Glamor Economics

Chapter 65

Chapter 9, Section 5 How to determine the cost of an investment—the time value of capital

Which is more valuable, 1 yuan now or 1 yuan in the future?In economics, there is a concept of the time value of capital, that is, under the condition of commodity economy, even if there is no inflation, the value of the same amount of money at different time points is not equal.Generally speaking, 1 yuan today has greater economic value than 1 yuan in the future.When we analyze operating costs, we cannot ignore the time value of capital.

For example, Xiao Wang invested 6 million yuan to set up a factory six years ago, but this year the company stopped production and closed down.During these 100 years, the total annual income of the enterprise is 6 yuan, and the total income in 20 years is 6 million yuan.Calculated in this way, the total cost is 120 million yuan, the total income is 100 million yuan, the profit is 120 yuan, and the investment profit rate is 20%.

This algorithm can be said to be correct or it can be said to be incorrect.This calculation is incorrect because the total income, total investment, and profit are all calculated in currency, and the actual value of the current 20 yuan is not the same as the future 20 yuan, that is to say, 20 yuan The actual purchasing power of money is not the same.

For example, inflation will occur in the economy. If the inflation rate is 10%, in this case, the purchasing power of 1 yuan will depreciate by 10% in one year, that is, the current 1 yuan cannot be bought in a year. same thing.Looking at it from another perspective, even if there is no inflation, if we deposit 1 yuan in the bank, if the interest rate is 10%, it will become 1.1 yuan after one year. Obviously, this 1 yuan will be more than 1 yuan after one year.

Here, two concepts are introduced, present value and discount.We call the current value of a future currency the present value, and the value of converting the currency in a certain year in the future into the current currency is called discounting.The most important factors affecting the value of a sum of money are the inflation rate and the interest rate. The sum of the two is the nominal interest rate, so we often use the nominal interest rate for discounting.Suppose the nominal interest rate is r, the amount of money in a certain year is Mn, the current value of money is M0, and n represents the nth year.The discount formula is as follows:

M0=Mn/(1+r)n
For example, the amount of money one year in the future is 110 million, and the nominal interest rate is 10%. The present value of this money is:

M0=110万/（1+10%）1=100万

That is to say, when the nominal interest rate is 10%, the present value of 110 million yuan after one year is 100 million yuan, or the actual value of 110 million yuan after one year is 100 million yuan this year.

When determining whether an investment is profitable, what we want to compare is not the current investment and future returns, but the present value of the current investment and future returns.This is the way in which profit-maximizing businesses decide to invest.In other words, it is not how much money you can earn in the future, but what is the present value of the money you earn.In our example of Xiao Wang’s investment, if the interest rate is 10%, the present value of each year’s income is as follows:
第一年（n=1）：20万／（1+10％）1 =18.18万

第二年（n=2）：20万／（1+10％）2 =16.53万

第三年（n=3）：20万／（1+10％）3 =15万

第四年（n=4）：20万／（1+10％）4 =13.66万

第五年（n=5）：20万／（1+10％）5 =12.42万

第六年（n=6）：20万／（1+10％）6 =11.29万

The present value of the total return over the next 6 years is:

18.18万+16.53万+15万+13.66万+12.42万+11.29万=87.08万

If discounting is not carried out, the total income is 120 million, but when discounted at 10% interest rate, the present value of this 120 million is 87.08 yuan.The investment is 100 million, and the present value of the future income is 87.08. Obviously, this investment is a loss, and the loss is 100 million - 87.08 = 12.92.Obviously this investment cannot be made.

It can also be seen from the above analysis that the present value of a future currency depends on the nominal interest rate.When we assume that the nominal interest rate is 5%, the present value of the returns for each year is as follows:
第一年（n=1）：20万／（1+5％） 1 =19万

第二年（n=2）：20万／（1+5％） 2 =18.14万

第三年（n=3）：20万／（1+5％） 3 =17.28万

第四年（n=4）：20万／（1+5％） 4 =16.45万

第五年（n=5）：20万／（1+5％） 5 =15.67万

第六年（n=6）：20万／（1+5％） 6 =14.92万

The present value of the total return over the next 6 years is:

19万+18.14万+17.28万+16.45万+15.67万+14.92万=101．46万元
This means that only when the nominal interest rate is 5%, the investment of 100 million yuan will be slightly profitable, that is, 101.46 - 100 million = 1.46 yuan.It can be seen that if the interest rate is above 5%, this investment is not suitable.

The concept of discounting is extremely important when making long-term investment decisions.The method of discounting highlights the importance of the time factor in economics.Entrepreneurs must also consider the time factor when making investment decisions.The longer the return period of the investment, the more important the time factor.

When considering the time factor, there is not only discounting but also investment risk.The establishment of a factory is often a long-term investment, so when making this investment, not only should the determination of the scale be considered, so that the output can reach the level of the lowest average cost, but also the present value of the benefits that these outputs can bring should be considered.Of course, if the investment is made over a period of many years in the future, the present value of the future investment should also be considered.Therefore, you must be cautious when making long-term investments or building a factory.

[links to related words]

Time Preference People's current preference for an equivalent amount of currency is greater than the future, which reflects the role of time.Economists call this phenomenon "time preference."

The time value of money In the commodity economy, even if there is no inflation, the value of the same amount of money at different points in time is not equal.It should be said that 1 yuan today has greater economic value than 1 yuan in the future.

(End of this chapter)