Fundamentals of Financial Management (Concise 6th Edition)

Appendix A Solutions to Self-Test Questions and Problems A-9

certainty as interest rates over time will change; the amount may be higher (if

interest rates fall) or lower (if interest rates rise).

d. Annual debt service costs will be $100,000,000(0.12) $ $7,237,750!

$19,237,750.

e. If interest rates rose, causing the bond’s price to fall, the company would use

open market purchases. This would reduce its debt service requirements.

Chapter 8

a. The average rate of return for each stock is calculated simply by averaging the

returns over the 5-year period. The average return for Stock A is as follows:

rAvg A! ("24.25% # 18.50% # 38.67% #14.33% # 39.13%)/5

! 17.28%

The average return for Stock B is as follows:

rAvg B! (5.50% # 26.73% # 48.25% # "4.50% # 43.86%)/5

! 23.97%

The realized rate of return on a portfolio made up of Stock A and Stock B

would be calculated by! nding the average return in each year as rA(% of Stock

A) $ rB(% of Stock B) and then averaging these annual returns.

Year Portfolio AB’s Return, rAB

2004 (9.38%)

2005 22.62

2006 43.46

2007 4.92

2008 41.50

rAvg! 20.62%

b. The standard deviation of returns is estimated using Equation 8-2a as

follows:

Estimated σ!

√^

____________

(^) #
t! 1
N
(

r (^) t "

r (^) Avg)^2

N " 1
8-2a
For Stock A, the estimated σ is 25.84%:
σA!
√^

("24.25%^ " 17.28%)
(^2) # (18.50% " 17.28%) (^2) # (38.67% " 17.28%) (^2) # (14.33% " 17.28%) (^2) # (39.13% " 17.28%) 2
___ (^5) " 1
! 25.84%
The standard deviations of returns for Stock B and for the portfolio are simi-
larly determined, and they are as follows:
Stock A Stock B Portfolio AB
Standard deviation 25.84% 23.15% 22.96%
c. Since the risk reduction from diversi! cation is small (σAB falls only to
22.96%), the most likely value of the correlation coef! cient is 0.8. If the corre-
lation coef! cient was "0.8, the risk reduction would be much larger. In fact,
the correlation coef! cient between Stocks A and B is 0.76.

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