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Valuation of Securities

Stock Valuation

The value of a stock can be calculated using two methods: absolute valuation models and relative valuation models.

Investors use stock valuation, free cash flow, and discounted cash flow to determine a company's value. The discounted cash flow uses a company's projected free cash flows to calculate a company's valuation. The stock valuation is the company's value divided by the number of outstanding shares. Thus, to determine a company's value, a potential investor calculates the free cash flows and discounts those cash flows at the desired discount rate to reach the company's valuation.

Stock valuation may be sorted into two primary categories: absolute valuation models and relative valuation models. Absolute valuation models determine the inherent value of a stock based on the financials of the company. The scope of absolute valuation models is limited to the individual company subject to valuation. Included in the absolute valuation models are the discounted cash flow model, residual income model, and dividend discount model.

The residual income model is a valuation method that modifies a company's forecasted earnings to adequately reflect the actual cost of equity, thus providing an appropriate value for the company. Calculating the equity charge is the first step when employing the residual income model, which is done by multiplying the total equity capital by the cost of equity. Next, residual income is computed by deducting the equity charge from the company's net income.

The residual income model shows the volume of cash flows created after the total cost of capital has been deducted. The forecasted residual income value is then discounted to the present value using the cost of capital as the discount rate. The present value of the residual incomes and the company's net value are added together to yield the actual value of the firm.
Firm’s Value=Firm’s Net Book Value+Residual11+Cost of Capital1+Residual21+Cost of Capital2{\text{Firm's Value}=\text{Firm's Net Book Value}+\frac{{\text{Residual}}_1}{1+\text{Cost of Capital}^1}+\frac{{\text{Residual}}_2}{1+\text{Cost of Capital}^2}}
For example, a potential investor wishes to value Larry's Flower Company using the residual income valuation method. First, the investor analyzes Larry's Flower Company's annual report to identify an asset’s book value, which is equal to its carrying value on the balance sheet, in which companies calculate it netting the asset against its accumulated depreciation. Book value is also the net asset value of a company calculated as total assets minus intangible assets, such as patents and goodwill, and liabilities. Thus, in the case of Larry’s Flower Company the book value is $156,000 in 2018 and its target rate of return is five percent. A target rate of return is a desired return on investment over a specified period of time. Next, the investor projects the residual income for the next three years.
Residual Income=Operating Income(Operating Assets×Target Rate of Return)\text{Residual Income}=\text{Operating Income}-(\text{Operating Assets}\times\text{Target Rate of Return})
The investor expects an annual increase of 10% year over year for operating assets. Operating assets are components that are needed to generate a business and generate revenue.

Larry's Flower Company's Operating Rate of Return

Year Calculation
2018 $200,000\$200{,}000
2019 $200,000+$20,000(or10%)=$220,000\$200{,}000+\$20{,}000\;(\text{or}\;10\%)\;=\$220{,}000
2020 $220,000+$22,000(or10%)=$242,000\$220{,}000+\$22{,}000\;(\text{or}\;10\%)=\$242{,}000
2021 $242,000+$24,200(or10%)=$266,200\$242{,}000+\$24{,}200\;(\text{or}\;10\%)\;=\$266{,}200

The targeted operating rate of return can be calculated based upon assets and income.

The investor expects Larry's operating income to double year over year.
Year Calculation
2018 $67,000\$67{,}000
2019 $67,000+$67,000=$134,000\$67{,}000+\$67{,}000=\$134{,}000
2020 $134,000+$134,000=$268,000\$134{,}000+\$134{,}000=\$268{,}000
2021 $268,000+$268,000=$536,000\$268{,}000+\$268{,}000=\$536{,}000

Operating income can be calculated from cash flow.

Thus, the residual incomes are calculated at a 35 percent growth rate:

Larry's Flower Company's Residual Income Expectations

Year Calculation
2019 $134,000($220,000×0.35)=$57,000\$134{,}000-(\$220{,}000\times0.35)=\$57{,}000
2020 $268,000($242,000×0.35)=$183,300\$268{,}000-(\$242{,}000\times0.35)=\$183{,}300
2021 $536,000($266,200×0.35)=$442,830\$536{,}000-(\$266{,}200\times0.35)=\$442{,}830

Residual income can be calculated based upon a targeted growth rate.

The investor estimates Larry's Flower Company's cost of capital to be 10% based on the industry average. Now, the investor takes the present value of the projected residual incomes using the cost of capital as the discount rate.
Year Calculation
2019 $57,000(1+0.10)=$51,818\frac{\$57{,}000}{(1+0.10)}=\$51{,}818
2020 $183,300(1+0.10)2=$151,488\frac{\$183{,}300}{(1+0.10)^2}=\$151{,}488
2021 $442,830(1+0.10)3=$332,705\frac{\$442{,}830}{(1+0.10)^3}=\$332{,}705

Projected residual income can be calculated based upon the cost of capital and the discount rate.

Last, the investor adds the present value of the residual income to the book value to reveal Larry's Flower Company's value.
Larry’s Flower Company’s Value=$156,000+$51,818+$151,488+$332,705=$692,011{\text{Larry's Flower Company's Value}=\$156{,}000+\$51{,}818+\$151{,}488+\$332{,}705=\$692{,}011}
The dividend discount model computes the value of a business from the dividends paid out to owners. The dividend discount model discounts the cash flow of dividends to the present value to determine the inherent value of a stock. For the dividend discount model to be used as an effective valuation method, the firm must pay dividends in reliably regular intervals. A common practice is to calculate the growth rate of dividends using historical dividend payouts to forecast future dividend payouts. This is common practice because the year-over-year dividend growth rate calculated from historical dividend payouts is a reasonable rate to expect dividends to grow for the next period. The value per share is now calculated by dividing the expected value of the next dividend by the difference of the firm's cost of equity and dividend growth rate.
Value Per Share=Expected DividendCost of Equity CapitalDividend Growth Rate\text{Value Per Share}=\frac{\text{Expected Dividend}}{\text{Cost of Equity Capital}-\text{Dividend Growth Rate}}
Relative valuation models measure a firm's value through analysis of its financial ratios and its performance on industry benchmarks relative to its competitors in the sector. The market multiples valuation approach is a frequently used method because of the availability of multiples for public companies. Frequently used ratios or multiples include price to sales, price to earnings, and price to book. The price-to-sales ratio considers a company's outstanding shares and price of each share over the company's total revenue over the past year. The price-to-earnings ratio indicates the amount an investor can expect to invest in order to receive $1 in company earnings. The price-to-book ratio compares market value to book value.

For example, Larry's Flower Company has 100,000 shares and is selling shares at $75 per share. An investor reviews Larry's Flower Company's most recent financial statements and finds that the company's sales are $100,000, net earnings are $37,000, and book value is $156,000. The investor calculates the market capitalization of Larry's Flower Company to be $7.5 million. Market capitalization is the total dollar value of a company’s outstanding shares. With this information, the investor can calculate related ratios.

Ratio Calculation
Price to Sales $7,500,000$100,000=75\frac{\$7{,}500{,}000}{\$100{,}000}=75
Price to Earnings $7,500,000$37,000=203\frac{\$7{,}500{,}000}{\$37{,}000}=203
Price to Book $7,500,000$156,000=48\frac{\$7{,}500{,}000}{\$156{,}000}=48

Financial valuation metrics, such as price to sales, price to earnings, and price to book are used to evaluate a firm’s value.