The time value of money refers to the appreciation of money over time.

It means that a certain amount of currency currently held has higher value than the equivalent currency obtained in the future. From an economic point of view, the reason why the purchasing power of the current unit currency is different from that of the future unit currency is that in order to save the current unit currency from consumption and convert it into consumption in the future, there must be more than one unit currency available for consumption in the future as a discount to make up for the delayed consumption.

The forms of time value of money are: (1) relative number, risk-free and inflation-free social average capital profit rate; (2) Absolute number, that is, time value, is the real value-added amount brought by funds in the process of production and operation, that is, the product of a certain amount of funds and time value rate.

0 1

Time value of money

The time value of money can't be generalized, and those static monetary funds (such as money locked at the bottom of a box, hidden under a pillow or put in a pocket) will never produce time value; What's more, the original value of these currencies will depreciate with domestic inflation. Therefore, to be exact, only when monetary funds are put into the process of lending or investment, so that they can be effectively moved and used, will the time value of money be formed. The so-called time value of money refers to the appreciation after a certain period of investment and reinvestment. For lending behavior, it is the interest obtained (or paid) after lending (or borrowing) the principal; Interest is a kind of compensation or reward that the depositor or lender obtains from the borrower by giving up the right of current consumption and temporarily transferring monetary funds to others for use on the basis of credit. Therefore, the manifestation of the time value of money can be regarded as the interest rate under the conditions of relative risk-free and inflation-free, and it is the lowest rate of return required by the owner of monetary funds to transfer the right to use funds. The time value of money is the lower limit of the profit rate of enterprise funds and the basic standard for evaluating investment schemes.

Because of the time value of money, it is not appropriate to directly compare the amount of funds at different time points, because the information conveyed by this comparison result has been distorted to a considerable extent. For example, investors will intuitively think that 1 yuan today and 1 yuan a year later are not equivalent. If you deposit 1 yuan in the bank today, you will get 1. 1 yuan one year later according to the bank interest rate. The extra interest of 0. 1 yuan is the appreciation of 1 yuan after one year of investment, which is the time value of money. Obviously, 1 yuan today is equal to 1. 1 yuan a year later. Because the value of funds at different time points is different, we must convert the funds at different time points to the same time point when comparing the values. Therefore, the schedule of expected future cash flow and interest rate level are very important for the pricing of financial assets.

02

Calculation of final value and present value

By adjusting the amount of money at different time points through the final value and present value, the problem of currency comparability across time can be solved.

Futurevalue (FV) refers to the value of a sum of money or a series of income and expenses at a given interest rate at a certain moment in the future, that is, the sum of principal and interest.

Present value (PV) refers to the present value of a sum of money or a series of income and expenditure in the future calculated at a given interest rate, that is, the present value calculated from the final value, which is generally called discount, and the interest rate used is also called discount rate.

The calculation of final value and present value involves three elements: cash flow, interest rate and time.

1. Final value and present value of simple interest

Simpleinterest refers to the method that only the principal can bring interest, but interest can't. Let SI be the interest amount of simple interest, P0 be the principal of 0 periods, I be the simple interest rate, and n be the number of interest periods. The interest calculation formula of simple interest is:

SI=P0×i×n

Under the condition of simple interest, the calculation formula of the final value of the nth period is:

FVn=P0+SI=P0( 1+i×n)

situation

The investor deposits 100 yuan in the bank, with an annual interest rate of 2%. At the expiration of three years, the sum of the principal and interest he can get is:

Fv3 = P0 (1+i× n) =100× (1+2 %× 3) =106 (yuan).

The present value of simple interest can be calculated by the formula of final value of simple interest and the inverse principal P0 method:

PV=P0=FVn 1 1+i×n

situation

Investors hope to get the principal and interest and 30 thousand yuan within five years to pay a sum of money. If the interest rate is 10%, then the principal that this person needs to deposit in the bank now is:

PV = fvn11+i× n = 30000×11+10% × 5 = 20000 (yuan).

The calculation of simple interest is relatively simple. When discussing the time value of money, compound interest is usually used, but the study of simple interest helps us understand compound interest.

2. The final value and present value of compound interest

The following case introduces the calculation method of the final value under the condition of compound interest.

situation

The difference between extending the data in the first case is that the bank pays interest at compound interest every year. So, how much money can investors get after the expiration of three years?

1 At the end of the year, the investor's bank account balance is:

Fv1= P0 (1+I) =100× (1+2%) =102 (yuan).

At the end of the second year, the interest generated at the end of 1 is added to the principal to calculate the interest. At this time, the balance of the investor's bank account is:

Fv2 = Fv1(1+I) = P0 (1+I) 2 =100× (1+2%) 2 =104.04 (Yuan

Similarly, at the end of the third year, the investor's bank account balance was:

FV3 = FV2 (1+I) = P0 (1+I) 3 =100× (1+2%) 3 =106.12 (.

From the above example, we can get the formula for calculating the final value under the condition of compound interest:

FVn=P0( 1+i)n

In the formula of compound interest final value, (1+i)n is called compound interest final value factor, and its abbreviated form is FVIFi, n, which is represented by symbols (F/P, i, n). For example, in this example, the interest rate is 2%, and the final value coefficient of 3-year compound interest can be symbolically expressed as (F/P, 2%, 3). The final value coefficient of compound interest can be obtained by looking up the "Table of Final Value Coefficient of Compound Interest".

Compared with simple interest, the funds under compound interest have greater time value, because interest can generate interest and bring value. Moreover, with the extension of time, the final value difference generated by these two interest-bearing methods will further expand. The following short story helps us to understand the power of compound interest. A few years ago, an anthropologist found this expression in a relic: Caesar lent someone money equivalent to 1 Roman penny, because there was no record to show whether this 1 penny had been repaid. Anthropologists want to know, if Caesar's descendants want to get this money back from the descendants of borrowers in the 20th century, what is the total value of principal and interest? He thinks 6% interest rate is more appropriate. But to his shock, if the interest rate is 6%, after more than 2000 years, the principal and interest value of 1p will exceed all the wealth on earth.

Like simple interest, the present value calculation under compound interest can also be obtained by inverting P0 in the final value formula:

PV=P0=FVn 1( 1+i)n

In the present value formula of compound interest, 1( 1+i)n is called the present value coefficient of compound interest. Its abbreviation is PVIFi, n, which is represented by symbols (P/F, i, n), and the present value coefficient of compound interest can be obtained by looking up the present value coefficient table of compound interest.

situation

An investment project with an expected income of 5 million after 8 years. What is the current value of this income at the annual interest rate 10%?

PV = fvn1(1+I) n = 500×1(1+10%) 8 = 233.25 (ten thousand yuan).