94 CHAPTER 2 Time Value of Money
An amortized loanis one that is paid off in equal payments over a specified
period. An amortization scheduleshows how much of each payment constitutes
interest, how much is used to reduce the principal, and the unpaid balance at each
point in time.
The concepts covered in this chapter will be used throughout the remainder of the
book. For example, in Chapters 4 and 5, we apply present value concepts to find the
values of bonds and stocks, and we see that the market prices of securities are estab-
lished by determining the present values of the cash flows they are expected to pro-
vide. In later chapters, the same basic concepts are applied to corporate decisions in-
volving expenditures on capital assets, to the types of capital that should be used to pay
for assets, and so forth.
Questions
Define each of the following terms:
a.PV; i; INT; FVn; PVAn; FVAn; PMT; m; iNom
b.FVIFi,n; PVIFi,n; FVIFAi,n; PVIFAi,n
c.Opportunity cost rate
d.Annuity; lump sum payment; cash flow; uneven cash flow stream
e.Ordinary (deferred) annuity; annuity due
f.Perpetuity; consol
g.Outflow; inflow; time line; terminal value
h.Compounding; discounting
i.Annual, semiannual, quarterly, monthly, and daily compounding
j.Effective annual rate (EAR); nominal (quoted) interest rate; APR; periodic rate
k.Amortization schedule; principal versus interest component of a payment; amortized loan
What is an opportunity cost rate?How is this rate used in discounted cash flow analysis, and where
is it shown on a time line? Is the opportunity rate a single number which is used in all situations?
An annuityis defined as a series of payments of a fixed amount for a specific number of periods.
Thus, $100 a year for 10 years is an annuity, but $100 in Year 1, $200 in Year 2, and $400 in
Years 3 through 10 does notconstitute an annuity. However, the second series containsan annu-
ity. Is this statement true or false?
If a firm’s earnings per share grew from $1 to $2 over a 10-year period, the total growthwould be
100 percent, but the annual growth ratewould be less than10 percent. True or false? Explain.
Would you rather have a savings account that pays 5 percent interest compounded semiannually
or one that pays 5 percent interest compounded daily? Explain.
Self-Test Problems (Solutions Appear in Appendix A)
Assume that one year from now, you will deposit $1,000 into a savings account that pays 8 per-
cent.
a.If the bank compounds interest annually, how much will you have in your account four years
from now?
b.What would your balance four years from now be if the bank used quarterly compounding
rather than annual compounding?
c.Suppose you deposited the $1,000 in 4 payments of $250 each at Year 1, Year 2, Year 3, and
Year 4. How much would you have in your account at Year 4, based on 8 percent annual
compounding?
d.Supposeyoudeposited4equalpaymentsinyouraccountatYear1,Year2,Year3,andYear4.
Assuming an 8 percent interest rate, how large would each of your payments have to be for
you to obtain the same ending balance as you calculated in part a?
ST–1
FUTURE VALUE
2–5
2–4
2–3
2–2
2–1
92 Time Value of Money
