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# 207__

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BUS 207
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Present value of indefinitely lived assets
PV (perpetuity) =CF/i (i is the interest). Examples of such an asset include perpetual bonds and
preferred stocks. I.e. the value of a perpetual bond that pays the owner \$100 at the end of each
year when the interest rate is fixed at 5 percent is given by PV=100/0.05=2000
Present value analysis is also useful in determine the value of the firm, since the value of the
firm is the present value of the stream of profits (cash flow) generated by the firms physical,
human, and intangible assets. In particular, if pi(0) is the firms current level of profits, then
pi(1) is the next years profit, and so on. Therefore the value of the firm is:
PV(firm)=pi(0)+pi(1)/(1+i)+pi(2)/(1+i)^2+pi(3)/(1+i)^3+.....
In other words, the value of the firm today is the present value of its current and future profits.
Notice that the value of the firm takes into account the long-term impact of managerial
decisions on profits. So the goal of the firm is to maximize the present value of current and
future profits.
Profit maximization
As previously mentioned, the profit maximization is to maximize the present value of current
and future profits.
Suppose a firms current profits are pi(0), and that these profits have not yet paid out to
shareholders as dividends. Imagine that these profits are expected to grow at a constant rate of
g percent each year, and that profit growth is less than the interest rate (g<i). In this case,
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