Financial Mathematics

9. (Shortcut) Gavin Jones is inquisitive and determined to learn both the theory and the mer for additional information application of investment theory. He pressed the tree far and learned that it was possible to delay cutting the trees of Example 2.4 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? Example 2.4 (When to cut a tree) Suppose that you have the opportunity to plant trees that later can be sold for lumber. This project requires an initial outlay of money in order to purchase and plant the seedlings. No other cash flow occurs until the trees are harvested. However, you have a choice as to when to harvest: after 1 year or after 2 years. If you harvest after 1 year, you get your return quickly: but if you wait an additional year, the trees will have additional growth and the revenue generated from the sale of the trees will be greater. We assume that the cash flow streams associated with these two alternatives are (a) (-1,2) cut early (b) (-1,0,3) cut later. we also assume that the prevailing interest rate is 10%. Then the associated net present values are (a) NPV =-1 + 2/1.1 = .82 (b) NPV-1+3/(1.1)2 1.48. Hence according to the net present value criterion, it is best to cut later. The net present value criterion is quite compelling, and indeed it is generally regarded as the single best measure of an investment's merit. It has the special advan- tage that the present values of different investments can be added together to obtain a meaningful composite. This is because the present value of a sum of cash flow streams is equal to the sum of the present values of the corresponding cash flows. Note, for example, that we were able to compare the two investment alternatives associated with tree farming even though the cash flows were at different times. In general, an