Question

Ignore picture question--wrong image was chose!!

Don Draper has signed a contract that will pay him $80,000 at the end of each yesr for the next 5 years, plus an additional $110,000 at the end of year 5. If 12 percent is the appropriate discount rate, what is the present valye of this contract? (Comprehensive Problem) 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 45 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 $75,000 per year. Moreover, you expect your salary to grow by 7 percent per year until you retire 38 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

a. To calculate the present value of the future earnings if you go directly to work, we need to calculate the present value of the salary stream over the 45 years. The salary is expected to grow at a rate of 5% per year. The discount rate is 3%.

Let's break down the calculation:

Year 1:

Salary = $40,000

Present Value = $40,000 / (1 + 0.03)^1

Year 2:

Salary = $40,000 * (1 + 0.05)

Present Value = $40,000 * (1 + 0.05) / (1 + 0.03)^2

Year 3:

Salary = $40,000 * (1 + 0.05)^2

Present Value = $40,000 * (1 + 0.05)^2 / (1 + 0.03)^3

...

Year 45:

Salary = $40,000 * (1 + 0.05)^44

Present Value = $40,000 * (1 + 0.05)^44 / (1 + 0.03)^45

To calculate the present value, we sum up the present values of each year's salary:

Present Value = Σ [Salary / (1 + 0.03)^t] for t = 1 to 45

b. To calculate the present value of your future earnings if you decide to attend law school, we need to consider the salary stream starting after the 3 years of law school. The salary is expected to grow at a rate of 7% per year. The discount rate is 3%.

Let's break down the calculation:

Year 4:

Salary = $75,000

Present Value = $75,000 / (1 + 0.03)^4

Year 5:

Salary = $75,000 * (1 + 0.07)

Present Value = $75,000 * (1 + 0.07) / (1 + 0.03)^5

...

Year 42:

Salary = $75,000 * (1 + 0.07)^38

Present Value = $75,000 * (1 + 0.07)^38 / (1 + 0.03)^42

To calculate the present value, we sum up the present values of each year's salary:

Present Value = Σ [Salary / (1 + 0.03)^(t+3)] for t = 1 to 42

c. To calculate the present value of the law school tuition, we consider the payment at the beginning of each year for 3 years. The tuition is $25,000 per year. The discount rate is 3%.

Let's break down the calculation:

Year 1:

Tuition = $25,000

Present Value = $25,000 / (1 + 0.03)

Year 2:

Tuition = $25,000

Present Value = $25,000 / (1 + 0.03)^2

Year 3:

Tuition = $25,000

Present Value = $25,000 / (1 + 0.03)^3

To calculate the present value, we sum up the present values of each year's tuition:

Present Value = Σ [Tuition / (1 + 0.03)^t] for t = 1 to 3