Risk, Return, and the Time Value of Money

  • Relationship Between Risk and Return
    • Return – profit as a percentage of total investment
    • Risk – uncertainty about the actual rate of return an investment will provide over an anticipated investment period
    • Risk and return are directly related (investors require greater returns for greater risk)
  • Types of Risk
    • Business risk – uncertainty arising from changing economic conditions that affect an investment’s ability to generate returns
    • Financial risk – uncertainty associated with the possibility of defaulting on borrowed funds used to finance an investment
    • Purchasing power risk – uncertainty arising from the possibility that the amount of goods and services that can be acquired with a given amount of money will decline over time (inflation)
    • Liquidity risk – possibility of loss resulting from not being able to convert an asset into cash quickly should the need arise
  • Time Value of Money Principle
    • Money in hand today is worth more than money to be received in the future
  • Future Value of a Lump Sum
    • Compound interest – during any given period, interest is earned not only on the original principal amount, but also on any interest previously earned by the principal amount
    • Compounding – the process of determining future value
    • Example: What is the future value of $70,000 compounded at 10% annual interest over 3 years?
  • Present Value of a Lump Sum
    • Discounting – the process of determining present value of a single amount (lump sum) to be received in the future
    • Example: What is the present value of $93,170 to be received in 3 years discounted at 10% annual interest?
  • Present Value of an Annuity
    • Annuity: a series of equal amounts received one per period for a specified number of periods
    • Example: What is the present value of a series of three payments of $1,000 received at the end of each year if the discount rate is 10%?
  • Future Value of an Annuity
    • Example: What is the future value of a series of five payments of $100 received at the end of each year if the compound interest rate is 10%?
  • Sinking Fund Payments
    • Sinking Fund Payments: equal amounts of money that are deposited into an account earning for a specific number of years to accumulate a specific amount.
    • Example: What is the amount of money that must be deposited into an account each year that earns 10% for five years in order to accumulate $20,000?
  • Mortgage Payments
    • Mortgage Payment: equal amount of money that must be paid to a lender each period to fully amortize a loan.
    • Example: What annual payment would be necessary to amortize a loan for $100,000 over ten years at 10% interest?
  • Financial Decision Rules
    • Net Present Value (NPV) – difference between how much an investment costs and how much it is worth to an investor in present value dollars
      • NPV = present value of cash inflows minus present value of cash outflows
      • NPV Decision Rule: If the NPV is equal to or greater than zero, we choose to invest
    • Internal Rate of Return (IRR) – the discount rate that makes the NPV equal to zero
      • IRR = the rate of return on the investment
      • IRR Decision Rule: If the IRR is greater than or equal to our required rate of return, we choose to invest