Please show formulas

c. Now assume that the project cannot be shut down. However, expertise gained by taking it on will lead to an opportunity at the end of Year 3 to undertake a venture that would have the same cost as the original project, and the new project's cash flows would follow whichever branch resulted for the original project. In other words, there would be a second $10 million cost at the end of Year 3, and then cash flows of either $9 million, $4 million, or -$1million for the following 3 years. Use decision tree analysis to estimate the value of the project, including the opportunity to implement the new project in Year 3. Assume the $10 million cost at Year 3 is known with certainty and should be discounted at the risk-free rate of 6 percent. Hint: do one decision tree for the operating cash flows and one for the cost of the project, then sum their NPVs.

WACC=

12%

Risk-free rate=

6%

Decision Tree Analysis

Cost

Future Operating Cash Flows (Discount at WACC)

NPV this

Prob.

0

Probability

1

2

3

4

5

6

Scenario

x NPV

27

$9

$9

$9

$9

$9

$9

8

30%

-$0.39

-$10

40%

$4

$4

$4

(0)

30%

$12.40

-$1

-$1

-$1

(4)

Expected NPV of Future Operating CFs =

4

Future Cost of Implementing Additional Project (Discount at Risk-free rate)

NPV this

Prob.

0

Probability

1

2

3

4

5

6

Scenario

x PV

(8)

(2)

$50

$50

$50

-$10

30%

40%

30%

Expected NPV of Future Operating CFs =

(2)

Total NPV (NPV of Future Operating CF plus NPV of Future Year 3 cost of implenting additional project) =

2