Question

?Suppose that you are in the fall of your senior year and are faced with the choice of either getting a job when you graduate or going to law school. Of? course, your choice is not purely financial. ? However, to make an informed decision you would like to know the financial implications of the two alternatives. ? Let's assume that your alternatives are as? follows:??

If you take the? "get a? job" route you expect to start off with a salary of $40,000 per year. There is no way to predict what will happen in the? future, your best guess is that your salary will grow at 5 percent per year until you retire in 40 years. As a law? student, you will be paying ?$25,000 per year tuition for each of the 3 years you are in graduate school. ? However, you can then expect a job with a starting salary of $70,000 per year. ? Moreover, you expect your salary to grow by 7 percent per year until you retire 35 years later.???Clearly, your total expected lifetime salary will be higher if you become a lawyer. ? However, the additional future salary is not free. You will be paying 25,000 in tuition at the beginning of each of the 3 years of law school. In? addition, you will be giving up a little more than $126,000 in lost income over the three years of law? school: $40,000 the first? year, $42,000 the second? year, and $44,100 the third year.

a.??To start your analysis of whether to go to law? school, calculate the present value of the future earnings that you will realize by going directly to? work, assume a discount rate of 3 percent.

b.??What is the present value today of your future earnings if you decide to attend law? school, assuming a discount rate of 3 ?percent? Remember that you will be in law school for 3 years before you start to work as a lawyer. ? (Hint: assume that you are paid at the end of each year so that your first salary payment if you decide to go to law school occurs 4 years from? now.)

c.??If you pay your law school tuition at the beginning of each? year, what is the present value of your? tuition, assuming a discount rate of 3 ?percent?

Answer 1

Part a. You will earn $ 40000, which will grow at 5% per annum for 40 years. This is like an increasing annuity cash flows and we can calculate the present value of this cash stream using the following formula:

Present Value of growing annuity =

where A is the first annuity amount ($ 40000), r is the discount rate (3%), g is the growth rate of annuity (5%), and t is the time period (40 years). Plugging in these values we get:

PV = 40000/(3%-5%) * [1 - {(1+5%)/(1+3%)}⁴⁰?] = $2,316,313.40

Part b. The cash flows of going to law school is also like an increasing annuity and we can use the above formula except that the cash inflows will start from the end of 4th year. We will use the same formula as above which is the formula for present value of growing annuity (normal annuity where cash flows are at the end of the period).

PV of annuity at end of Year 3 = 70000/(3%-7%) * [1 - {(1+7%)/(1+3%)}³⁵?] = $ 4,889,989.66

However this needs to be further discounted to present Year 0, as below:

PV of future earnings today = 4889989.66/(1+3%)^?3? = $ 4,475,033.25

Part c. Present value of tuition fee will be as below:

Begining of Year 1 (present) = $ 25000

Begining of Year 2 (1 year hence) = $ 25000

Begining of Year 2 (2 years hence) = $ 25000

PV of future earnings = 25000 +25000/(1+3%) + 25000/(1+3%)²? = $ 72,836.74