Interest rate

The value of NPV is, of course, directly dependent on the choice of the fractional interest rate i. 

The higher the value of the DCFRR for a project, the more attractive it is. The minimum acceptable value of the DCFRR is the market interest rate. If the DCFRR is lower than market interest rate, it would be better to put money in the bank. For a DCFRR value greater than this, the project will show a profit for a lesser value, it will show a loss. 

How are the big deals made Which are the institutions that really matter What causes the pound to rise or interest rates to fall This book provides clear and concise answers to these and many other money-related questions. 

Suppose you have to meet an obligation to pay a bill of 10,000 in 5 years time. If you could be guaranteed a compound interest rate in your bank of 7% per annum (after tax) over each of the next 5 years, then the sum which you would have to invest today to be able to meet the obligation in 5 years time would be ... 

If you were offered 7,130 today, or 10,000 in exactly 5 years time, you should be indifferent to the options, unless you could find an alternative investment opportunity which yielded a guaranteed interest rate better than the bank (in which case you should accept the money today and take the alternative investment opportunity). 

In the above example, the discount rate used was the annual compound interest rate offered by the bank. In business investment opportunities the appropriate discount rate is the cost of capital to the company. This may be calculated in different ways, but should always reflect how much it costs the oil company to borrow the money which it uses to invest in its projects. This may be a weighted average of the cost of the share capital and loan capital of a company. 

Fuel costs are taken to be 1.00/GJ ( 1.05/MBtu) the escalation and interest rates are 6.5% and 10%, respectively and the factor used for calculating levelized fuel and operating and maintenance cost is 2.004. 

Optimism about economic growth in the period 1960—1975 led to a large number of reactor orders. Many of these were canceled even after partial completion in the period after the 1974 oil crisis, as the result of a reduction in energy demand. Inflation, high interest rates, long constmction periods, and regulatory delays resulted in severe cost overmns. Moreover, the reactor accidents of TMI and, later, Chernobyl produced an atmosphere of pubHc concern. 

Interest rate 0 End-of-year flows Line-item interest neglected... 

Prevailing interest rates probably tend to reflect an estimate of future inflation and contain a component that can be attributed loosely to inflationary expectations. However, the classical treatment is to assume that an inflation-free interest rate, r and average inflation rate, r, over the project lifetime can be identified. A discount factor (1 + r) can be modified (25) so that... 

The same formula applies to the value of an annuity (PW) now, to provide for equal payments R at the end of each of n years, with interest rate 7,... 

Various i Interest rate per period, usually annual, often tbe cost of capital Dimensionless... 

Dimensionless Dimensionless K Effective interest rate defined by Eq. (9-111) Dimensionless... 

A fourth method of computing depreciation (now seldom used) is the sinking-fund method. In this method, the annual depreciation A is the same for each year of the life of the equipment or plant. The series of equal amounts of depreciation Aq, invested at a fractional interest rate i and made at the end of each year over the life of the equipment or plant of s years, is used to build up a future sum of money equal to (Cpc S). This last is the fixed-capital cost of the equipment or plant minus its salvage or scrap value and is the total amount of depreciation during its useful life. The equation relating i Fc S) and Ao is simply the annual cost or payment equation, written either as... 

The fractional interest rate of return based on the net annual profit after tax and the original investment is... 

For the case of different annual fractional interest rates -,K in successive years), Eq. (9-32) should be written in the form... 

Short-Interval Compound Interest If interest payments become due m times per year at compound interest, mn payments are required in n years. The nominal annual interest rate Y is divided by m to give the effective interest rate per period. Hence,... 

The annual interest rate equivalent to a compound-interest rate of 5 percent per month (i.e., i /m = 0.05) is calculated from Eq. (9-38) to be... 

A comparison of Eqs. (9-32) and (9-39) shows that the nominal interest rate i on a continuous basis is related to the effective interest rate i on an annual basis by... 

Let us suppose that 100 is invested at a nominal interest rate of 5 percent. We then compute the future worth of the investment after 2 years and also compute the effective annual interest rate for the following lands of interest (I) simple, (2) annual compound, (3) monthly compound, (4) daily compound, and (5) continuous compound. The following tabulation shows the results of the calculations, along with the appropriate equation to be used ... 

Factors presented for two interest rates only. By using the appropriate formulas, values for other interest rates may he calculated. 

Annual Cost or Payment A series of equal annual payments A invested at a fractional interest rate i at the end of each year over a period of n years may be used to build up a future sum of money E These relations are given bv... 

Equation (9-41) represents the future sum of a series of uniform annual payments that are invested at a stated interest rate over a period of years. This procedure defines an ordinaiy annuity. Other Forms of annuities include the annuity due, in which payments are made at the beginning of the year instead of at the end and the deferred annuity, in which the first payment is deferred for a definite number of years. 

Ck is in excess of Cpc by an amount which, when compounded at an annual interest rate i for n years, will have a future worth of less the salvage or scrap value S. 11 the renewal cost of the equipment remains constant at (Cp S) and the interest rate remains constant at i, then Ck is the amount of capital required to replace the equipment in perpetuity. 

Example 1 Capitalized Cost of Equipment Apiece of equipment has been installed at a cost of 100,000 and is expected to have a working life of 10 years with a scrap value of 20,000. Let us calculate the capitalized cost of the equipment based on an annual compound-interest rate of 5 percent. 

The value of (NPV) is directly dependent on the choice of the fractional interest rate L An interest rate can be selected to make (NPV) = 0 after a chosen number of years. This value of i is found from... 

Equation (9-54) may be solved for i either graphically or by an iterative trial-and-error procedure. The value of i given by Eq. (9-54) is known as the discounted-cash-flow rate of return (DCFRR). It is also known as the profitability index, true rate of return, investor s rate of return, and interest rate of return. 

The cost of capital may also be considered as the interest rate at which money can be invested instead of putting it at risk in a manufacturing process. Let us consider the process data listed in Table 9-4 and plotted in Fig. 9-10. If the cost oi capital is 10 percent, then the appropriate discounted-cash-flow curve in Fig. 9-10 is abcdef. Up to point e, or 8.49 years, the capital is at risk. Point e is the discounted breakeven point (DEEP). At this point, the manufacturing process... 

Comparisons on the basis of interest can be summarized as (1) the net present value (NPV) and (2) the discounted-cash-flow rate of return (DCFRR), which from Eqs. (9-53) and (9-54) is given formally as the fractional interest rate i which satisfies the relationship... 

For this simphfied case the net present value (NPV) after n years with money invested at a required aftertax compound annual fractional interest rate i is given by the equation... 

With a disbursement of 1000 in Year 0, the discounted breakeven point (DEEP) will be reached in 3 years at a compound-interest rate of 30 percent if the annual net profit Avp = 550.63 per year. Thus, a... 

In effec t, in computing the average net annual cash flow per dollar invested, the value of f p of Eq. (9-46) has been obtained for this example. From tables of the annuity present-worth factor/ p the value of the interest rate is found to be = 0.25 when f p = 0.5124 with n = 3 years. 

The same money invested in a project with a (DCFRR) of 10 percent would, by Eq. (9-108), obtain an entrepreneurial return i = 8.37 percent on the whole investment, i.e., 8.37/ 100. Investment of the entrepreneur s own money would only achieve an aftertax return of (0.1)(1 — 0.40) = 6 percent on 50, or 3/ 100 of total investment. The incentive to the entrepreneur to manage the projeci thus corresponds to a tax-free income of 5.37/ 100 of total investment. In practice, money is borrowed from more than one source at different interest rates and at different tax liabihties. The effective cost of capital in such cases can be obtained by an extension of the above reasoning and is treated in detail by A. J. Merrett and A. Sykes Capital Budgeting and Company Finance, Longmans, London, 1966, pp. 30 8). 

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