1 - (1 + r)^-n] = A / 5% x [1 - (1 + 5%)^-47] = 17.9810A

PV of this today = 17.9810A x (1 + r)^-m = 17.9810A x (1 + 5%)^-35 = 3.2598A

We therefore need to solve for A such that, 3.2598A = 700,869

Hence, his permanent income, that is, the equal annual consumption Linus could enjoy over the rest of his life, A = 700,869 / 3.2598 = $ 215,005