. Naughty Pine Lumber Company is evaluating a new saw with a life of two years. The saw costs $3,000, and future after-tax cash flows depend on demand for the company's pro- ducts. The tabular illustration of a probability tree of possible future cash flows associated with the new saw is as follows: YEAR I YEAR 2

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1. Naughty Pine Lumber Company is evaluating a new saw with a life of two years. The saw
costs $3,000, and future after-tax cash flows depend on demand for the company's pro-
ducts. The tabular illustration of a probability tree of possible future cash flows associated
with the new saw is as follows:
YEAR I
YEAR 2
CONDITIONAL
PROBABILITY
P(2 | 1)
INITIAL
NET
NET
PROBABILITY
P(1)
CASH
FLOW
CASH
FLOW
BRANCH
$1,000
1,500
2,000
0.30
0.40
$1,500
0.40
2
0.30
3
1.00
0.40
2,000
4
2,500
3,000
0.60
2,500
0.40
0.20
1.00
6.
1.00
a. What are the joint probabilities of occurrence of the various branches?
b. If the risk-free rate is 10 percent, what is (i) the net present value of each of the six com-
plete branches, and (ii) the expected value and standard deviation of the probability
distribution of possible net present values?
c. Assuming a normal distribution, what is the probability that the actual net present
value will be less than zero? What is the significance of this probability?
Transcribed Image Text:1. Naughty Pine Lumber Company is evaluating a new saw with a life of two years. The saw costs $3,000, and future after-tax cash flows depend on demand for the company's pro- ducts. The tabular illustration of a probability tree of possible future cash flows associated with the new saw is as follows: YEAR I YEAR 2 CONDITIONAL PROBABILITY P(2 | 1) INITIAL NET NET PROBABILITY P(1) CASH FLOW CASH FLOW BRANCH $1,000 1,500 2,000 0.30 0.40 $1,500 0.40 2 0.30 3 1.00 0.40 2,000 4 2,500 3,000 0.60 2,500 0.40 0.20 1.00 6. 1.00 a. What are the joint probabilities of occurrence of the various branches? b. If the risk-free rate is 10 percent, what is (i) the net present value of each of the six com- plete branches, and (ii) the expected value and standard deviation of the probability distribution of possible net present values? c. Assuming a normal distribution, what is the probability that the actual net present value will be less than zero? What is the significance of this probability?
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