# As an example of the present-value analysis given in Exercise 8, consider four projects with cash…

As an example of the present-value analysis given in Exercise 8, consider four projects with cash flows and upper bounds as follows:

A negative entry in this table corresponds to a cash outflow and a positive entry to a cash inflow. The horizon-value model is formulated below, and the optimal solution and associated shadow prices are given:

a) Explain exactly how one additional dollar at the end of year 2 would be invested to return the shadow price 1.25. Similarly, explain how to use the projects in the portfolio to achieve a return of 1.35 for an additional dollar at the end of year 0.

b) Determine the discount factors for each year, from the shadow prices on the constraints.

c) Find the discounted present value  of each of the four projects. How does the sign of the discounted present value of a project compare with the sign of the reduced cost for that project? What is the relationship between the two? Can discounting interpreted in this way be used for decision-making?

d) Consider the two additional projects with cash flows and upper bounds as follows:

What is the discounted present value of each project? Both appear promising. Suppose that fun ds are transferred from the current portfolio into project E, will project F still appear promising? Why? Do the discount factors change?

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