The time value of money is one of the basic concepts of modern financial management, which involves all financial activities and is a very important concept of financial management. The time value of money refers to the increased value of money after a certain period of investment and reinvestment, also known as the time value of funds. In the commodity economy, the economic value of 1 yuan is not equal to the economic value of 1 yuan a year later, or its economic utility is different. Even without inflation. Why is this happening? The reason is this: we deposit 1 yuan in the bank, and after 1 year, we can get 1. 1 yuan (assuming the deposit interest rate is 10%). This 1 yuan and the 0. 1 yuan added one year later are the time value of money. Of course, letting 1 yuan go will not add value, so the time value of money must be discussed on the premise of use. Without the premise of use, there will be no time value of money. The time value of money has become the most basic standard of financial valuation. The study of time value in financial management mainly focuses on the quantitative analysis of fund raising, investment, use and recovery, so as to find out the mathematical model suitable for scheme analysis and improve the quality of financial analysis.
Currency values at different times should not be compared directly, and they need to be converted to the same time point to be compared. Then the conversion requires a conversion ratio, which is the embodiment of the time value of money. It is determined according to the average appreciation level of currency in use. Because the growth of money with time and the appreciation of interest are similar in mathematics (in fact, interest itself is a form of time value of money), various methods for calculating interest are adopted in the conversion.
Calculation of interest includes simple interest and compound interest. Simple interest means that interest is only calculated on the principal during the loan period, and interest is no longer added to the principal, that is, interest is only calculated on the principal, and interest is no longer calculated. "Principal" refers to the original amount of the loan, which is the basis for calculating interest, also known as "parent fund". "Interest" refers to the use fee paid by the borrower to the lender that exceeds the principal. Compound interest is another way to calculate interest. According to this method, after each interest period, the interest generated should be added to the principal to calculate interest, which is also commonly known as "rolling interest", not only the principal, but also interest.
Money will increase in value over time, but what is the form of value-added? In other words, is it in the form of simple interest? Or in the form of compound interest? Broadly speaking, from the perspective of the whole society, there are two forms of value-added. For example, bank deposit interest and general loan interest in our country are simple interests. The form of interest bearing may be related to the degree of economic development, and western developed countries often use compound interest to bear interest. From a narrow point of view, that is, from the perspective of value-added economic activities of enterprises, the time value of money is increased in the form of compound interest, because both the initial funds and the funds earned later can be used for reinvestment, that is, the increase in income is increased in the form of compound interest. Financial management is generally studied from the perspective of enterprises, so the discount calculation used in financial management is compound interest discount calculation.
Due to the degree of social development and people's acceptance of simple interest and compound interest, there are simple interest and compound interest in social objective reality. Moreover, due to the complexity of compound interest calculation and the difficulty for non-professionals to understand compound interest, there are a lot of simple interest forms in daily life.
In terms of quantity, the time value of money is the average social capital profit rate without risk and inflation, which is macroscopic. But when people are evaluating the scheme, who knows what the average social profit rate was at that time? Generally speaking, the average profit rate of social capital is the result of ex post statistics. Of course, people can guess, estimate or increase or decrease on the basis of the previous year. But who can guarantee that this ratio is correct? In the case of inaccurate statistical information or distorted accounting information, the average social profit rate of the previous year will of course be distorted. And this ratio is a concept of compound interest, who can easily understand it? Therefore, few people really use the social average capital profit rate that should be used in theory when making scheme decisions. So, which ratio do you usually use? Or how to determine this ratio? The author believes that when determining the proportion of evaluation schemes, people should usually contact the source of investment funds, that is, the way of financing should be considered when evaluating the feasibility of investment. If a person's investment funds are all borrowed from the bank, then usually he will consider whether the investment income exceeds the loan interest when determining whether the investment is feasible. It is feasible to exceed it, and it is not feasible to not exceed it. Investment income occurs according to compound interest, while loan interest may occur according to simple interest (especially in China). So, how do you compare these two growth rates? If it is self-owned funds, the bottom line of its value is the deposit interest rate, and the direct and better comparison object is the bank loan interest rate, that is, the rate of return of self-owned funds cannot be lower than the bank loan interest rate, because this is a question of the use of funds. The general deposit and loan interest rates are in the form of simple interest, so the minimum rate of return required in people's minds at first should generally appear in the form of simple interest. The minimum rate of return required by people at first is generally not in the form of compound interest, because the form of compound interest is difficult to understand and think clearly, especially when the investment involves many years, it is difficult to determine the expansion ratio of "rolling interest" without calculation. If the funds are both loans and self-owned, then the minimum rate of return required by the decision-makers at the beginning is generally in the form of simple interest, and the bottom line of its value is of course the deposit interest rate, which should generally not be lower than the bank loan interest rate. Of course, in determining the minimum rate of return required by investors, in addition to considering industry characteristics and personal preferences, the bank loan interest rate is a clear reference. Because the interest rate of bank loans is usually in the form of simple interest, the lowest rate of return initially formed by decision makers is usually in the form of simple interest and the rate of return on investment is in the form of compound interest, so it is necessary to convert the required minimum rate of return into the form of compound interest. So, how to convert? In order to simplify the problem and better explain the calculation method of transformation, we only consider the situation that all the funds come from bank loans, and other situations can be compared.
Suppose you borrow 6,543,800 yuan from the bank, with simple interest, with an annual interest rate of 654.38+00%, for five years, and repay the principal and interest at the end of the fifth year. Q: How much is compound interest equal to simple interest 10%?
Suppose that p represents the present value, f represents the final value, f represents compound interest, and (p/f, Ⅰ, 5) represents the five-year compound interest present value coefficient.
After five years, the sum of principal and interest is:100× (1+5×10%) =150 (ten thousand yuan), and the formula for solving compound interest is the same as that for simple interest: 150× (.
∴ (P/F，ⅰ)=0.6667
Looking up the present value coefficient table of compound interest, there is no value of 0.6667 in the row with the number of periods of 5, but two adjacent figures can be found (one is required to be greater than 0.6667 and the other is required to be less than 0.6667): 0.6806 and 0.6499, corresponding to the discount rates of 8% and 9% respectively. Let's find the value of I by interpolation:
ⅰ=8%+ [(0.6806-0.6667)/(0.6806-0.6499)]×(9%-8%)=8.45%
Let's discuss the application of converting simple interest into compound interest. There are many kinds of investment decisions, among which the methods to consider the time value are usually: net present value method, internal rate of return method, profitability index method and so on. Below, we take the net present value method as an example to illustrate.
Suppose an enterprise borrows 6,543,800 yuan from a bank to purchase and build a production line, with an annual interest rate of 654.38+00% and a service life of 5 years. Assuming that the construction period is zero, it is estimated that the annual average net cash flow will be 300,000 yuan and the final residual value will be 654.38+10,000 yuan. Suppose this is the only option that can be considered. Is this scheme feasible?
First of all, as in the previous example, the interest rate of bank loans should be converted into compound interest. Because the data about bank loans in our example is exactly the same as the previous example, we know that the converted compound interest is 8.45%.
Secondly, we calculate the net cash flow at the end of each year: 10,000 yuan.
Ncf (1-5) = 300,000 yuan.
Ending residual value ncf5 ′ = 654.38+ten thousand yuan.
Third, calculate the net present value of the scheme: (A is annuity)
Net present value (NPV) =- 100+30× (P/A, 8.45%, 5)+ 10× (P/F, 8.45%, 5).
Because the present value coefficient of 8.45% can't be found in the present value coefficient table of annuity and compound interest, it can't be found directly, so the present value NPV is found by interpolation.
The percentages closest to 8.45% in the annuity present value coefficient table and the compound interest present value coefficient table (one requires less than 8.45% and the other requires more than 8.45%) are 8% and 9%, and the corresponding NPV 1 and NP v2:(P/A, 8%, 5)+65438+ are obtained by substituting the above formulas respectively.
=- 100+30×3.9927+ 10×0.6806
=26.59 (ten thousand yuan)
NPV2=- 100+30×(P/A，9%，5)+ 10×(P/F，9%，5)
=- 100+30×3.8897+ 100.6499
=23. 19 (ten thousand yuan)
8.45% corresponds to ∴ NPV = NPV2+[(I2-I)/(I2-I1) ]× (NPV1-npv2).
= 23.19+[(9%-8.45%)/(9%-8%)] × (26.59-23.19) = 25.01(ten thousand yuan)
Because NPV is greater than 0, that is, its actual rate of return is 8.45% higher than the compound interest of bank loans, so this scheme is feasible.
The evaluation of investment schemes under other different financing methods is the same in principle. Firstly, the minimum simple interest required by investors is converted into compound interest, and then the scheme is evaluated by combining net present value method and other methods.
To sum up, the use of money has time value, and the value-added of funds used by enterprises is increased in the form of compound interest. It is usually easier for decision makers to evaluate the scheme intuitively with simple interest, so it is necessary to unify the form of simple interest evaluation to the form of compound interest growth of capital operation. When evaluating the scheme, we should first convert simple interest into compound interest, and then evaluate the scheme with investment decision analysis methods such as net present value method. In this way, the combination of investment evaluation and financing sources will make the scheme analysis more practical.