7.1 Two Stage

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Problem. Given the historical data, we can see that over last two years Hot Prospects Inc. has generated a

very high real Return On Investment (Real ROI) of 22.3% and 20.7%. Over the last three years, its

dividends per share has increased rapidly from $5.10 to $5.84 to $6.64. As the competition catches up

over the next five years, the Hot Prospects Real ROI is expected to gradually slow down. The long-run

forecast calls for the firm’s Real ROI to match the firm’s real discount rate (Real k), which is 9.0% per

year. Hot Prospects follows a policy of retaining 50.0% of its earnings and paying out the rest as

dividends. Going forward, the inflation rate is expected to be 3.0% per year indefinitely. What is the

firm’s intrinsic value / share?

Solution Strategy. Construct a two-stage discounted dividend model. In stage one, explicitly forecast the

firm’s dividend over a five-year horizon. In stage two, forecast the firm’s dividend from year six to

infinity and calculate it’s continuation value as the present value of this constant growth annuity. Then,

discount the future dividends and the date 5 continuation value back to the present to get the intrinsic

value per share.

FIGURE 7.1 Spreadsheet for Stock Valuation - Two Stage.

How To Build This Spreadsheet Model.

1. Inputs. Enter the inflation rate, real discount rate, and earnings retention rate into the range

B4:B6. Enter the historical data in the range C13:D18 and the cell B18. Input the projected

inflation rate by entering =$B$4 in cell E13 and copy it across.

2. Calculate The Nominal Discount Rate. The Nominal Discount Rate = (1 + Inflation Rate) * (1

+ Real Discount Rate) - 1. Enter =(1+B4)*(1+B5)-1 in cell B9.

3. Forecast Future Real and Nominal ROI. In the long-run, the firm’s Real ROI is forecast to

equal the firm’s real discount rate. Enter =B5 in cell J14. Given the Real ROI of 20.7% on date

0 and a forecast of 9.0% per year starting in year 6, forecast the intermediate years by entering a

smooth declining pattern, such as 19.0%, 17.0%, 15.0%, etc. from date 1 to date 5 in the range

E14:I14. For date 6, enter =B5 in cell J14. Calculate the Nominal Return On Investment (ROI) =

(1 + Inflation Rate) * (1 + Real ROI) - 1. Enter =(1+E13)*(1+E14)-1 in cell E15 and copy it

across.

4. Real and Nominal Growth Rate in Dividends. Calculate the Real Growth Rate in Dividend

(Real g) = (Real ROI) * (Earnings Retention Rate). Enter =E14*$B$6 in cell E16 and copy it

across. Calculate the Nominal Growth Rate in Dividend (g) = (1 + Inflation Rate) (1 + Real g) - 1.

Enter =(1+$B$4)*(1+E16)-1 in cell E17 and copy it across.

5. Nominal Dividend / Share. Calculate the Date t Nominal Dividend = (Date t-1 Nominal

Dividend) * (1 + Date t Nominal Growth Rate in Dividend). Enter =D18*(1+E17) in cell E18

and copy it across.

6. Date 5 Continuation Value. The Date 5 Continuation Value is the present value of the stream of

dividends from date 6 to infinity. Using the present value of an infinitely growing annuity

formula, calculate Date 5 Continuation Value = (Date 6 Dividend) / (Nominal Discount Rate –

Date 6 Nominal Growth Rate in Dividends). Enter =J18/(B9-J17) in cell I19.

7. Sum and PV of Future Dividends and the Continuation Value / Share. On each date, sum the

future dividend and continuation value / share. Enter =SUM(E18:E19) in cell E20 and copy it

across. Calculate the Present Value of the Future Dividend and Continuation Value / Share =

(Date t Sum) / ((1 + Nominal Discount Rate) ^ t). Enter =E20/((1+$B$9)^E12) in cell E21 and

copy it across.

8. Intrinsic Value Per Share. Sum the PV of Future Dividends and Continuation Value. Enter

=SUM(E21:I21) in cell D22.

Hot Prospects Inc. is estimated to have an intrinsic value per share of $176.26.