7.1 Now versus Later Concepts

Money's value changes over time due to factors like opportunity cost, inflation, and risk. This concept forms the basis of financial decision-making, with interest rates quantifying the time value of money. Higher rates indicate greater time value.

Future value and present value are key concepts in time value calculations. Future value represents money's worth at a future date, while present value is the current worth of future money. These calculations are crucial for evaluating investments and financial planning.

Time Value of Money

Effects of time on money value

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• Money has a time value due to:
  • Opportunity cost involves the potential earnings lost by not investing money available now (savings account, stocks)
  • Inflation erodes the purchasing power of money over time as prices increase (consumer goods, services)
  • Risk and uncertainty make future cash flows less certain than present cash flows (economic conditions, market volatility)
• Interest rates quantify the time value of money
  • Higher interest rates indicate a greater time value of money (10% vs 2% annual return)
• The relationship between time and money value forms the foundation of financial decision-making (investment choices, budgeting)

Future value vs present value

• Future value (FV) represents the value of a sum of money at a specific future date
  • Calculated by applying compound interest to a present sum over a given time period (5 years, 10 years)
  • Formula: $FV = PV(1 + r)^n$
    • $PV$ = Present value (initial investment)
    • $r$ = Interest rate per period (annual, quarterly)
    • $n$ = Number of periods (years, months)
  • Compounding frequency affects the growth rate of investments (daily, monthly, annually)
• Present value (PV) represents the current value of a future sum of money
  • Calculated by discounting a future sum at a given interest rate over a specific time period
  • Formula: $PV = \frac{FV}{(1 + r)^n}$
• Key differences between future value and present value:
  • Direction of time
    • Future value projects a present sum forward in time (growth)
    • Present value discounts a future sum back to the present (shrinkage)
  • Effect of interest rates
    • Higher interest rates lead to higher future values and lower present values (compounding, discounting)

Significance of lump sum cash flows

• Lump sum cash flows are single, one-time payments or receipts
  • Examples include investments (real estate purchase), loans (mortgage), and asset purchases or sales (business acquisition)
• Lump sum cash flows serve as building blocks for more complex financial calculations
  • Annuities and perpetuities are series of equal, periodic lump sum cash flows (monthly rent, annual dividends)
• The timing of lump sum cash flows is crucial in determining their value
  • Cash flows occurring at different times must be adjusted for the time value of money to be comparable (net present value analysis)
• Lump sum cash flows are used in various financial applications:
  1. Capital budgeting decisions compare the present value of future cash flows to the initial investment (project viability)
  2. Loan amortization determines the periodic payments required to pay off a lump sum loan (car financing, student loans)
  3. Retirement planning estimates the future value of current lump sum investments (401(k) contributions, IRA deposits)

Interest rates and investment evaluation

• Nominal interest rate is the stated rate on financial instruments, not accounting for compounding or inflation
• Effective annual rate represents the true annual cost of borrowing or return on investment, considering compounding
• Net present value (NPV) is used to evaluate investments by comparing the present value of all cash inflows to the present value of all cash outflows
• Internal rate of return (IRR) is the discount rate that makes the NPV of all cash flows equal to zero
• The yield curve shows the relationship between interest rates and time to maturity for debt securities