🗃️Corporate Finance Unit 4 – Time Value of Money

What's Time Value of Money?

• Fundamental concept in finance recognizing that money has different values at different points in time
• Based on the principle that a dollar today is worth more than a dollar in the future
• Accounts for the opportunity cost of holding money over time instead of investing it
• Incorporates the impact of inflation eroding the purchasing power of money over time
• Enables comparison of cash flows occurring at different times by discounting them to a common point
• Provides a framework for making financial decisions involving future cash flows
• Relies on the assumption that individuals prefer to receive money sooner rather than later

Why TVM Matters in Finance

• Helps businesses and investors make informed decisions about investments, loans, and financial planning
• Allows for the comparison of different investment opportunities with cash flows occurring at different times
• Enables the determination of the present value of future cash flows, essential for valuation and capital budgeting
• Assists in setting appropriate interest rates for loans and determining the feasibility of borrowing
• Facilitates the calculation of the future value of investments, aiding in long-term financial planning
• Provides a basis for evaluating the profitability and viability of projects and investments
• Helps individuals make decisions about saving, investing, and retirement planning

Key TVM Concepts

• Present Value (PV) represents the current value of a future sum of money or cash flow
• Future Value (FV) represents the value of a current sum of money or cash flow at a specified future date
• Discount Rate is the interest rate used to calculate the present value of future cash flows
• Compounding is the process of earning interest on previously earned interest
• Discounting is the process of determining the present value of future cash flows using a discount rate
• Time Period is the duration over which cash flows occur (years, months, etc.)
• Interest Rate is the cost of borrowing money or the return earned on an investment

Calculating Present Value

• Present Value (PV) is calculated by discounting future cash flows using a discount rate
• The PV formula is: $PV = FV / (1 + r)^n$, where FV is the future value, r is the discount rate, and n is the number of periods
• A higher discount rate results in a lower present value, while a lower discount rate results in a higher present value
• The discount rate should reflect the risk and opportunity cost associated with the cash flows
• PV calculations are essential for making investment decisions and determining the value of financial assets
• Example: If you expect to receive $1,000 in 5 years with a discount rate of 5$783.53 ($1,000 / (1 + 0.05)^5)

Calculating Future Value

• Future Value (FV) is calculated by compounding a present sum of money using an interest rate over a specified period
• The FV formula is: $FV = PV * (1 + r)^n$, where PV is the present value, r is the interest rate, and n is the number of periods
• Compounding frequency (annual, semi-annual, quarterly, etc.) affects the future value calculation
• The interest rate and the number of compounding periods have a significant impact on the future value
• FV calculations are useful for estimating the growth of investments and setting financial goals
• Example: If you invest $1,000 today at an annual interest rate of 5$1,276.28 ($1,000 * (1 + 0.05)^5)

Annuities and Perpetuities

• An annuity is a series of equal cash flows occurring at fixed intervals over a specified period
• The present value of an annuity is the sum of the present values of each individual cash flow
• The PV of an annuity formula is: $PV = PMT * [(1 - (1 + r)^-n) / r]$, where PMT is the periodic payment, r is the discount rate, and n is the number of periods
• A perpetuity is an annuity that continues indefinitely, with no end date
• The PV of a perpetuity formula is: $PV = PMT / r$, where PMT is the periodic payment and r is the discount rate
• Annuities and perpetuities are commonly used in financial planning, such as retirement planning and valuing financial instruments (bonds)

TVM Applications in Corporate Finance

• Capital Budgeting involves using TVM to evaluate the profitability and feasibility of long-term investment projects
• Net Present Value (NPV) is calculated by discounting a project's future cash flows to their present value and subtracting the initial investment
• Internal Rate of Return (IRR) is the discount rate that makes the NPV of a project equal to zero
• Valuation of financial assets (stocks, bonds) relies on discounting expected future cash flows to determine their present value
• Determining the cost of capital for a company involves calculating the weighted average of the costs of debt and equity financing
• Evaluating mergers and acquisitions requires comparing the present value of expected synergies with the acquisition cost
• Lease vs. buy decisions can be analyzed using TVM to compare the costs and benefits of each option

Common TVM Pitfalls

• Ignoring the time value of money can lead to suboptimal financial decisions and inaccurate valuations
• Using nominal interest rates instead of real interest rates (adjusted for inflation) can overestimate future values and underestimate present values
• Failing to consider the impact of taxes on cash flows can distort TVM calculations and decision-making
• Incorrectly estimating future cash flows or using unrealistic growth assumptions can lead to flawed TVM analyses
• Neglecting to account for the risk and uncertainty associated with future cash flows can result in overly optimistic valuations
• Inconsistently applying discount rates across different cash flows or time periods can lead to incorrect conclusions
• Misinterpreting the results of TVM calculations or relying on them without considering qualitative factors can lead to poor financial decisions