стр. 132 |

A (8 ( A -A)' (9

( A - A ) ($) ( A -&"p ($1

p

-1,200 432,000

1,440,000

1,000 0.3

40,000 16,000

0.4 -200

2,000

64,000

640,000

3,000 0.1 800

3,240,OOO 648,000

0.2 1,800

4,000

u2= 1,160,000

1,077

U=$

The standard deviation of the expected NPV is:

+ $642,857 + $727,776 = <$2,340,672

= d$970,039 = $1,530

From the normal distribution table Appendix E, this value of z gives a probability of 0.3409, or

approximately a 34 percent chance that NPV will be zero or less.

( d ) The probability of the NPV being greater than zero is the compliment of 34 percent, or 66 percent.

$630 - $630

=O

z=

$1,530

Reading from Appendix E, at z = 0, there is 50 percent probability that the NPV will be greater than

the expected value.

CAPITAL BUDGETING UNDER RISK

276 [CHAP. 9

Portfolio E f c s

f e t .The projected cash inflows of three projects--, Y, 2-for the period 1 x

91

9.14 and

to 19x5are given below.

Project Z

Year Project X Project Y

19x1 $2,000 $6,000 $1,000

19x2 $3,000 $4,000 $2,000

19x3 $4,000 $3,000 $3,000

19x4 $5,000 $2,000 $3,000

19x5 $7,000 $1,000 $6,000

Project Z

Project X Project Y

A $4,200 $3,200 $3,000

$3,847 $3,847 $3,742

U

( a ) Calculate the expected cash inflows and standard deviation of cash inflows for project

combinations X Y and XZ, and (b) determine the portfolio effects of the above combinations of

projects upon the portfolio risk.

SOLUTION

Since the probabilities associated with the cash inflows are not given (in fact, their cash inflows are

equally likely), the formulas for A and U are

i n

where n is the number of terms.

(a) For projects XY

( A -A)*6)

( A - 3 ) ($)

Cash MOW )($)

(A

8,000 600 360,000

7,000 -400 160,000

-400

7,000 160,000

7,000 -400 160,000

8,000 600 360,000

37,000 1,200,000

Thus

$490

U=

For projects XZ:

( A -A)($) ( A -A)2 ($)

Cash M o w ( A ) ($)

-4,200

3,000 17,640,000

-2,200 4,840,000

59 0 0

-200

7,000 40,000

8,000 800 640,000

13,000 5,800 33,640,000

36,000 56,800,000

277

CAPITAL BUDGETING UNDER RISK

CHAP. 91

02= $56˜800˜000 $11,360,000

=

5

Thus

$3,370

U=

(b) The greatest reduction in overall risk occurs when the portfolio combines projects which are

negatively correlated such as projects XY (i.e., axy= $490).

91

.5 CAPM and Capital Budgeting Decision. The Taylor Corporation is evaluating some new capital

budgeting projects. Their evaluation method involves comparing each projectвЂ™s risk-adjusted

return obtained from the capital asset pricing model (CAPM) with the projectвЂ™s average rate of

return. The following data are provided:

Projects Beta

-0.5

A

B 0.8

1.2

C

D 2.0

Possible rates of return and associated probabilities are:

Rates of return (%)

(0.4) (0.5) (0.1)

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