July 9, 2020

Calculating Net Present Value

The Return on Education Model projects annual cash flows to 39 years for both the proposed  career (education and working) and the alternate career. The net difference in cash flow between the proposed career and the alternate career is determined for each of the 39 years, with the result being a series of negative values followed by a series of positive values. Years during the training period consist of cash outflows from the perspective of the proposed career (invested funds). Cash inflows begin immediately upon graduation with employment in the proposed career.

The formula for calculating the net cash flow to the proposed career for each year is:

Net Annual Cash Flow = Proposed Career Total Compensation – Direct Education Costs Not Borrowed – Alternate Career Total Compensation – Education Loan Payment – Foregone Interest on Personal Funds

Step-by-Step Example

What follows is a step-by-step example of how the cash flow for each year is determined. This example assumes a first-year direct cost of education to be $25,000, a starting compensation of $65,000 with annual increases of 11%, 24%, 7%, 5% and 3% thereafter, and the percentage of financing set at 50%, of which repayment is amortized over 15 years with the first annualized payment beginning at the end of the first year of employment. The discount rate is 3% and the investment rate is 5%. To simplify this example, nominal dollar values are used rather than discounted values.

During the first four years of training when compensation is not received, all cash flows to the proposed career are negative. While the four-year direct cost of education is $106,161, which is based on a $25,000 first-year cost with 4% increases each year, only the portion not borrowed ($53,081 that is paid from personal funds) is counted as a cash outflow. Foregone income from the alternate career is $198,365, which is based on a starting total compensation of $40,000 per year with increases of 11%, 24%, 7%, 5%, and 3% thereafter to maintain parity with the annual increases in the proposed career, though this is not a requirement. In addition, foregone interest income during the four years is $6,830. Therefore, the NPV upon graduation is based on the financial difference between the proposed and alternate career, which is a negative $246,077. Since the portion of borrowed tuition ($53,081) and interest on borrowed tuition and living expenses ($12,825) are repaid during the loan repayment period, they are accounted for in the cash flow during those years. However, if one views these values as commitments made during the first four years, the net difference in nominal dollars at the end of four years is a negative $324,181.

In year five of this example, employment in the proposed career begins and a total compensation of $65,000 is received, which is $3,146 more than what would have been received from working in the alternate career in that same year. In addition, foregone interest income is $2,994. Also in year five, education costs are $0 and remain so from then on, and the first annualized loan payment of $8,516 is due, which results in a net negative cash flow of $8,364. Recall that this negative cash flow is used solely to calculate the NPV when compared to the alternate career. The actual gross income after the first loan payment for year five in this example is $56,484. During years six, seven, eight, and nine, compensation in the proposed career increase by 11%, 24%, 7%, and 5%, which results in annual compensations of $72,150; $89,466; $95,729 and $100,515 respectively. During this same period, the annual compensations from the alternate career are considerably lower at $63,710; $65,620; $67,589; and $69,616 respectively. The initial increases that are just now influencing the compensation in the proposed career have already been applied in the alternate career beginning with its first annual increase.

Net Present Value

Net Present Value (NPV) is the value today of a series of cash flows over time and is reported in dollars. These cash flows can represent past financial activity or activity that is projected to occur. The cash flows used to calculate NPV can be all positive or negative, or a mix of positive and negative values that are consecutive or interspersed.

Discount Rate for Net Present Value

One might be tempted to use the nominal value of dollars (the actual amounts) invested and received each year during one’s training and working in a proposed career to calculate a profit or loss, but this would not account for the declining value of dollars over time. For example, if one receives $1,000 each year for 39 years, the purchasing power or value of the $1,000 received in year 39 would be considerably less than the $1,000 received in the first year. In order to account for this decline in value over time, the NPV calculation uses a discount rate that is a percentage by which the nominal value of dollars invested and received in the future is adjusted downward (discounted) to reflect their decrease in value relative to the value of dollars received in the first year. For example, a discount rate of 5% means that the $1,000 received in the second year would be equivalent to $952.38 of value ($1,000/1.05) when compared to $1,000 received in the first year. In the same way, $1,000 received in the third year is reduced by an additional 5% ($1,000/1.05/1.05) because it was received two years from the first year. Therefore, $1,000 in the third year would have a NPV of $907.03 when compared to the value of first year dollars. Returning to the example of receiving $1,000 each year for 39 years with a discount rate of 5%, receiving $17,867.89 as a one-time payment in the first year would have the same NPV as receiving $1,000 every year for 39 years.

Foregone income from the alternate career consisted of two sources. The first was direct compensation, which is the total salary and benefits that would have been received from working in the alternate career. In the example above, this compensation was set at $40,000 for the first year and then increased by the same annual percentages as those used for the proposed career.

The second source of foregone income is interest on personal funds that would have been received during the alternate career had those funds not been used to obtain the additional education for the proposed career. This amount is calculated on the percentage of the direct cost of education that is not borrowed. In the above example, the interest rate for these funds had they been invested for 39 years was set at 5%.

Foregone interest income is not always a factor. For example, if no funds were borrowed, meaning that all expenses were paid from personal funds, the foregone interest on those personal funds is calculated at 5% on 100% of the direct cost of education. However, if the level of financing was 75% then foregone interest is calculated on only 25% of those costs. Finally, if 100% of the costs to acquire the additional education were financed, meaning that no personal funds were used, there is no foregone interest income.

Future Work

The Return on Education Model is intended in its current form to be used as a tool for studying broad trends and potential impacts of various personal and organizational interventions in the cost of education such as changes in the direct cost of education to students, increasing the availability of cost-effective financing, and the establishment of alternative repayment programs.

That said, future enhancements to this model could include: 1) the capacity to track income earned while in training, 2) the ability to assign different living expenses to both careers, as students in training often make sacrifices and live in a way that differs from others who would be more established in an alternate career, 3) the ability to account for income taxes in both the proposed and alternate careers, 4) various options of loan repayment or forgiveness, and 5) a provision for temporary interruptions in both the proposed and alternate careers such as could occur with having children or taking care of a family member who has a prolonged illness.