Principles of Managerial Finance

CHAPTER 6 Interest Rates and Bond Valuation 295

TABLE 6.7 Summary of Key Valuation Definitions

and Formulas for Any Asset and for Bonds

Definitions of variables

B 0 bond value

CFtcash flow expectedat the end of year t

Iannual interest on a bond

kappropriate required return (discount rate)

kdrequired return on a bond

Mpar, or face, value of a bond

nrelevant time period, or number of years to maturity

V 0 value of the asset at time zero

Valuation formulas

Value of any asset:

V 0 .. . [Eq. 6.5]

[CF 1 (PVIFk,1)][CF 2 (PVIFk,2)].. .[CFn(PVIFk,n)] [Eq. 6.6]

Bond value:

B 0 I

n

t 1 

M  [Eq. 6.7]

I(PVIFAkd,n)M (PVIFkd,n) [Eq. 6.7a]

^1

(1kd)n

^1

(1kd)t

CFn

(1k)n

CF^2

(1k)^2

CF^1

(1k)^1

PROBLEMS

6–1 Interest rate fundamentals: The real rate of return Carl Foster, a trainee at an

investment banking firm, is trying to get an idea of what real rate of return

investors are expecting in today’s marketplace. He has looked up the rate paid on

3-month U.S. Treasury bills and found it to be 5.5%. He has decided to use the

rate of change in the Consumer Price Index as a proxy for the inflationary expecta-

tions of investors. That annualized rate now stands at 3%. On the basis of the

information that Carl has collected, what estimate can he make of the real rate of

return?

6–2 Real rate of interest To estimate the real rate of interest, the economics division

of Mountain Banks—a major bank holding company—has gathered the data

summarized in the following table. Because there is a high likelihood that new

tax legislation will be passed in the near future, current data as well as data

reflecting the probable impact of passage of the legislation on the demand for

funds are also included in the table. (Note:The proposed legislation will not

have any impact on the supply schedule of funds. Assume a perfect world in

which inflation is expected to be zero, funds suppliers and demanders have no

liquidity preference, and all outcomes are certain.)

LG1

LG1