The Time Value of Money in Farm Decision Making - Part 1

The Time Value of Money refers to the fact that a dollar today is worth more than a dollar in the future. This principle is based on the opportunity cost of capital, which means that money available now can be invested in earning returns over time.

The Time Value of Money (TVM) is a fundamental concept and a critical principle in financial decision-making. Farm managers can use TVM to make more informed decisions about the allocation of resources and the viability of projects.

Investment or project evaluation using TVM Analysis provide farm managers with several advantages.

For example, managers can make more accurate investment decisions. Considering the TVM can reveal the true costs and uses of investment options like loans, capital projects and leases. It factors in opportunity costs and the effects of inflation, leading to more informed choices, identifying higher returns.

Managers can compare the present net value and internal rate of return and account for the timing of several cash flows, enabling accurate "apples to apples" comparisons of options. Ignoring time value can lead to unrealistic projections of future costs and revenues.

Including TVM into decision making helps managers better allocate their financial capital to earn higher returns and create more value.

Farms that apply time value of money concepts to decisions related to investing, financing and operations tend to be more profitable and better over time. It can make a competitive advantage.

Accounting for time value helps to clarify the risks in options like taking out loans or delaying capital costs. This supports more effective risk management.

However, there are also limitations of TVM investment evaluations. Time Value of Money analysis relies on managers’ assumptions about interest/discount rates, inflation and opportunity costs that may prove wrong over time which may lead to overestimating cash flows or underestimating risk. Many times, constant interest rates and inflation are used, ignoring market fluctuations. Over a long-term projection, as the assumed interest rate accuracy can weaken/deteriorate, project re-evaluation and adjustments would be warranted. Time Value of Money evaluation can also be perceived as too complex requiring specialized knowledge which can add costs.

For instance, if you have $1,000 today (present value, PV) you have a few choices to make to decide what to do with the money. You can do nothing and keep it for future, but you know that it will lose value over time due to inflation. To avoid this devaluation, you can protect yourself either by spending it today on food or other basic needs and utilize the current value immediately. You could also invest it and earn interest, making it worth more in the future.

There are two basic concepts: compounding (or future value of present money) and discounting (or present value of future money).

The Future Value of Present Money - Compounding

Compounding is the process of calculating the future value of present money that is invested today. It involves earning interest on both the initial principal and the accumulated interest from previous periods.

Figure 1 shows changes in compounded value of a dollar for interests of 3, 5, 8, and 10% over a 20 year period.

The only numbers needed to know are the initial investment, interest rate, and number of years or investment periods of the investment.

For example, a $1,000 invested today at an annual interest rate of 5% will have a future value (FV) of $1,050 after one year.

The formula is:

PV * (1+ r) = FV

$1,000 * (1+0.05) = $1,050

PV = Present Value

r = Interest Rate

FV = Future Value

In the second year, with the same interest rate, an interest will be earned not only on the initial $1,000 but also on $50 in the first year.

PV * (1+ r)ⁿ = FV

$1,000*(1+0.05)² = $1,102.50

PV = Present Value

r = Interest Rate (Table 1)

n = Number of Years

FV = Future Value

The total at the end of the second year would be $1,102.50. This process continues, and the investment grows exponentially over time.

Table 1 demonstrates the impact of annual compounding of different interest rates on a value of one dollar for a timeline of 20 years.

For example, the value of one dollar will double in nine years at eight percent interest rate. An investment of $1,000 will have value of $1,999 (Table 1).

In the above example it is assumed that the interest rate is compounded annually where nominal interest rate equals to effective interest rate.

However, payments can be made more frequently than annually, from semi-annually to daily. The frequency of compounding affects the future and present values of cash flows as well. The nominal interest rate can deviate significantly from the effective interest rate.

The nominal or quoted interest rate does not account for compounding. The effective interest rate or Effective Annual Rate (EAR) is the true interest rate paid, reflecting the effect of compounding interest. It is charged more frequently than the nominal interest rate. Both nominal and effective interest rates are before inflation is taken out.

The only time when nominal interest rate is equal to effective interest rate is when compounding is calculated annually. The distinction is important when interest is compounded over a period different from that expressed by the interest rate, e.g. more than once a year.

If the compounding is semi-annually, the interest rate is r/2 per six months, and the compounding occurs twice a year (2 times in n years) the formula would change as follows:

FV = PV (1+r/2)²ⁿ

FV = future value

PV = present value

r/2 = interest rate for six months

n = number of years or compounding periods

For instance, when 10% nominal annual interest rate is compounded semiannually or daily the effective interest rate would be 10.25 and 10.51 percent, respectively (Table 2).

¹⁾ r/2 = Interest Rate for 6 months; n - Number of Years or Compounding Periods

For example, if it is expected that during the next four-year investment period the interest rate will change twice during the first year (or first 12 months) and then again during next three years, the four-year formula would look as follows:

FV = PV* (1+r/12)⁴ⁿ * (1+r/12)⁸ⁿ * (1+r)² * (1+ r)

Where:

PV = Present Value

Year 1 = interest (r) for first year for four and eight months

Year 2, 3 = interest (r) for two years

Year 4 – interest (r) for the fourth year

To follow the above formula, an investment of $50,000 for the next four years, where it is expected that current interest of 5% will stay unchanged for the first four months and then it will drop to 3% for the rest of the year, but the following two years the interest will be steady at 4% and increases to 6% in the fourth year.

FV = $50,000 *(1+0.05/12)⁴ *(1+0.03/12)⁸ * (1+0.04)² * (1+ 0.06)

FV = $50,000 * (1.0041)⁴ *(1.0025)⁸ * (1.04)² * (1.06)

FV = $59,441

The future value will be $59,441.

Tax Implications

For purposes of an investment analysis, it is recommended to evaluate the after-tax returns as well. Since interest earnings are a subject to taxation, the nominal rate should be reduced by the income tax rate.

For example, the income tax rate is 30% and your investment pays six percent return then the after-tax rate would be as follows:

After Tax Rate = Investment Rate of Return - ((Investment Rate of Return/100) * Income Tax Rate)

After Tax Rate = 6 – ((6/100) * 30) = 4.2 percent

The 4.2 percent after-tax rate is risk-free return to time and inflation. However, for planning purposes, the choice of risk-free, after-tax rate depends on the managers' market position. If the operation accumulated lots of debt the manager should aim for a higher risk-free return. Paying off loans saves costs on interest and also the loan interest is an income tax deduction.

The Importance of Time Value of Money in Decision Making – Part 2

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.