Chapter 5 Notes
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Chapter 5 Time Value of Money Notes
5.1 Opportunity Cost
•time value of money the idea that money invested today has more value than the same amount invested later
•medium of exchange something that can be used to facilitate transactions
•the opportunity cost of money is the interest rate that would be earned by investing it—interest rate is called the price of money
•required rate of return or discount rate the market interest rate (k) or the investor’s opportunity cost
•simple interest interest paid or received on only the initial investment (the principal)
5.3 Compound Interest
Compounding (Computing Future Values)
•compound interest interest that is earned on the principal amount invested and on any accrued interest
•compound interest growth is directly related to the length of the period, as well as to the level of return earned
•reinvest to keep interest earned on any investment fully invested
•compound value interest factor (CVIF) represents future value of an investment at an interest rate and for a number of periods
•basis point 1/100 of 1 percent
Discounting (Computing Present Values)
•discounting finding the present value of a future value by accounting for the time value of money
•discount factors (the PVIF) are always less than one, which means that future dollars are worth less than the same dollars today
•discount factors are the reciprocals of their corresponding compound factors and vice versa (PVIF = 1 / CVIF)
5.4 Annuities and Perpetuities
•annuity regular payments on an investment that are for the same amount and are paid at the same interval
•cash flows the actual cash generated from an investment
•ordinary annuities equal payments that are made at the end of each period
•lessee a person who leases an item
•annuity due an annuity (such as a lease) for which the payments are made at the beginning of each period
•perpetuities special annuities that provide payments forever
•effective rate rate at which a dollar invested grows over a given period; stated in percentage terms based on an annual period
Summary of Learning Objectives
1. Explain the importance of the time value of money and how it is related to an investor’s opportunity costs.
Time value of money is the idea that money invested today has more value than the same amount invested later. This concept
helps us to understand how interest is earned and why investors are indifferent to investment today and future value later.
The opportunity cost is the interest rate that would be earned by investing it. For this reason, we also call the interest rate the
price of money.
2. Define simple interest and explain how it works.
Simple interest is interest earned on the original principal. The growth in the value of an investment is simply the sum of annual
3. Define compound interest and explain how it works.
Compound interest is interest earned on the principal amount invested and on any accrued interest. Compound interest can result
in dramatic growth in the value of an investment over time.
4. Differentiate between an ordinary annuity and an annuity due, and explain how special constant payment problems can
be valued as annuities and, in special cases, as perpetuities.
Annuities are streams of level payments at regular time intervals. An ordinary annuity has payments at the end of each period.
An annuity due has the same number of payments as an ordinary annuity, but the payments occur at the beginning of each
period. The present value of an ordinary annuity can be found with a formula that is equal to the sum of the present value factors.
The future value of an ordinary annuity can be found with a formula that is equal to the sum of the future value factors. To get
the present and future value factors for an annuity due, just multiply the ordinary annuity factors by (1 + k).
5. Differentiate between quoted rates and effective rates, and explain how quoted rates can be converted to effective rates.
Quoted rates are also called stated rates or annual percentage rates, which are measured annually and used for quoting purposes.
The effective rate for a period is the rate at which a dollar invested grows over that period. It is usually stated in percentage terms
based on an annual period. The relation can be found in the formula k = (1 + QR / m)
– 1, where QR is the quoted rate, m is the
compounding frequency, and k is the annual effective rate.
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