The Time Value of Money in Farm Decision Making – Part 2.

Discounting works in the opposite direction of compounding. It is the present value for money that can be paid now or be equally compared to receiving a payment or series of payments in the future.

Discounting determines the Present Value (PV) of a sum of money to be received in the future, so income and costs from different years can be compared. This concept is essential for project evaluation because it allows us to compare the value of future cash flows with their value today.

For example, if you are to receive $1,000 in two years and the discount rate is 5%, the present value of that $1,000 today would be $907, almost 10% loss in value.

To obtain the present value, we need to rearrange the present value of future money to its present value:

PV = FV/(1+r)ⁿ

PV = 1,000/(1+0.05)² = $907

PV = 1,000/(1.1025) = $907

Alternatively, this formula can be expressed as:

PV = FV(1+r)^-n

PV = 1,000(1+0.05)^-2

PV = 1,000(0.907) = $907

PV = present value
FV = future value
r = interest rate
n - number of years or discounting periods

The present value factors for given discount rates over 10 years period for one dollar are also shown in Table 1.

For example, the present value of one dollar will lose half of its value in nine years at eight percent interest rate (Table 1). Today's present value of $1,000 in nine years at eight percent interest rate would be $500 today.

Determining Discount Rate

The most important thing for each farm operation is to select the best discount rate that fits its needs. There is no discount rate that will fit every operation at all times. Operators must determine how much return they need and how much risk they are willing to accept. The selection of the interest and discount rate should answer the question of what the investment is for. If it is for a long-term investment, a few points difference in discount rate can make a large difference in present value results.

The discount rate can also be viewed as the desired minimum rate of return required to offset time, inflation, and risk premiums.

To quickly determine a discount rate, a producer can look at the nominal rate used by local banks on U.S. government-insured security accounts that are comparable to the lifetime of the farm’s investment or the farm's current loan rate. For example, a farmer decides to expand a livestock facility at the value of $150,000. It is expected that there will be $35,000 per year additional income for the next 5 years. So, the total return would be $175,000 in 5 years. But considering the market fluctuation, the producer would settle with a return of $30,00 per year or $150,000 in 5 years. A local lender charges an interest rate of 9 percent. The producer should research the best option for 5-year return on the investment.

In order to compare the additional income during next five years with today’s money or present value, the additional income needs to be discounted. Adding all discounted values for all five years gives the total PV of the projected income.

The formulas to calculate the present values of the future income is as follow:

PV = FV/(1+r)ⁿ

PV = 35,000/(1+0.09)¹ ………..….  35,000/(1+0.09)⁵
           (Year 1)                                (Year 5)

r = interest rate
n - number of years or discounting periods

Alternatively, discount factors from Table 1. can be used to calculate the present values of the future income for different interest rates.

If the Time Value of Money (TVM) is ignored, the expected annual income would be $35,000 per year in today’s value, or $175,000 for five years, which would exceed the initial investment. However, the cash inflow needs to be discounted for each of the five years. Adding all five-year discounted values gives the total Present Value (PV) of the projected income (Table 2).

The results in Table 2 suggest that the desired five-years return timeline is not feasible under the interest rate of 9 percent. In the first year after the investment, the annual income would be only $32,095, the second year $29,470, and finally in the fifth year only $22,860 (Table 2). The return would only be $136,115 in 5 years, well below the $150,000 mark. With the projected income and 9 percent interest, it would take six years to recover the $150,000 mark.

Another way is to estimate how much income in future money would be needed during next five years when the interest rate is 9 percent.

Based on the future value of present money calculation, the $35,000 annual income at 9 percent interest rate would be as follows: Year 1: $38,150, Year 2: $41,584; Year 3: $45,326; Year 4: $49,405; and Year 5: $53,582; a five-year total of $228,317. The producer would have to increase income by about $3,500 to $4,500 every year for the next five years.

This discounted cash flow projection is based on annual discounts. Should the interest be discounted monthly, the present value of the future cash flow for the five-year period would be about $1,311 less, $134,804 total (Table 3).

Conclusion

The Time Value of Money is a fundamental concept in project evaluation and financial decision-making. By understanding the principles of compounding and discounting, farmers and managers can make informed decisions about the allocation of resources and the viability of projects. In agriculture, TVM plays a crucial role in evaluating investment, allocating resources, and avoiding wrong decisions that can negatively impact a farmer's bottom line.

The Importance of Time Value of Money in Decision Making – Part 1

References

Cushing T. 2024. Time Value of Money. University of Florida.

Damodaran A. 2020. The Time Value of Money.

Hanson, J.C., Lessley, B. V., Johnson, D. M. 1991. Analyzing Investment Opportunities: Time Value of Money Farm Decision Making. University of Maryland.

Hofstrand, D. 2023. Understanding the Value of Money. Iowa State Extension.

Hussain R. 2012. Time Value of Money, Penn State Scranton.

LaDue, E. L. 1993. Time Value of Money. Cornell University.

Rita. 2005. Understanding the Value of Time and Money. NM Agriscience.