Question

Suppose we can think of dividing a person’s working years up into three periods. The person has three alternatives. The first is for her to start working immediately, earning $100,000 ($100k) in period 1, $110k in period 2, and $90k in period 3. The second is to spend $50k to attend college in period 1, then earn $180k in each of periods 2 and 3. The third is to attend college in period 1 (as in the previous option), attend graduate school in period 2 (which entails no spending or earnings), and earn $400k in period 3.

a. If her period discount rate is 20%, which option maximizes the net present value (NPV) of her lifetime earnings (net of costs)?

b. How low must her discount rate get to change the answer you got for part (a)? (Using a spreadsheet would be very helpful. Try lowering her discount rate 1 percentage point at a time so see how the NPV of each alternative is affected.)

Answer 1

Answer:

a)

Given that the discounting rate is 20%.

Option 1:

If the person starts earning in period 1:

Net Present Value of earnings in three periods($100,000 in period 1, $110000 in period 2 and $90000 in period 3) =$100000/(1+20/100)+$110000/(1+20/100)2+$90000/(1+20/100)3=$83,333+76,389+52083=$2,11,805.

Option 2:

NPV=-$50000/(1+20/100)+$180000/(1+20/100)2+$180000/(1+20/100)3=-$41,667+125,000+104,167=$187,500.

Option 3:

NPV=-$50000/(1+20/100)+$400000/(1+20/100)3=-$41,667+$231,481=$189,814.

NPV is highest in Option 1.

b)

Option 3 is giving the second alternative to Option 1 as it is giving NPV higher than the Option 2.

If she want to change the answer from Option 1 to Option 3 then calculation will be as follows:

At 12 % discount rate:

Option 1:

NPV=100000/1.12+110000/(1.12)2+90000/(1.12)3=241,037.

Option 3:

NPV=-50000/1.12+400000/(1.12)3=240,070.

At 11% discount rate:

Option 1:

NPV=100000/1.11+110000/(1.11)2+90000/(1.11)3=245,206.

Option 3:

NPV=-50000/1.11+400000/(1.11)3=247,432.

So, at the discounting rate of 11% Option 3 is having higher NPV and the answer from a) is changed from Option 1 to Option 3

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