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Two-period Risk Neutral Valuation: European

Valuation

A firm is considering a project, Project V.1, whose expected cash flows have a PV of $40 but requires an initial investment of $55. Management is evaluating the value that can be added by an expansion option that can be created by Project V.1.

• In particular, management is considering the possibility that at the end of two years, as a result of undertaking Project V.1, the firm can invest $100 in some project, Project V.2.

• The current value of Project V.2 is $80 with a project wacc of 20%. In year 1, its value can go up to 160 with a robust economy or down to $40 with a soft economy. In the second year, the value of Project V.2 can change again:

14. if the year-one value is $160 (robust) the year-two value can go up to $320 (very robust) or down to $80 (mediocre) in the second year;

14. if the year-one value is $40 (soft) the year-two value can go up to 80 (mediocre) or down to 20 (very soft) in the second year.

• The risk free rate is 8%.

BACKWARD INDUCTION

Step 1. Calculate DERIV T

DERIVuu

DERIVud

DERIVdd

Step 2. Node B: Calculate q and DERIV u

Step 3. Node C: Calculate q and DERIV d

Step 4. Node A: Calculate q and DERIV o

Step 5. What is the optimal investment (option exercise) plan?

Other questions:

1. Calculate the NPV of the Project V.1 without the option to invest.

2. Is Project V.1 attractive with the expansion option? Why?