Investment Science: Present value analysis of cash flow streams

Tuesday, August 17, 2010

In the last post, we saw the formula for calculating the present value and future value of a stream, in this section, we will see an example on how to apply the present value analysis to arrive at an investment  decision, for illustrating this, we will solve an exercise problem from by Investment Science David G. Luenberger (Problem 2.7) to make things clear.

The investment scenario is as follows.

Suppose there exists an opportunity to plant trees which can be harvested in future and there are two choices to cut the tree

1. Cut early with an associated cash flow stream of (-1, 2) (Get quick returns)
2. Cut later with an associated cash flow stream of (-1, 0, 3) (Wait an extra year so that the trees will grow, hence there is a chance for a greater revenue).

Suppose the interest rate is 10% and cash flows occur at the end of the year.

Case 1: Cut early with an associated cash flow stream (-1, 2)


Case 2: Cut later with an associated cash flow stream (-1, 0, 3)


As obvious, based on the present value analysis, it's better to cut later, but now a different case arises.

Problem 2.7: Gavin Jones is inquisitive and and determined to learn both the theory and the application of investment theory. He pressed the tree farmer for additional information and learned that it was possible to delay cutting of trees for another year. The farmer said that from a present value perspective, it was not worthwhile to do so. Gavin instantly deduced that the revenue obtained must be less than x, What is x?

Let's first calculate the present value this cash flow stream.

In case Gavin decided to wait one more year, then the present value of this cash flow stream would be (assume that the cash flow of this stream is (-1, 0, 0, x) where x > 0)

Case 3: Wait one more year than in case 2 and cut the tree with a cash flow stream (1, 0, 0, x)


But since the farmer mentioned that from the present value analysis, it's not worthwhile to do so, therefore

Therefore the revenue obtained must be less than 3.3 (or the cash flow stream at the end of three years should be <3.3)

In short, one can analyze different cash flow streams based on computing their present values to arrive at an investment decision.

References: Investment Science by Gavin G. Luenberger.

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