Present Value and The Opportunity Cost of Capital - How to Calculate Present Values

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Present Value and the Opportunity Cost of Capital
All firms make new investments in different real assets and their goal is to find the assets that worth more than they cost. 
The basic method to value a real asset is to find its present value. For example if a person which receive money from the fire insurance company, after his house was burned, can rebuild his house, can put the money in an office building or can invest in government securities maturing in a year. 
If he chose to construct the office building, his estate adviser anticipates a shortage of offices space and predicts that in a year the new building will worth more if he sold it. The question is that the present value of this expected payoff is greater than his investment. 
The present value of a cash flow one year from now must be less than the cash flow, to correspond with the first basic principle of finance, which says that a dollar today is worth more than a dollar tomorrow. The present value of a payoff is the payoff multiply by a discount factor, which is the value today of a $ 1 received in the future. It depends on the rate of return which is the compensation that investors demand for accepting delayed payments. 
PV= discount factor C1= C1
The rate of return or the opportunity cost is the return foregone by investing in the project rather than in investing in securities. 
If the building has a present value, this doesn't mean that the person has all this money. The net present value that the person has is the difference between the present value and the required investment. And for that we can say that his building worth more than it costs. 
NPV= C0 + 
When we speak about the future value of office building, we don't think at a sure thing. There is a second basic principle of finance which says that a safe dollar is worth than a risky one. If investors must chose between buying a building and buying government securities, they will choose the second version because it is safer. Most investors avoid risk when they can do so without sacrificing the gain. Each investment has different risks. The buildings are more risky than government securities but less risky than a start-up biotech venture. 
There are two decision rules for capital investment:
1. Net present value rule which says that we need to accept investments that have positive net present value. With other words, we need to accept investments that worth more than it costs. The NPV is the difference between the discounted or present value, of the future income and the amount of the initial investment
2. Rate of return rule. The rate of return on the investment is the profit as a proportion of the initial costs. We need to accept investments that offer rates of return in excess of their opportunity costs of capital.
The opportunity cost of capital for an investment project is the expected rate of return, which is the expected profit divided by investment, demanded by investors in common stocks subject to the same risks as the project. 
We can introduce the term capital market which is a market where people trade cash flow across time. We can imagine that on this market are two different investors. First, A, wants to save for the future and the second, B, prefer to spend now all his money. Both investors can buy a share in an office building or can borrow or land in the capital rate at the same rate. A will invest in office building because at the end of the year he will have much money, than if he would invest in capital market. On the other side G who wants money in the present can spend a higher sum if he invests in building and than borrow his future income from a bank than if he spends his money today.
There is a special case when the investors don't care about in which they will invest: in office building or in capital market, because the gains will be the same. The project will be on a knife edge when the interest rates in buildings and that in capital market are the same. In this case the NPV of the office building is zero.
If G couldn't borrow his future income and he will want to spend the money in the present. And if the both investors were shareholders in the same company, it will be so hard to conciliate their different objectives. 
Every manager has to satisfy the desires of the stockholders that want to be rich, to spend their wealth when they want and to choose the risk characteristic. For satisfy the stockholders, managers should make investments with a positive net present value and to maximize net present value. Stockholders can spend their money when they want because they have free access on the competitive market and they can choose the risk characteristic when they invest in more or less risky securities.
Each corporate has different goals. Managers can maximize the profit for the next year at the expense of profit in later years, an other method is maximizing profits by reducing the stockholder's dividends.

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