Question

Let’s say Sam just finished high school and is deciding whether to enroll in a two-year nursing program at the local community college. The cost of the program is $10,000 per year for tuition and supplies. Because the program is so intensive, Sam cannot work if he enrolls in the program until after he graduates. Sam believes if he doesn’t enroll in the program, he’ll earn $60,000 per year. He believes that if he completes the program, he’ll earn $110,000 per year once he starts working. Because of visa issues, Sam is only allowed to stay in the country for 5 years (he will not work when he returns to his home country). Answering the following questions (showing your work):

1. Set up what Sam’s net present value calculation should look like.
2. At an interest rate of 3% (r=0.03), would you suggest that Sam enrolls in the program?
3. At an interest rate of 2%, would you suggest that Sam enrolls in the program?
4. What if Sam’s visa allowed him to stay for an extra year at the original 3% interest rate?

Answer 1

Solution

Given that Sam just finished his high school.She needs to choose between the 2 choices - to join (or) to not join the 2 year nursing program.The net present value of both the choices would be different.He will have to choose the one with the highest net present value.He has a time limit to stay only for the next 5 years.

a.

Option 1 - Not enrolling into the program

NPV 1 = (60000 / (1+(r/100))) + (60000 / (1+(r/100) ^2)) + (60000 / (1+(r/100) ^3)) + (60000 / (1+(r/100) ^4)) + (60000 / (1+(r/100) ^5))

Option 2 - Enrolling into the program

Assuming that the tuition fee is to be paid at the end of each year for the 2 year course

NPV 2 = - (10,000 / (1+(r/100))) - (10,000 / (1+(r/100) ^2)) + (110,000 / (1+(r/100) ^3)) + (110,000 / (1+(r/100) ^4)) + (110,000 / (1+(r/100) ^5))

Here,in the above equations,"r" is the rate of interest.

b.At an interest rate of 3%

NPV 1 = (60000 / (1+(3/100))) + (60000 / (1+(3/100) ^2)) + (60000 / (1+(3/100) ^3)) + (60000 / (1+(3/100) ^4)) + (60000 / (1+(3/100) ^5))

=> 58252.42 + 56555.75 + 54908.49 + 53309.22 +51756.52

=> $ 274,782.40

NPV 2 = - (10,000 / (1+(3/100))) - (10,000 / (1+(3/100) ^2)) + (110,000 / (1+(3/100) ^3)) + (110,000 / (1+(3/100) ^4)) + (110,000 / (1+(3/100) ^5))

=> - 9708.73 - 9425.95 + 100665.58 + 97733.57 + 94886.96

=> $ 274,151.43

So SAM needs to choose the option to NOT enrol into the 2 year nursing course

c. At an interest rate of 2%

NPV 1 = (60000 / (1+(2/100))) + (60000 / (1+(2/100) ^2)) + (60000 / (1+(2/100) ^3)) + (60000 / (1+(2/100) ^4)) + (60000 / (1+(2/100) ^5))

=> 58823.53 + 57670.12 + 56539.34 + 55430.72 +54343.84

=> $ 282,807.55

NPV 2 = - (10,000 / (1+(2/100))) - (10,000 / (1+(2/100) ^2)) + (110,000 / (1+(2/100) ^3)) + (110,000 / (1+(2/100) ^4)) + (110,000 / (1+(2/100) ^5))

=> - 9803.92 - 9611.68 + 103655.45 + 101622.99 + 99630.39

=> $194,033.23

SAM would not enrol into the program

d.If SAM was allowed to stay for an additional 1 year and the interest rate is 3% p.a

NPV 1 = (60000 / (1+(3/100))) + (60000 / (1+(3/100) ^2)) + (60000 / (1+(3/100) ^3)) + (60000 / (1+(3/100) ^4)) + (60000 / (1+(3/100) ^5)) + (60000 / (1+(3/100) ^6))

=> 58252.42 + 56555.75 + 54908.49 + 53309.22 +51756.52 + 50,249.05

=> $ 274,782.40

NPV 2 = - (10,000 / (1+(3/100))) - (10,000 / (1+(3/100) ^2)) + (110,000 / (1+(3/100) ^3)) + (110,000 / (1+(3/100) ^4)) + (110,000 / (1+(3/100) ^5)) + (110,000 / (1+(3/100) ^6))

=> - 9708.73 - 9425.95 + 100665.58 + 97733.57 + 94886.96 + 92,123.26

=> $ 3,66,274.69

In this case,SAM would choose to enrol into the 2 year nursing program

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