стр. 131 |

SOLUTION

The standardized normal variate is:

For NPV of zero or less:

(a)

0 - $30,000 = -2

z=

$15,000

From Appendix E, z = 2 2 corresponds to a probability of 0.0228 or 2.28 percent.

CAPITAL BUDGETING UNDER RISK

274 [CHAP. 9

(b) For NPV of $45,000 or more:

$45,000 - $30,000

= 1.0

Z=

$15,000

From Appendix E, the probability for this value of z is 15.77 percent.

For NPV of $7,500 or less:

(c)

$7,500 - $30,000

= -1.5

Z=

$15,000

From Appendix E, the probability for z 21.5 is 6.68 percent.

=

Normal Distribution and NPV Analysis. The Halo Shipping Company is considering

9.13

an investment in a project that requires an initial investment of $6,000, with a projected

after-tax cash inflow generated over the next 3 years as follows:

Period 2 Period 3

Period 1

Probability Cash Flow ($)

Cash Flow ($) Probability Probability

Cash Flow ($)

1,000 1,000

0.2 1,000 0.3

0.10

0.30 2,000 0.4 2,000 0.4 2,000

0.20 3,o 0.1

0.3 3,000 3,000

0.40 4,000 0.1 4,000 0.2 4,000

Assume that probability distributions are independent and the after-tax risk-free rate of

return is 6 percent. Calculate: (a) the expected NPV of the project; ( b ) the standard deviation

of the expected NPV; ( c ) the probability that the NPV will be zero or less (assume that the

probability distribution is normal and continuous); ( d ) the probability that the NPV will be

greater than zero; and ( e ) the probability that the NPV will be greater than the expected

value.

SOLUTION

Period 1 Period 3

Period 2

$1,ooo(0.1)= $ 100 $L000(0.3) = $ 300

$1,000(0.2) = $ 200

$2,000(0.4) = 800

$2,000(0.4) = 800

$2,000(0.3) = 600

$3,000(0.3)= 900 $3,000(0.1) = 300

$3,000(0.2) = 600

$4,000(0.4) = 1,600 $4,000(0.1) = 400 $4,000(0.2) = 800

- - -

$2,200

$2,900 $2,300

NPV=PV-I

- (1$27900 (1$2,300 (1$2,200 - $6,000

+ 0.06) + 0.06)2 + 0.0613

+ +

$2,900(PVIF,,,l) + $2,3OO(PVIF,,,z) + $2,2OO(PVIF,%,3)- $67@)0

=

= $2,900(0.943) + $2,300(0.89) + $2,200(0.84) - $6,ooo

= $2,735 + $2,047 + $1,848- $6,000 = $6,630- $6,000 = $630

275

CAPITAL BUDGETING UNDER RISK

CHAP. 91

(b) Calculations for standard deviation of NPV are as follows:

For period 1:

p (A-A) (A-A)* (A-A)'p

A

$3,610,000 $ 361,000

0.1 -$1,900

$I,OoO

$ 810,000 243,000

-$ 900

0.3

$2,000

$ 10,Ooo 2,000

$ 100

0.2

$3,000

484,000

$1,210,000

$4,000 0.4 $1,100

$1,090,000'

1,0M6

$

"$1,090,000 = a2

b$1,044 = CT

For period 2:

( A -A)'p ($)

( A -2)' ($1

( A - A ) ($1

A ($1 p

-1,300 1,690,000 338,000

1,000 0.2

90,000 36,000

0.4

2,000 -300

490,000 147,000

3,000 0.3 700

2,890,000 289,000

0.1 1,100

4,000

u2= 810,000

800

U= $

стр. 131 |