Chapter 5: Time value of money Flashcards
If you invest money at a given interest rate, what will be the future value of your investment? (LO5-1)
An investment of $1 earning an interest rate of r will increase in value each period by the factor (1 + r). After t periods, its value will grow to $(1 + r)t. This is the future value of the $1 investment with compound interest.
What is the present value of a cash flow to be received in the future? (LO5-2)
The present value of a future cash payment is the amount that you would need to invest today to produce that future payment. To calculate present value, we divide the cash payment by (1 + r)t or, equivalently, multiply by the discount factor 1/(1 + r)t. The discount factor measures the value today of $1 received in period t.
How can we calculate present and future values of streams of cash payments? (LO5-3)
A level stream of cash payments that continues indefinitely is known as a perpetuity; one that continues for a limited number of years is called an annuity. The present value of a stream of cash flows is simply the sum of the present value of each individual cash flow. Similarly, the future value of an annuity is the sum of the future value of each individual cash flow. Shortcut formulas make the calculations for perpetuities and annuities easy.
How should we compare interest rates quoted over different time intervals, for example, monthly versus annual rates? (LO5-4)
Interest rates for short time periods are often quoted as annual rates by multiplying the per-period rate by the number of periods in a year. These annual percentage rates (APRs) do not recognize the effect of compound interest; that is, they annualize assuming simple interest. The effective annual rate annualizes using compound interest. It equals the rate of interest per period compounded for the number of periods in a year.
What is the difference between real and nominal cash flows and between real and nominal interest rates? (LO5-5)
A dollar is a dollar, but the amount of goods that a dollar can buy is eroded by inflation. If prices double, the real value of a dollar halves. Financial managers and economists often find it helpful to reexpress future cash flows in terms of real dollars—that is, dollars of constant purchasing power.
Be careful to distinguish the nominal interest rate and the real interest rate—that is, the rate at which the real value of the investment grows. Discount nominal cash flows (that is, cash flows measured in current dollars) at nominal interest rates. Dis- count real cash flows (cash flows measured in constant dollars) at real interest rates. Never mix and match nominal and real.
