Time Value of Money

Introduction

The time value of money is a foundational concept in financial accounting and finance, reflecting the idea that money available today is worth more than the same amount in the future due to its earning potential. This principle impacts investment decisions, loan agreements, and valuation of financial instruments.

Interest and Its Role

• Interest is the cost of using money. For borrowers, it is a fee paid for access to funds; for lenders, it is revenue earned for providing capital.

• Money earns interest over time, increasing its future value.

Future Value

Future value (FV) is the amount an investment will grow to at a specified time in the future, given a certain interest rate.

• Example: Investing $4,545 in corporate bonds at 10% annual interest will result in $5,000 after one year.

Key factors needed to calculate future value:

1. The amount of initial payment (or receipt)

2. The length of time between investment and future receipt (or payment)

3. The interest rate

Compound interest is interest earned on both the principal and previously earned interest, leading to exponential growth over time.

Compound Interest Table Example

Present Value

Present value (PV) is the current worth of a future sum of money, discounted to reflect the time value of money. It is often referred to as discounting.

• Depends on the amount of the payment, the time until receipt, and the interest rate.

Formula:

Example:

General Equations for Time Value of Money

• Future Value:

• Present Value:

• Where n is the number of periods.

Present Value Example

If $5,000 is to be received two years from now at a 10% interest rate:

• Amount invested (present value): $4,132

• Expected earnings for first year: $4,132 × 0.10 = $413

• Value after one year: $4,545

• Expected earnings for second year: $4,545 × 0.10 = $455

• Amount to be received after two years: $5,000

Formula:

Using Microsoft Excel to Calculate Present Value

Excel provides financial functions to calculate present value and future value for various interest rates and periods.

• To calculate the present value of an annuity in Excel:

• Open a blank cell, click the insert function button (fx), select the "financial" category, and choose PV.

• Enter the interest rate, number of periods, and payment (as a negative number).

Example: An investment returning $20,000 per year for 20 years at 8% interest.

Applications of Time Value of Money

Calculating Car Payments

Loans are a common application of time value of money. For example, purchasing a car with a 5-year loan at 6% annual interest, compounded monthly:

• Loan amount (PV): $18,000

• Number of periods (N): 60 (5 years × 12 months)

• Interest rate per period (I/Y): 0.5% (6% ÷ 12)

• Future value (FV): $0

• Monthly payment (PMT): $347.99

Calculated using a financial calculator (e.g., HP BAII+ or TI BAII+).

Calculating Future Values for Retirement

Consistent investing over time can lead to significant future value due to compound interest.

• Invest $75 per week for 45 years (2,340 weeks) at a 7% annual return, compounded weekly.

• Future value: $1,241,687

Demonstrates the power of compound interest in long-term financial planning.

Present Value of an Investment in Bonds

Bond valuation uses present value concepts to determine the market price of bonds.

• Face value: $100,000

• Face interest rate: 9% annually (4.5% semiannually)

• Market interest rate: 10% annually (5% semiannually)

• Present value (market price): $96,149

TI BAII+ Key Inputs for Bond Valuation

Summary Table: Key Formulas

Conclusion

The time value of money is essential for understanding investment growth, loan payments, and the valuation of financial instruments. Mastery of present and future value calculations, including the use of financial calculators and Excel, is critical for financial accounting students.