Ralph is trying to decide whether to go to graduate school. If he spends two years in graduate school, paying \(15,000 tuition each year, he will get a job that will pay \)60,000 per year for the rest of his working life. If he does not go to school, he will go into the workforce immediately. He will then make \(30,000 per year for the next three years, \)45,000 for the following three years, and $60,000 per year every year after that. If the interest rate is 10 percent, is graduate school a good financial investment?

The present value if Ralph goes to graduate school is calculated below:

$$\begin{gathered} \text{r =}\frac{\text{10}}{\text{100}} \\ \text{= 0.1} \\ \text{n = 1,2,3,4,5,6} \\ {\text{PV}}_{\text{GS}}\text{= - 15,000}{\left(\text{1 + 0.1}\right)}^{\text{- 1}}\text{- 15,000}{\left(\text{1 + 0.1}\right)}^{\text{- 2}}\text{+ 60,000}{\left(\text{1 + 0.1}\right)}^{\text{- 3}}\text{+} \\ \text{60,000}{\left(\text{1 + 0.1}\right)}^{\text{- 4}}\text{+ 60,000}{\left(\text{1 + 0.1}\right)}^{\text{- 5}}\text{+ 60,000}{\left(\text{1 + 0.1}\right)}^{\text{- 6}} \\ =\text{- 15,000}\left(\text{0.9091}\right)\text{- 15,000}\left(\text{0.8264}\right)\text{+ 60,000}\left(\text{0.7513}\right)\text{+} \\ \text{60,000}\left(\text{0.6830}\right)\text{+ 60,000}\left(\text{0.6209}\right)\text{+ 60,000}\left(\text{0.5645}\right) \\ =\text{- 13636.5 - 12396 + 45078 + 40980 + 37254 + 33870} \\ =\text{\$ 131149.5} \end{gathered}$$

The present value if Ralph does not go to graduate school is calculated below:

$$\begin{gathered} \text{r =}\frac{\text{10}}{\text{100}} \\ \text{= 0.1} \\ \text{n = 1,2,3,4,5,6} \\ {\text{PG}}_{\text{WGS}}\text{= 30,000}{\left(\text{1 + 0.1}\right)}^{\text{- 1}}\text{+ 30,000}{\left(\text{1 + 0.1}\right)}^{\text{- 2}}\text{+ 30,000}{\left(\text{1 + 0.1}\right)}^{\text{- 3}}\text{+} \\ \text{45,000}{\left(\text{1 + 0.1}\right)}^{\text{- 4}}\text{+ 45,000}{\left(\text{1 + 0.1}\right)}^{\text{- 5}}\text{+ 45,000}{\left(\text{1 + 0.1}\right)}^{\text{- 6}} \\ =\text{30,000}\left(\text{0.9091}\right)\text{+ 30,000}\left(\text{0.8264}\right)\text{+ 30,000}\left(\text{0.7513}\right)\text{+} \\ \text{45,000}\left(\text{0.6830}\right)\text{+ 45,000}\left(\text{0.6209}\right)\text{+ 45,000}\left(\text{0.5645}\right) \\ =\text{27273 + 24792 + 22539 + 30735 + 27940.5 + 25402.5} \\ =\text{\$ 158682} \end{gathered}$$

The present value of not going to graduate school is more than that of going to graduate school. Hence, the best option for Ralph is not to go to graduate school.