Future value and Present value

Future value and present value are important concepts in finance that help businesses calculate the worth of an investment at a future point in time and the current value of an investment, respectively. Let’s take a closer look at these concepts and their formulas.

Future value and present value are important concepts in finance that businesses need to understand. Future value is the value that an investment is expected to be worth at a specific future point in time, based on the principal amount invested, the interest rate earned, and the time period of the investment. Present value is the current value of an investment or a stream of cash flows that are expected to be received in the future, discounted to account for the time value of money. By using these formulas, businesses can make informed decisions about investing and ensure that they are maximizing their returns and minimizing their costs.

Assumptions

The calculation of future value and present value is based on certain assumptions that are important to consider.

It is important to consider these assumptions when using future value and present value calculations to make financial decisions. While the formulas provide a useful framework for understanding the value of an investment over time, they are based on certain simplifying assumptions that may not reflect the complexity of real-world financial situations. Therefore, it is important to use these calculations as a starting point and to consider other factors that may impact the investment’s value.

Some of the key assumptions include:

• The interest rate remains constant: The formulas for future value and present value assume that the interest rate remains constant over the entire investment period. In reality, interest rates can fluctuate, which can affect the accuracy of the calculations.
• The investment is held for the entire period: The formulas assume that the investment is held for the entire investment period without any withdrawals or additional deposits. If there are withdrawals or deposits, the actual future value or present value may be different from the calculated value.
• Interest is compounded: The formulas assume that interest is compounded, meaning that interest earned in each period is reinvested and earns additional interest. If interest is not compounded, the actual future value or present value may be lower than the calculated value.
• The time period is fixed: The formulas assume that the time period for the investment is fixed and does not change. If the investment period changes, the actual future value or present value may be different from the calculated value.
• No taxes or fees are considered: The formulas do not consider any taxes or fees that may be associated with the investment. If taxes or fees are applied, the actual future value or present value may be lower than the calculated value.

Future Value:

Future value is the value that an investment is expected to be worth at a specific future point in time, based on the principal amount invested, the interest rate earned, and the time period of the investment. The formula for calculating future value is as follows:

Future Value = P(1 + r)^n

Where:

P is the principal amount invested

r is the interest rate earned per period

n is the number of periods for which the investment is made

Example:

Suppose a business invests $10,000 in a fixed deposit account that offers a 5% annual interest rate for a period of 5 years. The future value of the investment after 5 years will be:

Future Value = P(1 + r)^n

Future Value = 10,000(1 + 0.05)^5

Future Value = $12,763.59

Therefore, the business can expect to have $12,763.59 in the fixed deposit account after 5 years.

Present Value:

Present value is the current value of an investment or a stream of cash flows that are expected to be received in the future, discounted to account for the time value of money. The formula for calculating present value is as follows:

Present Value = FV/(1 + r)^n

Where:

FV is the future value of the investment

r is the discount rate or the required rate of return

n is the number of periods in the future when the cash flows will be received

Example:

Suppose a business expects to receive $15,000 in 3 years from an investment with a 8% required rate of return. The present value of the investment will be:

Present Value = FV/(1 + r)^n

Present Value = 15,000/(1 + 0.08)^3

Present Value = $11,059.52

Therefore, the present value of the investment is $11,059.52, which represents the current value of the future cash flows adjusted for the time value of money.

Uses:

Some common uses of these concepts include:

• Investment analysis: Future value and present value are used to determine the potential return on an investment and to compare investment options. For example, businesses can use these concepts to calculate the future value of a savings account, mutual fund, or stock investment and to compare the returns of different investments.
• Capital budgeting: Future value and present value are used in capital budgeting to evaluate the profitability of long-term investment projects. Businesses can use these concepts to estimate the future cash flows of a project, discount them to their present value, and compare them to the initial investment to determine the net present value (NPV) of the project.
• Financing decisions: Future value and present value are used in financing decisions to determine the cost of borrowing and to evaluate different financing options. For example, businesses can use these concepts to calculate the future value of a loan, the present value of loan payments, and to compare the costs of different financing options.
• Retirement planning: Future value and present value are used in retirement planning to determine the amount of savings required to achieve a specific retirement goal. Businesses can use these concepts to calculate the future value of their retirement savings, determine the present value of their retirement income needs, and make informed decisions about their retirement savings and investment strategies.
• Risk management: Future value and present value are used in risk management to assess the financial impact of potential losses or gains. Businesses can use these concepts to calculate the expected future value of potential risks and to determine the present value of potential losses, which can inform risk management and insurance decisions.