Question

To quantify the values of two potential career paths (work or go to college), you assume the followings.

1. Your parents will give you $55,000 from a college fund today whichever career path you choose.

2. Your salary directly goes to your saving account and sits there.

3. Your total living cost and taxes are always zero.

4. You will retire in 45 years from now.

5. The interest rate of your saving account is 2% per year, compounded annually. You will withdraw all at once from your saving account when you retire. Assume that your saving account is perfectly protected by the government. The discount rate is also 2% per year, compounded annually.

If you choose to go to a college, which is the option (a), then your career path and cash-flows will be as follows.

1. The school starts today.

2. The total cost of getting a degree is $55,000 and needs to be paid in full today.

3. You need full four years to get a BBA degree.

4. You will work at NTN Inv after graduation, starting in 4 years. NTN Inv pays $68,000/year for 41 years. You will receive 41 annual paychecks in total.

If you choose not to go to a college (b), then your career path and cash-flows will be as follows.

1. You deposit $55,000 from your parents into your saving account and never withdraw until you retire.

2. The job at ABC INC starts today and the company pays $39,000/year for 45 years. You will get your first paycheck in a year after you work there for a year. You will receive 45 annual paychecks in total.

The firms will persist forever and your employment is guaranteed until your retirement.

Your decision on the college education is irreversible and you are stuck with the chosen

career path until your retire.

Question 1. Compute “the (present) value when you start the job” of 41 annual paychecks from NTN Inv when you choose the career path (a) going to College. You go to the future, 4 years from now, and compute the present value there. Here you can use the formula for an annuity.

1. $1,830,365.28

2. $1,850,365.28

3. $1,870,365.28

4. $1,890,365.28

5. $1,910,365.28

Question 2. Compute “the present value as of today” of the career path (a) going to College. You can forget about the actual cash flows from the paychecks. Instead, you can assume there is only one hypothetical cash flow in 4 years from now whose amount is the same as your answer for the question 1. Therefore, the present value of the career path (a) is equal to the present value (as of today) of such hypothetical cash flow (in 4 years from now) that you computed for the question 1.

1. $1,744,405.32

2. $1,746,405.32

3. $1,748,405.32

4. $1,750,405.32

5. $1,752,405.32

Question 3. Compute ‘the present value (as of today) of the career path (b) not going to college. This Present value is the sum of the present values of one big lump-sum cash flow from your parents today and a standard annuity with 45 paychecks from ABC INC

1. $1,205,116.24

2. $1,225,116.24

3. $1,245,116.24

4. $1,265,116.24

5. $1,285,116.24

Question 4. Which career path is more valuable in terms of the present value (as of today) among (go to college) and (not going to college), and how much more valuable is it?

1. (not going to work), by $561,289.08

2. (not going to work), by $511,289.08

3. (not going to work), by $541,289.08

4. (go to college), by $511,289.08

5. (go to college), by $541,289.08

Question 5. Calculate the balance of your saving account at your retirement when you choose the career path (a) going to College. Since you already computed the present value of the career path(a), you can forget about all other cash-flows and focus on the present value which is a transformation of the whole cash-flows from the option (a). you can treat the present value as cash in your hand today. Use the formula for the future value of a single cash flow.

1. $4,057,481.55

2. $4,107,481.55

3. $4,157,481.55

4. $4,207,481.55

5. $4,257,481.55.

Question 6. Calculate the balance of your saving account at your retirement when you choose the career path (b) not going to college.

1. $2,907,897.69

2. $2,937,897.69

3. $2,967,897.69

4. $2,997,897.69

5. $3,027,897.69.

Answer 1

A.present value of paychecks when start the job

= Paycheck amount*PVAF(2%, 41 years)

= 68,000*27.799

=$1,890,365.28

I.e. 4

B.Present value of cash flows going to college

= 1,890,365.28*PVF(2℅,4 YEARS)

= $1,746,405.32

I.e. 2

3. Present value = 55,000 + 39000*PVAF(2℅, 45 YEARS)

= 1,205,116.24

I.e. 1

4. Going to college of more valuable by 1,746,405.32-1,205,116.24

=$541,289.08

I.e. 5

5.future value of single cash flow = 1,746,405.32*(1.02)^45

=$4,257,481.55

I.e. 5

6.not going to college

= 1,205,116.24*(1.02)^45

=$2,937,897.69

I.e. 2