# 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