Dividend Discount - from Valuation Technologies
In Section I, you will find a spreadsheet, in which you can enter cash flows and compute their present value.
In Section II, you can value a company with a known dividend growth rate. Dividends can be related to earnings through a fixed payout ratio. You can copy these dividends back into the section I spreadsheet for display, modification and evaluation.
Section III lets you examine a company with an initial high growth, no dividend period, followed by normal growth with a fixed payout.
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OVERVIEW
A standard way to value a company, or any investment, is the Dividend Discount approach (DD). Other closely related approachs are : Discounted Cash Flow, Free Cash Flow, and Economic Value Added (EVA), a trademark of Stern & Stewart. To use any of these methods, the analyst projects future payoffs to the investor, then discounts these payoffs to their present value. This concept was systematized by John Burr Williams in his seminal book, "The Theory of Investment Value", 1938.
The first step is to estimate cash flow to the investor in each year. If we wish to value the common stock directly, the Cash Flows are the annual dividends. If we wish to value a bond, or similar debt, the cash flows are the interest payments, plus the principle payment at maturity. To value the entire company, all cash flows to investors are considered, including dividends, re-purchase of shares, interest payments, principle payoff etc.
Future cash flows are discounted by the rate commensurate with the risk level of the investment. When computing the value of common stock, the company's Equity Discount Rate is used. When valuing the entire company, as in computing Free Cash Flow or Economic Value Added, the Weighted Average Cost of Capital is used. You can estimate the discount rate using our Cost of Capital page. If you want to work with more detailed data, monthly or quarterly, rather than annual, you can adjust the discount rates.
Adding together all future cash flows, appropriately discounted, gives the current value of the investment. Mr. Williams developed this familiar concept to aid investors in seeking out under or over valued companies.
This idea has been refined and made more useful by corporate finance experts, such as Tom Copeland of McKinsey and Company. Corporate finance practitioners focus on in view of a manager who is trying to increase shareholder value. The manager may be considering an operational investment, or a change in financing. He wants to know which decision will most increase the value of the company to its shareholders. Relating accounting reports to valuation will be helpful.
In these pages we take the view of the manager making operational and financing decisions, the investor seeking out undervalued firms, and the investor relations officer, responsible for bridging the gap between the other two. We provide tools to let you explore the Dividend Discount and related methods framework, from both the investor and manager's perspectives.
In Section I, you will find a spreadsheet, in which you can enter cash flows and compute their present value. In Section II, you can value a company with a known dividend growth rate. Dividends can be related to earnings through a fixed payout ratio. You can copy these dividends back into the section I spreadsheet for display, modification and evaluation. Section III lets you examine a company with an initial high growth, no dividend period, followed by normal growth with a fixed payout.
I. VALUE OF FUTURE PAYMENT STREAM
Instructions for filling out this section are at the bottom.
Calculate Current Value of a Stream of Cash Flows
Year Number
Cash Flow This Year
Forward Rate
Discount Factor
Present Value of Cash Flow
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7
Year 8
Year 9
Year 10
Sum
Add in Terminal Value
Terminal Value
Discount Factor at Termination
Present Value of Termination
Total Present Value
1 2 3 4 5
The Description Below is to remind you of your analysis when you Restore
Instructions - Section I A. Enter projected cash flows in the Cash Flow this Year column, starting with the earliest in Year 1 (say 1998), toward the latest in higher years (say 2007). The spreadsheet is limited to only ten years, but the investment you are valuing may have a longer schedule of Cash Flows. To handle flows after 10 years, summarize the value of the investment at ten years,and enter as a Terminal Value. You can value the remaining payments using the uniform dividend growth rate model Section II. B. The Forward Rate is the rate at which payments are discounted. Each year's Forward Rate is the amount by which a dollar is discount, if received in the subsequent year. This rate would be the Cost of Equity Capital, expressed as annual percent, if you are directly valuing common stock, entering cash flows as expected dividends. If you are valuing the entire company cash flows are total flow from the company to investors, including interest payments, repayment of debt, and repurchase of shares. the Weighted Average Cost of Capital should be used. For the most basic analysis, a uniform set of rates are used, each year's rate the same as the previous year's. Since the risk level of the investment may change with time, you can use variable rates, entering a different value for each year. To use a uniform set of Forward Rates, you can enter a value in Year 1, then press "Copy Down". C. Press the "Discount" button; the Discount Factor column will be computed, finding the present value of $1.00 received in the future year. The discount factor will also be entered into the Terminal Value section. D. Press "Value" to compute Present Value of Cash Flow, the value today of the year's Cash Flow. The Sum is the sum of all Present Values, or the value today of the stream of payments. E. To handle flows after 10 years, sumarize the value of the investment at ten years, and enter as a Terminal Value. You can value the remaining payments using the known dividend growth rate model Section II. F. To get the total value of the investment, including Terminal Value, Press "Total" adding the value of the cash flows to the present value of the Terminal Value computing the Total Present Value of this investment. II. VALUE OF STOCK WITH CONSTANT GROWTH RATE This section lets you estimate the current value of a stock under the assumption of a uniform growth rate. With dividends growing at a fixed rate, a simple formula gives the current value of the stock. This model is often called the "Gordon Model". The formula gives Price = Dividend(1)/(Discount Rate - Growth) Dividend(1) is the current dividend, the Discount Rate is the Cost of Capital for Equity (since we are focusing on Dividends), not the Weighted Average Cost of Capital. Growth is the annual rate of growth in dividends. For this model to be meaningful, Growth must be less than the Discount Rate. Many companies are expected to grow at a rate faster than the Discount Rate, but clearly this high growth rate can only be temporary. Companies with an intial high growth rate are considered in Section III. Instructions for filling out this section are at the bottom.
A. Enter projected cash flows in the Cash Flow this Year column, starting with the earliest in Year 1 (say 1998), toward the latest in higher years (say 2007). The spreadsheet is limited to only ten years, but the investment you are valuing may have a longer schedule of Cash Flows. To handle flows after 10 years, summarize the value of the investment at ten years,and enter as a Terminal Value. You can value the remaining payments using the uniform dividend growth rate model Section II.
B. The Forward Rate is the rate at which payments are discounted. Each year's Forward Rate is the amount by which a dollar is discount, if received in the subsequent year. This rate would be the Cost of Equity Capital, expressed as annual percent, if you are directly valuing common stock, entering cash flows as expected dividends. If you are valuing the entire company cash flows are total flow from the company to investors, including interest payments, repayment of debt, and repurchase of shares. the Weighted Average Cost of Capital should be used. For the most basic analysis, a uniform set of rates are used, each year's rate the same as the previous year's. Since the risk level of the investment may change with time, you can use variable rates, entering a different value for each year. To use a uniform set of Forward Rates, you can enter a value in Year 1, then press "Copy Down".
C. Press the "Discount" button; the Discount Factor column will be computed, finding the present value of $1.00 received in the future year. The discount factor will also be entered into the Terminal Value section.
D. Press "Value" to compute Present Value of Cash Flow, the value today of the year's Cash Flow. The Sum is the sum of all Present Values, or the value today of the stream of payments.
E. To handle flows after 10 years, sumarize the value of the investment at ten years, and enter as a Terminal Value. You can value the remaining payments using the known dividend growth rate model Section II.
F. To get the total value of the investment, including Terminal Value, Press "Total" adding the value of the cash flows to the present value of the Terminal Value computing the Total Present Value of this investment.
II. VALUE OF STOCK WITH CONSTANT GROWTH RATE
This section lets you estimate the current value of a stock under the assumption of a uniform growth rate. With dividends growing at a fixed rate, a simple formula gives the current value of the stock.
This model is often called the "Gordon Model". The formula gives Price = Dividend(1)/(Discount Rate - Growth)
Dividend(1) is the current dividend, the Discount Rate is the Cost of Capital for Equity (since we are focusing on Dividends), not the Weighted Average Cost of Capital. Growth is the annual rate of growth in dividends. For this model to be meaningful, Growth must be less than the Discount Rate. Many companies are expected to grow at a rate faster than the Discount Rate, but clearly this high growth rate can only be temporary. Companies with an intial high growth rate are considered in Section III.
Calculate Current Price of Stock (per share) with Constant Growth
Current Annual Dividend
Growth Rate (Percent)
Discount Rate (Percent)
Price of Stock
Dividend Yield (Percent)
Profit, Earnings and Dividends
While the value of the company to its investors comes through cash flow, the ability to pay dividends depends upon the profitability of the business. Earnings are the accountants attempt to depict economic profit. Reported Earnings are not a perfect way to understand a business's profitablity, but are a good point to start. Earnings have to support current dividends, plus be re-invested at a high enough return to support growth. We can assume that we know the current Earnings Growth Rate, current Earnings and current Dividends. Earnings not distributed as Dividends are re-invested. An indication of the profitability of the business is the Rate of Return on Capital Invested.
For this simple model, earnings grow at a fixed annual rate, with a constant portion of earnings going into dividends, Payout Ratio. Below, we calculate Payout Ratio (Percent), the percent of earnings paid out as dividends, the Increase in Invested Capital (Per Share), the amount of earnings that are retained in the business, and Rate of Return on Capital Invested (Percent), the amount by which earnings increase for one dollar re-invested. The resulting Price Earnings Ratio, current price divided by current earnings, is also computed.
Calculate Dividends, Price and Price Earnings with Constant Payout
Current Annual Earnings
Payout Ratio (Percent)
Increase in Invested Capital (Per Share)
Rate of Return on Capital Invested (Percent)
Price Earnings Ratio
Instructions - Section 2 A. Enter Current Annual Dividend per share B.Rate of growth of dividends Growth Rate (Percent), You can obtain estimates of Growth Rate from the past rate of increase, individual analysts estimates, or from the consensus of analysts. The following sites will provide useful information: XLS I/B/E/S First Call Market Guide Zacks . C. Enter Discount Rate. You can estimate the Discount Rate using our Cost of Capital page D. Press "Compute Price" button to get the price per share Price of Stock and Dividend Yield, current dividend as a percent of current price. E. Since most analysts think in terms of Earnings rather than dividend, you may Enter Current Annual Earnings, earnings per share, F. and press "Compute". G. The "Fill Table" button will place the stream of dividends implied by the starting Current Annual Dividend and Growth Rate into Section 1. III. VALUE OF STOCK WITH AN INITIAL HIGH GROWTH RATE, FOLLOWED BY NORMAL GROWTH Many companies have a period of high growth, with little or no dividend payout, followed by a mature period with more typical growth and dividends. Here is the calculation for a company with high growth, no dividends, for a number of years. After the High Growth period, at the start of Normal Growth, we know the company's earnings. To use this calculation, we need to know the Price Earnings Ratio by which the market would value these earnings. First, we estimate the Rate of Growth during the stable growth period to follow. We can estimate the PE from typical companies with same stable growth, or from the II. VALUE OF STOCK WITH CONSTANT GROWTH RATE section above. If you want to use this calculation, use Section II to arrive at a PE, then click "Copy PE". Note: the the Discount Rate during the High Growth period will be higher than during Normal Growth. Instructions for filling out this section are at the bottom.
A. Enter Current Annual Dividend per share
B.Rate of growth of dividends Growth Rate (Percent), You can obtain estimates of Growth Rate from the past rate of increase, individual analysts estimates, or from the consensus of analysts. The following sites will provide useful information:
XLS
I/B/E/S
First Call
Market Guide
Zacks .
C. Enter Discount Rate. You can estimate the Discount Rate using our Cost of Capital page
D. Press "Compute Price" button to get the price per share Price of Stock and Dividend Yield, current dividend as a percent of current price.
E. Since most analysts think in terms of Earnings rather than dividend, you may Enter Current Annual Earnings, earnings per share,
F. and press "Compute".
G. The "Fill Table" button will place the stream of dividends implied by the starting Current Annual Dividend and Growth Rate into Section 1.
III. VALUE OF STOCK WITH AN INITIAL HIGH GROWTH RATE, FOLLOWED BY NORMAL GROWTH
Many companies have a period of high growth, with little or no dividend payout, followed by a mature period with more typical growth and dividends. Here is the calculation for a company with high growth, no dividends, for a number of years. After the High Growth period, at the start of Normal Growth, we know the company's earnings. To use this calculation, we need to know the Price Earnings Ratio by which the market would value these earnings. First, we estimate the Rate of Growth during the stable growth period to follow. We can estimate the PE from typical companies with same stable growth, or from the II. VALUE OF STOCK WITH CONSTANT GROWTH RATE section above. If you want to use this calculation, use Section II to arrive at a PE, then click "Copy PE". Note: the the Discount Rate during the High Growth period will be higher than during Normal Growth.
Calculate Dividends, Price and Price Earnings with Initial High Growth Period
Annual Earnings at Start of High Growth
Years of High Growth
Growth Rate During High Growth (Annual Percent)
Earnings at End of High Growth
We can value earnings at end of high growth period if we know the Price Earnings Ratio that would apply. If we assume that the company is no longer a high growth firm, but is valued like a typical company, we can use the calculations above to find the PE at the end of high growth. Press the button "Copy PE" to fill this value in, then compute today's value by pressing "Compute Price".
Price Earnings Ratio at End of High Growth
Discount Rate During High Growth
Price at End of High Growth
Price at Beginning of High Growth
Price Earnings Ratio at Beginning of High Growth
Instructions - Section 3 A. Enter Annual Earnings at Start of High Growth B. The number of Years of High Growth C. The Growth Rate During High Growth, D. Press "Compute Earnings". The earnings will be compounded at the Growth Rate, resulting in Earnings at End of High Growth E. Enter Price Earnings Ratio at End of High Growth, either entering a value, or by using the "Copy PE" button. F. Enter the Discount Rate During High Growth, G. Press "Compute Price". The price at the beginning of the analysis, the Price at Start of High Growth, and associated PE, Price Earnings Ratio at Beginning of High Growth, will be computed. Home - Valuation Technologies All rights reserved Valuation Technologies LLC - Dec 26, 1998
A. Enter Annual Earnings at Start of High Growth
B. The number of Years of High Growth
C. The Growth Rate During High Growth,
D. Press "Compute Earnings". The earnings will be compounded at the Growth Rate, resulting in Earnings at End of High Growth
E. Enter Price Earnings Ratio at End of High Growth, either entering a value, or by using the "Copy PE" button.
F. Enter the Discount Rate During High Growth,
G. Press "Compute Price". The price at the beginning of the analysis, the Price at Start of High Growth, and associated PE, Price Earnings Ratio at Beginning of High Growth, will be computed.
All rights reserved Valuation Technologies LLC - Dec 26, 1998
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