Chapter 5 PPTs

Chapter 5: Time Value of Money Concepts

Overview

• The time value of money (TVM) concept emphasizes that money available today can earn interest, making it more valuable than the same amount in the future.

• Key applications include valuing assets and liabilities in accounting, such as leases, bonds, and pension obligations.

1. Simple vs. Compound Interest

Simple Interest

• Definition: Interest calculated only on the principal amount.

• Formula: Simple Interest = Principal × Annual Interest Rate × Time Period

• Example: For a $1,000 investment at 10% for 1 year, Simple Interest = $1,000 × 10% × 1 = $100.

Compound Interest

• Definition: Interest calculated on the principal and on the accumulated interest from previous periods.

• Formula: Future Value = Principal (1 + r)^n

• Example: Cindy Johnson’s $1,000 investment at 10% compound interest:

  • Year 1: Interest = $1,000 × 10% = $100; Total Balance = $1,100

  • Year 2: Interest = $1,100 × 10% = $110; Total Balance = $1,210

  • Year 3: Interest = $1,210 × 10% = $121; Total Balance = $1,331

2. Effective Interest Rate

• Definition: The actual rate at which money grows per year accounting for compounding frequency.

• Example: For an annual rate of 12%:

  • Semiannually: 6%, Quarterly: 3%, Monthly: 1%

3. Future Value of a Single Amount

• Definition: The amount an investment will grow to at a future date when interest is applied.

• Formula: FV = I × FV factor(n,i)

• Example: A $1,000 investment at 10% for 3 years:

  • FV = $1,000 × 1.331 = $1,331

4. Present Value of a Single Amount

• Definition: Today's value of a future amount after removing interest.

• Formula: PV = FV × PV factor(n,i)

• Example: Present value of $1,331 in 3 years at 10%:

  • PV = $1,331 × 0.75131 = $1,000

5. Present Value Techniques in Accounting

• Application: Used to value monetary assets and liabilities.

• Monetary Assets: Claims for future cash (e.g., receivables).

• Monetary Liabilities: Obligations to pay cash (e.g., notes payable).

6. Valuing Notes Receivable

A. One Payment, Explicit Interest

• Example: The Shoe Company sells shoes for $50,000 plus 10% interest for one year.

  • Future Value = $55,000

  • Present Value = $55,000 × 0.90909 = $50,000.

B. One Payment, No Interest Stated

• Example: Shoe Company’s sale for $60,500 due in 2 years.

  • Present Value = $60,500 × 0.82645 = $50,000 (using 10% market rate).

7. Annuities

A. Ordinary Annuity

• Payments made at the end of each period.

• Example: A three-year loan with annual payments.

B. Annuity Due

• Payments made at the beginning of each period.

• Example: A three-year lease requiring first payment upfront.

8. Computing Future Value of Annuities

A. Future Value of an Ordinary Annuity

• Example: Investing $10,000 annually for 3 years at 10%.

  • FVA = $10,000 × 3.31 = $33,100.

B. Future Value of an Annuity Due

• Payments made at the beginning.

• Example: $10,000 annually for 3 years at 10%.

  • FVAD = $10,000 × 3.641 = $36,410.

9. Computing Present Value of Annuities

A. Present Value of an Ordinary Annuity

• Example: Cost of a 3-year program at $10,000 yearly.

  • PVA = $10,000 × 2.48685 = $24,868.

B. Present Value of an Annuity Due

• Example: Cost of the program with payments at the beginning.

  • PVAD = $10,000 × 2.73554 = $27,355.

10. Valuation of Bonds

• Bonds issued with a stated interest rate versus market rate.

• Example: Fumatsu Electric’s 10% bonds valued against a 12% market rate.

• Price calculation involves determining present values of future cash flows.