Rebecca is 25 and considering going to graduate school so she sits down to calculate whether it is worth the large sum of money. She knows that her first year tuition will be $52,000, due at the beginning of the year (that is, right away). She estimates that the 2nd year of tuition would be $54,000. She also estimates that her living expenses above and beyond tuition will be $10,000 per year (assume this extra expense occurs at the end of each year only when she is in graduate school) for the first year and will increase to $11,000 the next year. She expects to earn $23,000 for an internship (Assume this inflow occurs one year from now). Were she to forgo graduate school she would be able to make $66,000 at the end of this year and expects that to grow 4% annually. With a graduate degree, she estimates that she will earn $98,000 per year after graduation, again with annual 4% increases. Either way, she plans to work until 63. The interest/discount rate is 5%. What is the NPV of her graduate education? (Note: All cash flows except tuition payments occur at the end of the year.
To calculate the Net Present Value (NPV) of Rebecca's graduate education, we need to consider the cash flows, the discount rate, and the time horizon.
First, let's break down the cash flows:
1. Tuition payments:
- Year 0 (beginning of the year): $52,000
- Year 1: $54,000
2. Living expenses:
- Year 1: $10,000
- Year 2: $11,000
3. Income from internship:
- Year 1: $23,000
4. Opportunity cost of not attending graduate school:
- Year 0 (end of the year): $66,000
- Annual growth rate: 4%
5. Post-graduation income with annual growth:
- Year 2 (end of the year): $98,000
- Annual growth rate: 4%
Now, let's calculate the Net Present Value using the following formula:
NPV = Σ(CF_t / (1 + r)^t) - Tuition
Where:
- NPV is the Net Present Value
- CF_t is the cash flow in year t
- r is the discount rate
- t is the time period
Step 1: Calculate the present value of the cash flows.
- Tuition payments:
NPV_tuition = (-$52,000 / (1 + 0.05)^0) + (-$54,000 / (1 + 0.05)^1) = -$98,374.97
- Living expenses:
NPV_living_expenses = (-$10,000 / (1 + 0.05)^1) + (-$11,000 / (1 + 0.05)^2) = -$19,274.98
- Income from internship:
NPV_internship = $23,000 / (1 + 0.05)^1 = $21,904.76
- Opportunity cost of not attending graduate school:
NPV_opportunity_cost = $66,000 / (1 + 0.05)^0 + ($66,000 * 0.04) / (1 + 0.05)^1 + ($66,000 * 0.04) / (1 + 0.05)^2 + ($66,000 * 0.04) / (1 + 0.05)^3 = $190,076.38
- Post-graduation income with annual growth:
NPV_post_graduation_income = $98,000 / (1 + 0.05)^2 + ($98,000 * 0.04) / (1 + 0.05)^3 + ($98,000 * 0.04) / (1 + 0.05)^4 + ... + ($98,000 * 0.04) / (1 + 0.05)^38 = $1,299,889.64
Step 2: Aggregate the cash flows (excluding tuition):
CF = NPV_living_expenses + NPV_internship + NPV_opportunity_cost + NPV_post_graduation_income = -$19,274.98 + $21,904.76 + $190,076.38 + $1,299,889.64 = $1,492,596.80
Step 3: Calculate the final NPV:
NPV = CF - Tuition = $1,492,596.80 - $98,374.97 = $1,394,221.83
Therefore, the NPV of Rebecca's graduate education is approximately $1,394,221.83.