A student is trying to decide whether or not to go to college. His two options a

Question

A student is trying to decide whether or not to go to college. His two options are to get 12 years of education or 16 years (nothing in between). If he stops after high school, he will earn $20,000 in the first year of work, and his salary goes up by $1,000 each year. He works for 50 years. If he goes to college, he pays $10,000 in tuition for each of the four years of college. He then earns $35,000 in his first year of work, and his salary goes up by $1,200 each year. He works for 46 years, since he was in school for the first four years of his “working-age” life.

For each of the following values of the discount rate r, find the present value of being a high school graduate and the present value of being a college graduate, and determine whether he will go to college or not. You will need to use a program like Excel to do this.

1. r = 0.05
2. r = 0.08
3. r = 0.15
4. Explain, in words, why the answer changes as the discount rate r gets higher.

Explanation / Answer

(The value are taken from compound interest factor tables)

1. If student stops at high school

Here A is $20000 and G is $1000, n is 50, i is 0.05

PW= 20000(P/A,5%,50)+1000(P/G,5%,50)=20000(18.2559)+1000(277.9147)=365118+277915=$643033

If student goes to college

Here A is $35000 and G is $1200, n1 is 46, n2 is 4, i is 0.05

PW= (35000(P/A,5%,46)+1200(P/G,5%,46))(P/F,5%,4) =(35000(17.88)+1200(260.0843))(0.8227) =$771611

2. If student stops at high school

Here A is $20000 and G is $1000, n is 50, i is 0.08

PW= 20000(P/A,8%,50)+1000(P/G,8%,50)=20000(12.2334)+1000(139.5927)=244668+139593=$384261

If student goes to college

Here A is $35000 and G is $1200, n1 is 46, n2 is 4, i is 0.08

PW= (35000(P/A,8%,46)+1200(P/G,8%,46))(P/F,8%,4) =(35000(12.1374)+1200(135.0384))(0.735) =$431338

3. If student stops at high school

Here A is $20000 and G is $1000, n is 50, i is 0.15

PW= 20000(P/A,15%,50)+1000(P/G,15%,50)=20000(6.6605)+1000(44.0958)=133210+44096=$177306

If student goes to college

Here A is $35000 and G is $1200, n1 is 46, n2 is 4, i is 0.015

PW= (35000(P/A,15%,46)+1200(P/G,15%,46))(P/F,15%,4) =(35000(6.6559)+1200(43.8777))(0.5717) =$163283

4. When the discount rate are getting higher then the present value is coming down because high interest rates means that future value of money will be high due to high interest rates and the present value will be small.

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