Question

1. Suppose you are trying to decide between medical school and working in the technology sector. To simplify let’s assume 4 time periods. If you go to medical school your earnings in period 1 are -$100,000, $50,000 in period 2, $300,000 in period 3, and $500,000 in period 4. Conversely if you choose to work in technology your earnings are: $50,000 in period 1, $75,000 in period 2, $125,000 in period 3, and $250,000 in period 4.
   1. If your discount factor is 0.2, what is the NPV for each job? Which would you choose?
   2. What about if the discount factor were 0.9?
   3. Would someone necessarily choose the job with the highest NPV? Explain why or why not.

Answer 1

Case (a) NPV for each job, discounting factor = 0.2

NPV will be calculated using formula:

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r = discounting factor

C_i=future cash flows

C₀=initial cash flow

Medical School

Period	Cash Flows ($)	Present Value Factor		Present Value
0	-1,00,000	1	1	-1,00,000.00
1	50,000	1/(1+r)^1	0.833333	41,666.67
2	3,00,000	1/(1+r)^2	0.694444	2,08,333.33
3	5,00,000	1/(1+r)^3	0.578704	2,89,351.85

r = Discounting Factor

Present Value = Cash Flow * Present Value Factor

NPV = - 1,00,000.00 + 41,666.67 + 2,08,333.33 + 2,89,351.85 = 4,39,351.85 ---> (sum of present values)

Technology Sector

Period	Cash Flows ($)	Present Value Factor		Present Value
0	50,000	1	1	50,000.00
1	75,000	1/(1+r)^1	0.833333	62,500.00
2	1,25,000	1/(1+r)^2	0.694444	86,805.56
3	2,50,000	1/(1+r)^3	0.578704	1,44,675.93

r = Discounting Factor

Present Value = Cash Flow * Present Value Factor

NPV = 50,000.00 + 62,500.00 + 86,805.56 + 1,44,675.93 = 3,43,981.48 ---> (sum of present values)

Since, NPV of Medical School is higher than working in Technology Sector, thus, I will choose Medical School.

Case (b) NPV for each job, discounting factor = 0.9

using case (a) approach, we will calculate NPV

Medical School

Period	Cash Flows ($)	Present Value Factor		Present Value
0	-1,00,000	1	1	-1,00,000.00
1	50,000	1/(1+r)^1	0.526316	26,315.79
2	3,00,000	1/(1+r)^2	0.277008	83,102.49
3	5,00,000	1/(1+r)^3	0.145794	72,896.92

r = Discounting Factor

Present Value = Cash Flow * Present Value Factor

NPV = - 1,00,000.00 + 26,315.79 + 83,102.49 + 72,896.92= 82,315.21 ---> (sum of present values)

Technology Sector

Period	Cash Flows ($)	Present Value Factor		Present Value
0	50,000	1	1	50,000.00
1	75,000	1/(1+r)^1	0.526316	39,473.68
2	1,25,000	1/(1+r)^2	0.277008	34,626.04
3	2,50,000	1/(1+r)^3	0.145794	36,448.46

r = Discounting Factor

Present Value = Cash Flow * Present Value Factor

NPV = 50,000.00 + 39,473.68 + 34,626.04 + 36,448.46 = 1,60,548.18 ---> (sum of present values)

Since, with discounting factor of 0.9, NPV of working in Technology Sector is higher than Medical School, thus, I will choose working in Technology Sector.

Case (c) Yes, someone should choose job with highest NPV because present value of money is higher than future value of money as inflation or interest rates reduce the value of money. This will result in higher purchasing power for the user or higher return on investments. Thus, with cases of highest NPV, user can earn more or spend more in future in comparison to lowest NPV cases.