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  Investment, Time and Risk

Investment, Time and Risk (Basic issues in Finance):

Intertemporal Investment Decisions- The Importance of Time and Discounting

1) Time as one of the most important factors affecting firm’s investment decisions: A firm’s decision to purchase a capital good, such as a new plant or a new piece of heavy machinery, differs from its decision to hire more labor or purchase additional raw materials, in large part because of very different time horizons for these decisions. Once a firm purchases a new capital good, the firm is stuck with that decision for years to come, while labor can be laid off on a short notice, and raw material orders can be quickly cancelled.

2) Present Value and Discounting:

• X dollars invested today at an interest rate r would increase in value to X (1+ r) dollars in one year, X (1+ r)(1+ r) = X (1+ r)2 dollars in two years, and X (1+ r)t dollars in t years. The present value of X (1+ r)t dollars received t years from today equals X (1+ r)t /(1+ r)t = X dollars. By similar reasoning, the promise to pay X dollars t years from today has a present value of:

PV= X/(1+ )t

• Present Value of Profit: Suppose π t represents the firm’s profit in time period t, and (1+ r) represents the rate at which the firm is willing to trade future for present income just as it represented the rate at which an individual would trade future for present consumption.

1063_present value of profit.jpg

The maximization of long-run profit implies the maximization ofπ PV . Equation shows that the maximization of long-run profit depends not only one the annual flow of economic profit, t π , but also critically depends on the discount rate, r. Firms with short time horizons place a low value on future profits and are willing to trade current profit for future profit only a at high interest rate, and therefore have high discount rates. These firms want to earn high profits in early periods even if it means sacrificing large future profits. Firms with longer time horizons are willing to trade current profits for future profits at a low interest rate, and therefore have lower discount rates. These firms are willing to sacrifice current profits in order to earn higher profits in the future.

Assuming that n goes to infinity and t πis constant and equal toπ for all values of t Equation can be rewritten as:

1850_value of profit.jpg

Generalized Present Value Calculations:

Equation can be generalized for any sum beginning at any time t, not just for t =1.

1777_present value of calculations.jpg

Where c is any digit less than equal to or greater than zero. In Equation, c represents the time when the flow of profit begins. If the profit flow begins in the current time period, c = 0. Rewriting Equation will yield:

1175_present value calculations.jpg

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