3.4 Applications of Time Value of Money

Time value of money applications are crucial in finance, helping us make smart money decisions. From loan repayments to investment analysis, these concepts show how money's worth changes over time. They're key tools for comparing different financial options and planning for the future.

In this part of the chapter, we'll look at real-world uses of time value money concepts. We'll cover loan amortization, investment analysis, and capital budgeting. We'll also explore how compounding frequency affects calculations and learn practical ways to solve time value problems.

Time Value of Money Applications

Loan Amortization

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• Time value of money (TVM) recognizes the value of money changes over time due to the potential to earn interest or returns
• Loan amortization gradually pays off a loan over time through a series of equal payments, which include both principal and interest components
  • The amortization schedule shows the breakdown of each payment into principal and interest, as well as the remaining loan balance after each payment
  • Factors affecting loan amortization include the loan amount, interest rate, compounding frequency, and loan term
• Example: A 30-year fixed-rate mortgage with monthly payments

Investment Analysis

• Investment analysis evaluates the potential returns and risks of different investment opportunities using TVM concepts
  • The net present value (NPV) method discounts all future cash flows of an investment to their present value using a required rate of return and compares the total present value to the initial investment
  • The internal rate of return (IRR) is the discount rate that makes the NPV of an investment equal to zero, representing the expected rate of return on the investment
• TVM concepts can be applied to various real-world financial decisions
  • Comparing the costs and benefits of renting versus buying a home
  • Evaluating the feasibility of a business expansion project
  • Determining the optimal debt repayment strategy
• Example: Analyzing the profitability of a new product launch by calculating its NPV and IRR

Time Value in Capital Budgeting

Capital Budgeting Process

• Capital budgeting evaluates and selects long-term investments or projects that are expected to generate future cash flows
• TVM concepts are crucial in capital budgeting because they allow decision-makers to compare the value of cash flows occurring at different points in time
• The NPV method is commonly used in capital budgeting to determine whether a project is worth undertaking by discounting all future cash inflows and outflows to their present value using the company's required rate of return
  • A positive NPV indicates that the project is expected to generate returns above the required rate and should be accepted, while a negative NPV suggests that the project should be rejected

Other Capital Budgeting Techniques

• The IRR method calculates the expected rate of return on a project, which can be compared to the company's hurdle rate or cost of capital to determine whether the project is financially viable
• Payback period measures the time required to recover the initial investment, although it does not consider the time value of money
• Sensitivity analysis and scenario analysis assess the impact of changes in key assumptions, such as cash flow projections or discount rates, on the project's financial viability
• Example: Deciding whether to invest in a new manufacturing facility by calculating its NPV, IRR, and payback period under different scenarios

Impact of Compounding Frequency

Future Value and Compounding

• Compounding frequency refers to the number of times per year that interest is calculated and added to the principal amount of an investment or loan
• The future value of an investment increases with higher compounding frequencies due to the effect of compound interest, where interest earned in previous periods also earns interest in subsequent periods
  • For example, an investment with an annual interest rate of 6% will have a higher future value if interest is compounded monthly compared to annually, assuming the same investment period
• Common compounding frequencies include annual, semi-annual, quarterly, monthly, and daily compounding

Present Value and Effective Annual Rate

• The present value of a future cash flow decreases with higher compounding frequencies, as the discount rate used to calculate the present value is applied more frequently
• The effective annual rate (EAR) compares investments with different compounding frequencies by converting the stated annual interest rate to an equivalent rate that accounts for the compounding frequency
• Continuously compounded interest represents the theoretical limit of increasing the compounding frequency to infinity, resulting in the highest possible future value for a given stated annual interest rate
• Example: Comparing the future value of a 5-year investment with an annual interest rate of 5% under different compounding frequencies (annual, quarterly, monthly, and continuous)

Solving Time Value Problems

Using Financial Calculators

• Financial calculators simplify and speed up the process of solving TVM problems
• Most financial calculators have built-in TVM functions that allow users to input the required variables (such as present value, future value, interest rate, number of periods, and payment amount) and solve for the unknown variable
  • Common financial calculator brands include Texas Instruments (BA II Plus) and Hewlett-Packard (HP 10bII+)
  • It is essential to understand the cash flow convention used by the calculator (typically, cash outflows are entered as negative values and cash inflows as positive values) and to set the compounding frequency correctly

Using Spreadsheets

• Spreadsheet software, such as Microsoft Excel or Google Sheets, can also be used to solve TVM problems using built-in financial functions or by creating custom formulas
  • Common financial functions in Excel include

    PV

    (present value),

    FV

    (future value),

    PMT

    (payment),

    RATE

    (interest rate), and

    NPER

    (number of periods)
  • Spreadsheets are particularly useful for creating amortization schedules, performing sensitivity analysis, and visualizing the results of TVM calculations
• Proficiency in using financial calculators or spreadsheets enables finance professionals to quickly and accurately analyze complex financial scenarios and make informed decisions
• Example: Using a financial calculator to determine the monthly payment on a car loan with a given loan amount, interest rate, and loan term