Question

3. Catherine is considering going to medical school. If she does, she will spend $80,000 on tuition and books to get a college education (during the first time period), $120,000 on tuition and books to get a medical degree (during the second time period), and her medical degree will earn her $500,000 during the remainder of her work-life (during the third time period). Her time preference for money (her discount rate) is 20 percent.

a. What is Catherine's present value of obtaining a medical degree?

b. Suppose that Catherine is also considering an alternative career path, in which she obtains a college education in the first period (with the same costs as before) and enters the work force immediately as a marketing analyst. She earns $100,000 in the second period and $200,000 in the third period under this option. Will she choose to become a doctor or a marketing analyst? Show your work.

c. If Catherine’s discount rate is 10 percent, will this change her decision? Show your work.

Answer 1

a.

Given information are

Catherine spends $80,000 in first time period , $120,000 in second time period m and earns $500,000 in thord time period. And her discount rate is 20%

To find total present value(PV) of her education we need to do following exercise –

Substract present value of her total spending from present value of her earnings.

And pv of any investment is calculated as

PV = A / (1 +r)ⁿ ;

where A = amount spent or earned , and

r = discount rate

n = time period elapsed

Now PV of first time period = $80,000 ( no discount rate effect will be here as it is paid in first time period i.e. at time elapsed =0)

PV of second time period =($120,000) / (1+ 0.2)¹ = ($120,000) / (1.2)¹ = 100,000

PV of third time period = ($500,000) / (1 +0.2)² = = ($500,000) / (1.2)² = $ 347222.2

So final PV is = $347222.2 – (80,000 +100,000) = $ 167222.2

So PV for medical education of Catherine is = $ 167222.2

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b.

in this case also the similar calculations would be there.

PV of first time period = $ 80,000

PV of second time period = $100,000 / 1.2 = $ 83,333.3

PV of third time period = $200,000 / (1.2)² = $138,888.9

So required PV = total pv of earnings – total pv of expenditure

= 83,333.3 + 138,888.9 - 80,000 = $142,222.2

So, PV for alternative career path = $142,222.2

Now we see that PV of becoming doctor is $ 167222.2 which is greater than PV for alternative career path is $142,222.2. So, she will choose to become a doctor.

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c.

now if her discount rate changes to 10% i.e. 0.1 , the calculations would change.

For being a doctor –

PV of first time period = $80,000

PV of second time period =($120,000) / (1+ 0.1)¹ = ($120,000) / (1.1)¹ = $109,090.9

PV of third time period = ($500,000) / (1 +0.1)² = = ($500,000) / (1.1)² = $ 413,223.1

So final PV is = $413,223.1– (80,000 +109,090.9) = $ 224,132

So PV for medical education of Catherine is = $ 224,132

Similarly for alternative career path

PV of first time period = $ 80,000

PV of second time period = $100,000 / 1.1 = $ 90909.09

PV of third time period = $200,000 / (1.1)² = $ 165,289.3

So required PV = total pv of earnings – total pv of expenditure

= 90909.09+ 165,289.3 - 80,000 = $176,198.3

So, PV for alternative career path = $176,198.3

Now again we see that PV of becoming doctor is $ 224,132 which is greater than PV for alternative career path is $176,198.3. So, she will choose to become a doctor