Accounting and the Time Value of Money

1. Accounting and the Time Value of Money Chapter 6

2. The time value of money is the relationship between time and money. According to the present value of money concept, a dollar today is worth more than a dollar in the future. This concept is used extensively to choose among alternative investment proposals. Basic Time Value Concept

3. Notes Leases Pensions Long-term assets Sinking funds Business combinations Disclosures Installment contracts Accounting Applications

4. Interest rate: A percentage rate usually expressed as an annual rate of return. Time: the number of years or fractional portion of a year (periods) that amounts compound. Present Value: The value now (present) of a set of future cash flows. Future Value: The value at a given future date of cash invested (may be multiple FV�s). Fundamental Variables

5. Basic Time Diagram

6. Specified in contracts Stated Coupon Nominal Face Demanded by investors Effective Discount Required rate of return Interest Rates

7. Determining the effective rate The appropriate interest rate depends on: the pure rate of interest expected inflation rate of interest credit risk rate of interest The higher the credit risk, the higher the interest rate.

8. Simple interest is determined using only the original principal amount. principal x interest rate (%) x time Compound interest is determined using: the principal, and any interest accrued (earned and not withdrawn or paid). Compound interest is used in virtually all time value applications. Simple vs. Compound interest

9. Future value of $1 Present value of $1 Future value of an ordinary annuity of $1 Present value of an ordinary annuity of $1 Future value of an annuity due of $1 Present value of an annuity due of $1 The basic calculations

10. Typically one of two types: Computing a future value of a known single sum present value. Computing a present value of a known single sum future value. FV = PV*(1+i)^n or PV = FV/(1+i)^n i = interest rate per period n = the number of periods Single cash flow problems

11. Given: Amount of deposit today (PV): $50,000 Interest rate 8% Frequency of compounding: Quarterly Time outstanding: 5 years What is the future value of this single sum? Single cash flow FV example

12. Given: Amount of deposit end of 3 years: $100,000 Interest rate (discount) rate: 12% Frequency of compounding: Quarterly Time outstanding: 3 years What is the present value of this single sum? Single cash flow PV example

13. An annuity requires that: the periodic payments or receipts (rents) always be of the same amount, the interval between such payments or receipts be the same, and the interest be compounded once each interval. Annuity Calculations

14. Annuities may be broadly classified as: Ordinary annuities: where the rents occur at the end of the period. Annuities due: where rents occur at the beginning of the period. Types of annuities

15. Given: Deposit made at the end of each period: $5,000 Compounding: Annual Number of periods: Five Interest rate: 12% What is future value of these deposits? Future Value of an Ordinary Annuity

16. Given: Rental receipts at the end of each period: $6,000 Compounding: Annual Number of periods (years): 5 Interest rate: 12% What is the present value of these receipts? Present Value of an Ordinary Annuity

17. Deferred Annuities: Rents begin after a specified number of periods. Valuation of Long-term Bonds: Two cash flows: principal paid at maturity and periodic interest payments Complex Situations

18. Introduced by SFAC No. 7 Uses a range of cash flows. Incorporates the probabilities of those cash flows to arrive at a more relevant measurement of present value. Expected Cash Flows