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|INTRODUCTION A company must have an objective, and that usually is to earn money. In some countries an objective can also be to reduce unemployment in an area or to develop nonindustrialized areas. Government-owned companies can also have as an objective that of serving the com¬munity. This discussion is limited to the consideration of normal companies wanting to earn money. Such an objective, however, has to be defined in more detail. It is not satisfactory only to maximize the total annual profit from, for example, a mining project. In comparison with most other branches, the mining in¬dustry is very capital intensive. When starting a new project, the mining company must invest a lot of money in mines, ore treatment plants, etc. It is normally many years before any income is received from the ore. Fig. 14 illustrates the payments for a new mining proj¬ect with an expected lifetime of 10 years. Whether this project is a profitable one depends on a lot of things. If the company has a shortage of money, it can be impossible to finance the project. Even if the company has enough money, the management may think that perhaps the project may not return the money fast enough. Such limitations will not be discussed here. Suppose that the company has internal funds from its own operation or can borrow them. Since the mining company must invest the money in advance, it is not satisfactory only to add all of the costs during the mine's lifetime and compare them with the total income during the lifetime. The company must include the time value of the capital. In this appendix, the basic investment theory neces¬sary to judge the profitability and costs of mining proj¬ects will be discussed. INVESTMENT THEORY Time Value of Money If a private person has a dollar and puts it into a bank, he or she will receive interest. If the interest rate is r%, the value after one year will be $(1 + r), after 2 years $(I + r)2 , etc. The interest rate represents the time value of money. If the same person wants to have $1 in the bank af¬ter one year, he or she has to put $(1 + r)-1 in the bank today. If the person wants $1 after 2 years, it is neces¬sary to put $(1 + r)-2 into the bank today, etc. So one dollar today is worth more than one dollar tomorrow. It is, of course, not correct to compare money at differ¬ent times since each dollar has a different value. It is necessary to transform all payments to the same point in time. That is called the calculation of the capital value of a cash flow, and to do this an interest rate is used. In the same way, the cash flow from a project like that shown in Fig. 14 can be translated to any other point in time. Most common is to translate all payments to the beginning of the mining period. That capital value is often called the present capital value. Interest Rate What interest rate will the company use? A com¬pany, just like an individual, has the basic alternatives of keeping its money in the bank and receiving interest, or borrowing money from a bank and paying an interest rate. The interest rate represents the time value of money for the company. If the company has a shortage of money, or many good potential investment projects, it has to use a higher interest rate than if it has a lot of money available. Most companies also increase their interest rate as a hedge against the risk involved by using money for uncertain investments, because of taxes, etc. Capital Value When the interest rate has been decided, it is possi¬ble to estimate the capital value of a project. Here the discussion will be limited to the estimation of present capital values. Suppose that one wants to know the present capital value of $1 (Fig. 15), which will be received after n years. To transform it n years back in time, one must multiply it by the factor (1 + r)-, where r is the inter¬est rate the company uses. Table 1 gives these factors for different years and interest rates. Example: At the end of year 5 a mining company has to invest $50 million in a new mine. What is the present capital value at the end of year 0? The company uses an interest rate of 15%a.|