stock pricing model

-zero growth model

ii. constant growth model

iii. multiple growth model

iv. valuation method of price-earnings ratio

v. discounted cash flow model

vi. price determination of open-end funds

vii. price determination of closed-end funds

viii. convertible securities.

[ Example ]

Suppose that the dividend per share paid by a company in the future is 8 yuan, and its company's necessary rate of return is 1%, we can know that the value of a share of the company is 8/.1 = 8 yuan, while the price of a share at that time is 65 yuan, and the net present value of each share is 8-65 = 15 yuan, so the stock is undervalued in 15 yuan, so it is suggested to buy this stock.

[ Application ]

The application of the zero-growth model seems to be quite limited. After all, it is unreasonable to assume that a certain stock will be paid a fixed dividend forever. However, under certain circumstances, this model is also quite useful in determining the value of ordinary stocks, especially in determining the intrinsic value of preferred stocks. Because the dividends paid by most preferred stocks will not change due to the change of earnings per share, and because preferred stocks have no fixed life, the expected payment can obviously go on forever.

second, the constant growth model

(1) general form. If we assume that dividends will grow at a constant growth rate forever, then a constant growth model will be established.

[ example] If a company paid a dividend of 1.8 yuan per share last year, it is expected that the dividend of the company's stock will increase at an annual rate of 5% in the future. Therefore, the expected dividend for the next year is 1.8× (1.5) = 1.89 yuan. Assuming that the necessary rate of return is 11%, the company's stock is equal to 1.8× [(1.5)/(.11-.5)] = 1.89/(.11-.5) = 31.5 yuan. At present, the price per share is 4 yuan, so the stock is overvalued by 8.5 yuan. It is suggested that investors who currently hold the stock sell it.

(2) the relationship with zero growth model. The zero growth model is actually a special case of the constant growth model. In particular, assuming that the growth rate is equal to zero, dividends will always be paid in a fixed amount. At this time, the constant growth model is the zero growth model.

From these two models, although the assumption of constant growth has less application restrictions than the assumption of zero growth, it is still considered unrealistic in many cases. However, the constant growth model is the basis of the multiple growth model, so this model is extremely important.

III. Diversified growth model

Diversified growth model is the most widely used discounted cash flow model to determine the intrinsic value of common stocks. This model assumes that there is no specific model to predict the dividend change within a period of 7 years, and after this period, the dividend changes according to the constant growth model. Therefore, the dividend flow can be divided into two parts.

the first part includes the present value of all expected dividends during the period of irregular dividend changes.

the second part includes the present value of all expected dividends in the period of constant dividend growth rate change from time point t. Therefore, the value Dz(1 VT) of this stock at the time point can be obtained by the equation of the constant growth model.

[ example] Assume that the dividend per share paid by Company A last year is .75 yuan, and the expected dividend per share next year is 2 yuan, so the expected dividend per share next year is 3 yuan, that is,

from t = 2, it is expected that the dividend will increase at a rate of 1% every year in the future. Assuming that the company's necessary rate of return is 15%, V7-and T can be calculated respectively according to the following formula. Compared with the current share price of 55 yuan, this price seems to be fairly priced, that is, the stock has not been wrongly priced.

(2) Internal rate of return. Both the zero growth model and the constant growth model have a simple formula about the internal rate of return, but it is impossible to get such a simple expression for the multiple growth model. Although we can't get a simple expression of internal rate of return, we can still use trial and error method to calculate the internal rate of return of multiple growth models. That is, after establishing the equation and substituting a hypothetical Iraq, if the value on the right side of the equation is greater than P, it means that the assumed P is too large; On the contrary, if you substitute a selected extreme value, the value on the right side of the equation is less than that, which means that the selected p is too small. Continue to try and choose, and finally the equation can be established.

according to this trial-and-error method, we can conclude that the internal rate of return of company A's stock is 14.9%. Comparing the given necessary income of 15% with the approximate internal rate of return of 14.9%, we can see that the pricing of the company's shares is quite fair.

(3) Binary model and ternary model. Sometimes investors use binary models and ternary models. The binary model assumes that there is a common constant growth rate before the time expires, and another constant growth rate city after time 7. The ternary model assumes that before working hours, the constant growth rate is body I, between 71 and 72 hours, and after 72 hours, the constant growth rate lasts for a period. Let VTl represent

the present value of all dividends after the last growth rate, and recognize-represent the present value of all dividends before that, which shows that these models are actually special cases of multiple growth models.

IV. Valuation method of price-earnings ratio

Price-earnings ratio, also known as price-earnings ratio, is the ratio between price per share and earnings per share, and its calculation formula is conversely, price per share = price-earnings ratio × earnings per share

If we can estimate the price-earnings ratio and earnings per share respectively, then we can indirectly estimate the stock price by this formula. This method of evaluating stock prices is the "P/E ratio valuation method".

v. discounted cash flow model

the discounted cash flow model uses the capitalization pricing method of income to determine the intrinsic value of ordinary stocks. According to the capitalization pricing method of income, the intrinsic value of any asset is determined by the cash flow accepted by investors who own such assets in the future. Because cash flow is the expected value in the future, it must be returned to present value at a certain discount rate, that is, the intrinsic value of an asset is equal to the discounted value of expected cash flow. For stocks, this expected cash flow is the dividend expected to be paid in the future. Therefore, the formula of discounted cash flow model is < P >: Dt is the expected cash flow associated with a specific common stock in time t, that is, the dividend per share expressed in cash in the future; K is the appropriate discount rate of cash flow under a certain degree of risk; V is the intrinsic value of the stock.

in this equation, it is assumed that the discount rate is the same in all periods. We can derive the concept of net present value from this equation. Net present value is equal to the difference between intrinsic value and cost, that is, in the formula

, p is the cost of buying stocks at t=.

if NPV > , it means that the sum of the net present value of all expected cash inflows is greater than the investment cost, that is, this stock is undervalued, so it is feasible to buy this stock;

if NPV < , it means that the sum of the net present value of all expected cash inflows is less than the investment cost, that is, this stock is overvalued, so it is not allowed to buy this stock.

after understanding the net present value, we can introduce the concept of internal rate of return. Internal rate of return is the discount rate that makes the net present value of investment equal to zero. If K* is used to represent the internal rate of return,

can be obtained by the equation, and the internal rate of return K* can be solved by the equation. Compare K* with the necessary rate of return (expressed by K) of stocks with the same risk level: if K * > K, you can buy such stocks; If k * < k, don't buy this stock.

there is a troublesome problem in the intrinsic value of a common stock, that is, investors must predict all dividends to be paid in the future. Because ordinary stocks don't have a fixed life cycle, it is suggested to use an indefinite dividend stream, which requires some assumptions.

these assumptions always revolve around the victory growth rate. generally speaking, at time t, the dividend per share is regarded as the dividend per share multiplied by the victory growth rate GT at time t-1, and its calculation is

for example, if the dividend per share is expected to be $4 at T=3 and $4.2 at T=4, then different types of discounted cash flow models reflect different assumptions of dividend growth rate.

VI. Price Determination of Open-end Funds

As open-end funds often buy back or sell shares of their own companies according to customers' requirements, the prices of open-end funds are divided into two types, namely, subscription price and redemption price.

1. Purchase price

As an open-end fund has the obligation to buy back its shares in the middle, its shares are generally not traded in the stock market, but mainly traded off-site. When investors buy open-end fund shares, they have to pay a certain sales additional fee in addition to the net asset value. That is to say, the subscription price of shares of an open company includes the net asset value and the sales expenses to cover the issuance cost. The surcharge is generally maintained at the level of 4%-9%, usually 8.5%, and investors can be given certain discounts when buying in large quantities. The relationship among the subscription price, net asset value and surcharge of open-end funds can be expressed by the following formula.

for example; The net asset value of an open-end fund is 1 yuan, and its surcharge is 8%, so its subscription price is 1/(1? %) = 1.87 yuan.

However, for ordinary investors, the surcharge is not a small cost, which increases the risk of investors. Therefore; There are some open-end funds without charging, and their sales price is directly equal to the net asset value. When investors buy such funds, they don't have to pay the sales fee, that is to say,

subscription price = net asset value

It can be seen that the subscription price of open-end funds with charging or without charging is directly related to their net asset value, which is in direct proportion.

2. redemption price.

Open-end funds promise to redeem their shares at any time according to the individual wishes of investors. For open-end funds that don't charge any fees when redeeming,

Redemption price = net asset value

Some open-end funds charge fees when redeeming, and the fees are charged at different redemption rates according to the investment years of the funds. The longer they hold the fund bonds, the lower the rates. Of course, some funds charge a uniform rate. In this case, the relationship between redemption price of open-end fund and net asset value and surcharge is

redemption price = net asset value+surcharge

. Therefore, the price of open-end fund is only closely related to net asset value (under the condition that relevant expenses are determined). As long as the net asset value is estimated accurately, there is no problem in fund subscription and redemption.

VII. Price Determination of Closed-end Funds

In addition to the above factors, the price of closed-end funds is also affected by the level of leverage. The issue of common shares by closed-end funds is one-off, that is, after the fund amount is raised, it will be closed and no common shares will be issued. However, due to management needs, such companies can also issue preferred shares and corporate bonds as part of the capital structure, form final repayment priority bonds, and obtain bank loans. For the shareholders of the company's common stock, their income will be affected by leverage. Priority securities have fixed rights to assets and income. Therefore, when the company's total assets and income (income paid by interest and preferred stock dividends) rise, the shareholder's income of common stock will increase, and he can not only get more dividends, but also get capital gains. In other words, when the value of fund assets increases, the common stock of the fund grows faster; Conversely, when the value of fund assets declines, the common stock of the fund also declines faster. This leverage effect often makes the market value of common stock of some closed-end fund companies increase or decrease more than that of the overall market. Because closed-end funds do not undertake the obligation to buy back their shares, their shares can only be recovered if they are sold in the open market. Sometimes, due to the influence of leverage, the common stock price of closed-end funds is not as stable as that of open-end funds. Their prices are just like the stock price of a commercial company, and there is a significant deviation between the value of their single assets and the market value. The price determination of closed-end funds can be carried out by using the price determination formula of ordinary stocks.

VIII. Convertible securities

1. The value of convertible securities

Convertible securities give investors the option to convert their debts or preferred shares into common shares at a specified price and proportion within a specified time. Convertible securities have two values: theoretical value and convertible value.

(1) theoretical value. The theoretical value of convertible securities refers to its value as a kind of securities without conversion option. To estimate the theoretical value of convertible securities, we must first estimate the necessary rate of return of non-convertible securities with the same credit standing and similar investment characteristics, and then use this necessary rate to calculate the present value of its future cash flow. We can refer to the bond valuation in the first section of this chapter.

(2) conversion value. If a convertible security can be transferred immediately, the product of the market value of its convertible common stock and the conversion ratio is the conversion value, that is,

conversion value = market value of common stock × conversion ratio

in the formula, the conversion ratio is the number of convertible shares per bond obtained by the creditor.

2. Market price of convertible securities.

the market price of convertible bonds must remain above its theoretical value and conversion value. If the price is below the theoretical value, the price of the securities is undervalued, which is obviously obvious; If the price of convertible securities is below the conversion value, it is profitable to buy the securities and immediately convert them into stocks, so that the price of the securities will rise until it is above the conversion value. In order to better understand this, we introduce the concept of conversion parity.

(1) conversion parity. Conversion parity is the price per share that holders of convertible securities can convert bonds into ordinary shares of the company within the conversion period, and the conversion price is generally not adjusted unless there are certain circumstances, such as the sale of new shares, allotment of shares, share delivery, dividend distribution, thinning and merger of shares, merger and acquisition of companies, etc. The conversion ratio mentioned above is essentially another way of expressing the conversion price.

conversion parity = market price/conversion ratio of convertible securities

conversion parity is a very useful figure, because once the actual stock market price rises to the conversion parity level, any further stock price rise will definitely increase the value of convertible securities. Therefore, the conversion parity can be regarded as a break-even point.

(2) Change the premium and discount. Generally speaking, investors have to pay a conversion premium when buying convertible securities. The conversion premium per share is equal to the difference between the conversion parity and the current market price (also known as the benchmark share price) of ordinary stocks, or the concession made by the holders of convertible securities when converting bonds into stocks, relative to the stock price (that is, the benchmark winning share price) when they originally subscribed for the convertible securities. It is usually expressed as the percentage of the current market price, and the formula is

conversion premium.