Time Value of Money Introduction

Time Value of Money

• The value of money changes over time due to investment potential. A dollar today is worth more than a dollar in the future.

Basic Concepts

• Future Value (FV): The value of an investment at a specified future date, considering compounding/growth over time.
• Present Value (PV): The value today of an amount to be received in the future, considering discounting.
• Single or series of cash flows can be analyzed.

Key Financial Terms

• Principal: The amount of money on which interest is calculated.
• Timelines: Used to visualize the timing of cash flows.

Computational Aids (Compounding and Discounting)

• Compounding: The process of accumulating interest on an investment over time, with interest earned also earning interest.
• Discounting: The process of determining the present value of future cash flows.

Future Values

• A dollar today is more valuable than a dollar in the future because it can be invested to earn interest or grow in value.
• Compounding is the process of converting present values into future values.

Future Value Example

• Assume $100 is deposited at 5% interest per year. At the end of year 3, the future value would be $115.76 using the formula ($100 * (1 + 0.05)^3).

Present Value

• Calculating present value reverses the process of future value. Determining the current value of money to be received in the future.

Present Value Formula

• Present value (PV) = (Future Value (FV)) / (1 + interest rate)^number of periods

What is a Discount Rate?

• A discount rate is a crucial financial metric determining the present value of future cash flows from an investment or project.
• It represents the opportunity cost of capital (the return investors could gain elsewhere).

Role Of The Discount Rate in Evaluating Project Cash Flows

• Cash flows are uncertain and must be discounted to a present value to assess their actual worth today.

Discount Rate Formula

• Present value (PV) = Future Cash Flow (CF) / (1 + r)^n

• Where:

  • CF = Future cash flow.
  • r = Discount rate.
  • n = Number of periods until cash flow.

Net Present Value (NPV)

• Net Present Value (NPV): Calculation subtracting the present value of outflows from that of inflows.
  • NPV = Σ [CFt/(1+r)^t] – CF0 where:
• CFt = cash flow received at time t
• r = discount rate
• t = number of the period
• CF0 = initial investment

Decision Criteria (NPV)

• If NPV > 0: Accept.
• If NPV < 0: Reject.
• If NPV = 0: Indifferent.

Overview of Capital Budgeting

• Capital Budgeting: Evaluating and selecting long-term investments aligned with maximizing owner wealth.
• Capital Expenditure: Outlays expected to generate benefits over more than one year.
• Operating Expenditure: Outlays generating benefits within one year.

Capital Budgeting Techniques

• Companies use processes like the Payback period and Net Present Value to evaluate capital projects.

Payback Period

• Payback period: measures time to recover an investment's cost.
• If the payback period is less than management's acceptable period: Accept the project
• If the payback period is greater than the acceptable period ; Reject the project

Payback Period Example

• A payback of 3 years for a $42,000 initial investment at $14,000 annual cash inflows is achievable. Project B's payback is 2.5 years. A more complex calculation since cash flows are not uniform.

Second Technique: Net Present Value (NPV)

• Net Present Value (NPV): A sophisticated capital budgeting technique found by subtracting a project's initial investment from the present values of future cash flows discounted at a rate equal to the firm's cost of capital.

NPV Decision Criteria

• If NPV is greater than zero; accept the project
• If NPV is less than zero ; reject the project
• If NPV = zero ; indifference result.

Bennett Company (Example)

• Presented projects with initial investments of $42,000 (Project A) and $45,000 (Project B)
• Future data provided on cash inflows per year are calculated into project A and B using a 10% discount rate.

This quiz covers the essential concepts of the Time Value of Money, including Future Value (FV) and Present Value (PV). Learn about important terms such as principal and how cash flows are analyzed using timelines. Understand the processes of compounding and discounting to enhance your financial decision-making skills.