Time Value of Money Concept

Time Value of Money (TVOM)

• The concept of TVOM is based on the idea that "time is money" and can be measured and proven quantitatively using financial mathematics.
• Money received today is worth more than the same amount received in the future.

Time Line

• A time line represents the timing of cash flows.
• Time 0 (t0) refers to the present time.
• Time 1 (t1) is the end of the first period (year, month, etc.) or the beginning of the second period.
• Time 2 (t2) is the end of the second period or the beginning of the third period.

Drawing Time Lines

• Examples of drawing time lines include:
  • Future value of a lump sum
  • Future value of an ordinary annuity
  • Uneven cash flow stream

Financial Table/Interest Factor Table

• The table includes values for:
  • Future Value (FV)
  • Present Value (PV)
  • Future Value Annuities (FVA)
  • Present Value Annuities (PVA)

Time Value Terms

• FV: future value at the end of "n" periods
• PV: present value or beginning amount
• i: interest rate
• n: number of compounding periods
• PMT: payment or receipt in an annuity

Compounding and Discounting Techniques

• Compounding: finding the future value of cash flows at the end of a project's life
• Discounting: finding the present value of cash flows

Future Value (FV)

• Measures cash flows at the end of a project's life
• Formula: FVn = PV x (1 + i)^n
• Example: If Fred Moreno places RM100 in a savings account paying 4% interest compounded annually, how much will he have in the account at the end of two years?

Finding FV using Table

• Formula: FVn = PV x (FVIFi%,n)
• Example: Finding FV using the interest factor table

Present Value (PV)

• The current dollar value of a future amount of money
• Formula: PVn = FVn / (1 + i)^n
• Example: Paul Shorter has an opportunity to receive RM300 three years from now. If he earns 6% on his investment, what is the most he should pay now for this opportunity?

Finding PV using Table

• Formula: PVn = FV x (PVIFi%,n)
• Example: Finding PV using the interest factor table

Annuity

• A series of equal payments or receipts at the same intervals throughout the period of valuation
• Types of annuities:
  • Ordinary annuity: occurs at the end of each period
  • Due annuity: occurs at the beginning of each period

Future Value Annuity (FVA)

• Formula: FVA = PMT x (FVIFA i%,n)
• Example: Jeff wishes to determine how much money he will have at the end of 10 years if he invests RM2500 per year at an annual interest rate of 7%.

Present Value Annuity (PVA)

• Formula: PVA = PMT x (PVIFA i%,n)
• Example: Braden Company wants to determine the most it should pay to purchase a particular annuity consisting of cash flows of $700 at the end of each year for 5 years at a required return of 1%.