Business Finance
FIN 460 Harvey Mudd College Home Depot Financial Modeling Paper

FIN 460

Harvey Mudd College

FIN

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Home Depot (HD) Homework – Financial Modeling - Stock Valuation Determine the intrinsic value per share for Home Depot at the end of the fiscal year using a “two-stage” model (use the following information to construct the model): 1. Assume D0 is current annual dividend per share listed in Bloomberg or from a different free source form the web. 2. Assume that in “first stage” (lasting 5 years), HD’s dividend per share grows by the “Next 5 years” growth estimate . (Be prepared to justify how would you choose this growth rate.....) 3. Assume that HD’s dividend per share is expected to grow by x% per year = Mean Growth rate forever AFTER the five-year “first stage” growth is completed. 4. Calculate HD’s cost of equity. Compare it to the cost of equity from Bloomberg or from a different provider you found online. Attach the report you used. Show formulas, calculations and interpretation. Have a nice table with your assumptions (CAGR using historical growth rates, independent analysts' estimates, management guidance, most recent growth rate etc- like we did in class). Submit it in electronic format attaching screenshots from Bloomberg screens or from a stick research report where you got the data from. 1. Build a table and a chart with the main operating segments for the most recent past year with the following columns: Revenues, % of each segment in Total Revenues, Operating Income, % of each segment in Total Operating Income 2. Build a graph with the dividend annual growth rates since 2005 to the present.Add the EPS growth rates to the same chart for the same period of time. 3. What is Home Depot's stock intrinsic value using the Gordon constant growth model? 4. What is Home Depot's stock intrinsic value using a 2 stage growth model? How accurately does the model above value a share of HD stock? 5. What was the closing price at the end of the trade day on March 13, 2020? 6. What was the closing price at the end of the fiscal year? Attach a chart with daily stock price performance for the past 12 months. On the same chart add the quarterly EPS. 7. What are the possible problems with the models? Please comment on the strengths and weaknesses of each valuation approach. 8. Did you encounter any difficulties or challenges? 9. Take screenshots of the data you used and attach them next to your calculations. 10. Would you buy/sell/hold this stock? Why? Why not? Do you trust your results? Why ? Why not? Attach only the reports you used. Stock Valuation Placing a value on a share of common stock is a more challenging task than we faced in valuing bonds. Remember that common stock represents an ownership stake in a firm and that shareholders are paid after other suppliers of capital (primarily lenders) have been paid. So, the cash flows available to shareholders can be fairly uncertain (i.e., risky). However, if investors can form an expectation about the amount of dividends that will be paid per share in the future, then we should be able to apply time value of money principles to find the price of stock. If Dt = dividend per share paid at year t. ks = required rate of return on stock s. Then Pˆ0 D1 (1 k s )1 D2 (1 k s ) 2 ...... D (1 k s ) In words, the current price of a share of stock should be the present value (PV) of its future dividends discounted at the required rate of return for the stock. Notice that the dividend cash flows are projected to go on forever. This reflects the fact that the ownership claim of shareholdings has no maturity. Given the “forever” nature of the cash flows from a share of stock, we generally try to forecast some type of systematic pattern for future dividends to make the above equation more workable. Valuing a stock with no projected growth in dividends per share Suppose that we are trying to value the stock of a firm that is expected to pay a “constant” dividend over time. Then our equation above becomes D D D Pˆ0 ...... (1 k s )1 (1 k s ) 2 (1 k s ) In mathematics, this type of equation represents the sum of a geometric progression. It is a fact that this equation reduces to: Pˆ0 D ks This equation solves for the value of a perpetuity. A perpetuity is an equal payment at regular intervals that lasts forever. 1 Assume that you are considering an investment in a stock that is expected to pay a constant dividend of $3 per share forever and that you will receive your first dividend payment 1 year from now. Further, you have determined that you require a 15% return on an investment in this stock. What is the value of this stock? P̂0 Note what happens to the price if investors require higher or lower rates of return on the stock. If investors require a 20% return on an investment in this stock, the value would be only $15 ($3 / 0.20). On the other hand, if the required return on the stock is 10%, the stock’s value would be $30 ($3 / 0.10). Sudden changes in investor’s required rates of return on buying stocks can cause significant changes in the values of stock (this is one reason why actual stock prices can be volatile). We can also use the structure of this formula to find the expected rate of return on this stock (if we know the “actual” price). kˆs D P0 Note that the price variable has “lost its hat”, while the return variable, k, has “put on a hat.” This reflects that from this equation, we are using a known price (which does not have to equal the “theoretical” price, P-hat) to solve for an “expected” rate of return (which does not have to equal the “required” rate of return). Suppose that this stock sells for $20 per share. What is its expected return based on this price? k̂ s Based on our earlier computation of the value of the stock, is it fairly priced? Note that for a zero-growth stock, the expected return consists entirely of the stock’s dividend yield, D1/P0. To illustrate this, calculate the price of this stock in 1 year (but immediately after the dividend is paid). P̂1 Note that the price 1 year from now is expected to be $20. Therefore, if you sold the share after 1 year, you would expect to receive no capital gain. Your entire expected return would be from the $3 dividend received. If you plan to sell your share after 1 year, illustrate why the $20 at t=0 is a fair price? 2 0 -20 P=? 1 23 What’s the Price today using a discount rate of 15% (annual compounding)? Have you forgotten about the Time Value of Money? Valuing a stock with constant growth in dividends per share Our initial analysis of a “zero-growth” stock should provide you with a basic understanding of the valuation process. However, an assumption of zero dividend growth is unrealistic for a large majority of companies. Most companies constantly strive to find new profit opportunities for their businesses. In other words, they are trying to “grow” and add value. If they are successful, they will be more profitable and be able to pay larger dividends. Thus, we need a valuation model that can incorporate growth. Suppose the stock that we are evaluating just paid a $3 per share dividend (i.e., yesterday). Future dividend payments on this stock are expected to grow at a rate of 5% forever. Investors require a 15% return on an investment in this stock. The expected dividend payment in 1 year = $3(1.05) = $3.15 The expected dividend payment in 2 years = $3(1.05)2 = $3.3075 The expected dividend payment in 3 years = $3(1.05)3 = $3.472875 And this pattern will continue on forever. Pˆ0 D0 (1 g )1 (1 k s )1 D0 (1 g ) 2 (1 k s ) 2 ..... D0 (1 g ) (1 k s ) It is a mathematical fact that this equation is equivalent to the following. Pˆ0 D0 (1 g ) ks g D1 ks g So, the value of the constant growth stock discussed above is Pˆ0 $3(1 0.05) 0.15 0.05 $3.15 0.15 0.05 $31.50 As with the zero-growth case, the value equation may be manipulated to find the expected rate of return on a constant growth stock (if the actual price is known). Assume that this stock trades at $31.50 currently. 3 kˆs D1 P0 g The first term is the expected dividend yield. The second term reflects the expected capital gains yield. kˆs $3.15 0.05 0.10 0.05 0.15 $31.50 So, the expected return on this stock is composed of a dividend yield of 10% and an expected capital gains yield of 5%. To see this, let’s calculate the expected price of this stock 1 year from now (immediately after the first dividend has been paid). Pˆ1 $3.15(1 0.05) 0.15 0.05 $3.3075 0.15 0.05 $33.075 So, after 1 year, I expect a capital gain of $1.575 ($33.075 - $31.50) which is a 5% gain over my purchase price of $31.50. Combining this capital gain with the dividend yield of 10%, the total expected return is 15%. How will the current price of the stock be impacted by changes in 1) the required rate of return, or 2) the growth rate? Suppose the required rate of return for this stock jumps to 20% from 15%, growth rate is 5% and current dividend is $3. P̂0 Suppose the growth rate of dividends is suddenly projected to be 8% forever rather than 5%, required rate of return is15% and current dividend is $3.. P̂0 Please note that we are talking about permanent dividend changes, not temporary manipulations by firm management trying to boost stock price. The market should not be fooled by temporary changes! Valuing a stock with nonconstant (supernormal) growth in dividends per share Many companies go through rapid growth phases before maturing into more stable (and lower) growth patterns. Note from the constant growth formula that growth can not be greater than the required rate of return forever (otherwise the formula would yield a 4 negative stock value). Therefore, if the growth rate is higher than the required rate of return for some period of time, then we must alter our valuation procedure. Suppose that the stock under consideration for investment just paid a $3 per share dividend, and projects 25% growth in dividends for the next 3 years. After that point in time, dividends are expected to grow at a 5% annual rate forever. Assume that the required rate of return on this stock is 15%. What is the value of this stock? The standard procedure to follow for valuing a nonconstant growth stock is as follows: 1) Find the PV of the dividends during the period of nonconstant growth. 2) Find the price of the stock at the end of the nonconstant growth period (using the constant growth formula). Find the PV of this price. 3) Add the PV’s found in steps 1) and 2) to find the current value of the stock. Step 1: Expected dividend at year 1 = $3(1.25) = $3.75 Expected dividend at year 2 = $3(1.25)2 = $4.6875 Expected dividend at year 3 = $3(1.25)3 = $5.859375 PV of D1 (at 15%) = $3.26086957 PV of D2 (at 15%) = $3.54442344 PV of D3 (at 15%) = $3.85263417 Sum of PV of dividends during supernormal growth = $10.65792718 Step 2: Pˆ3 $5.859375(1 0.05) 0.15 0.05 $6.15234375 $61.5234375 0.10 PV of value at year 3 (at 15%) = $40.45265883 Step 3: Pˆ0 $10.65792718 $40.45265883 $51.11 So, a fair price for this stock is $51.11! Stock Market Equilibrium (Overpriced and Underpriced stocks) Suppose a stock’s computed value is different than the observed price of its stock. Then, we would say that such a stock is mispriced (if the model used to value the stock is correct). 5 Assume that the stock we examined earlier with a value of $31.50 is observed to trade at $30. This stock is underpriced (i.e., investors can buy the stock at a price less than its value). Another way of looking at this is to calculate the expected return on the stock (as we did earlier). kˆs D1 P0 g $3.15 0.05 0.155 $30 At a price of $30, this stock has an expected return of 15.5%. This is greater than the required rate of return of 15%. The current market for this stock is out of equilibrium. The buying pressure will force current price higher (thus decrease the expected return). Once price has reached $31.50, the expected return equals the required return and the market for this stock is in equilibrium. Suppose instead that the stock is actually trading at $35. The price is greater than value, therefore, the stock would be overpriced. Investors would rush to sell such a stock, driving its price down to its fair value of $31.50. 6 STOCK VALUATION Dividend Discount Model Inputs Levered Cost of Equity Capital Dividend Discount Model Year Dividend Growth Rate Dividend Continuation Value Dividend + Continuation Value PV of Dividend + Contin. Value Stock Value 12,0% 0 $6,64 24 1 12,0% First Stage: Finite Horizon 2 3 4 11,0% 10,0% 9,0% 2nd Stage: Infin Horiz 5 6 8,0% 7,0% Dividend Discount Valuation - class examples Exxon Mobil (ticker: XOM) Application of Gordon constant growth model Input data: Most recent quarterly dividend Annualized dividend Assumed dividend growth rate Assumed cost of equity Value = $ 43.23 Closing price (03/23/20) = $0.870 $3.48 3.10% 11.40% $ 31.45 Thomson Reuters 2019 Dividends per share 3.43 Future Dividend growth rate based on 3 yr growth rate based on 5 yr growth rate Another straightforward use of constant growth formula: Solve for growth: Nominal GDP Growth Rate = Real GDP Grow P0= D1/(K-g) g= per year Any concerns? 2018 2017 2016 2015 2014 3.23 3.06 2.98 2.88 2.7 4.80% 𝐸𝑉 1 CAGR = 𝐺𝐴𝑉𝐺 = (𝐵𝑉)𝑁 − 1 4.90% wth Rate = Real GDP Growth Rate + Expected Inflation Rate 2020 3.10% Exxon Mobil (ticker: XOM) Application of nonconstant growth Input data: The valuation process for ALL e Most recent quarterly dividend Annualized dividend $3.48 Assumed dividend growth rate (yrs 1-3) 1.14% Assumed dividend growth rate (after yr 3) Assumed cost of equity Year Expected dividends P3 = Terminal value = 0 $3.48 Present values: dividends terminal value Current value = $ 40.98 1 $ 3.5197 $ 3.1595 1) 2) 3) 4) $0.870 2 $ 3.5598 $ 2.8685 3.10% 11.40% 3 $ 3.6004 $ 44.7228 $ 2.6043 $ 32.3499 Define forecast horizon. Construct a cash flow forecast Calculate the stock’s terminal Calculate the stock’s current v during the forecast horizon and 4 $ 3.7120 P3= D4/(K-g) Calculate the stock’s current value by adding the present values of the cash flows occurring Exxon Mobil (ticker: XOM) A 3-stage model that incorporates earnings growth & dividend growth as 2 separate components Input data: LT Expected EPS (2021) Expected dividend payout ratio (yrs 1 - 3) Expected EPS growth rate (yrs 1-3) Expected EPS growth rate (yr 4 only) Expected EPS growth rate (yr 5 only) Expected EPS growth rate (yr 6 only) Expected EPS growth rate (yrs 7+) Long-run expected ROE Long-run expected payout ratio Expected dividend payout ratio (yr 4 only) Expected dividend payout ratio (yr 5 only) Expected dividend payout ratio (yr 6 only) Assumed cost of equity Year 1 2 3 4 5 6 7 EPS DPS PV of DPS $2.44 $2.53 $ 2.27 $2.69 $2.78 $ 2.24 $2.96 $3.06 $ 2.22 $3.21 $2.96 $ 1.92 $3.42 $2.77 $ 1.62 $3.59 $2.50 $ 1.31 $3.70 $2.17 Terminal value at end of year 6 = PV of terminal value = Estimated value = 26.0958 13.6540 $ 25.23 $ 2.44 103.5% 10.15% 8.39% 6.63% 4.86% 3.10% 7.48% 58.6% 92.27% 81.03% 69.79% 11.40% rough estimate of current payout ratio roughly corresponds with expected EPS growth in sector f linear movement toward "long-run" linear movement toward "long-run" linear movement toward "long-run" assumed assumed consistent with long-run growth and ROE linear movement toward "long-run" linear movement toward "long-run" linear movement toward "long-run" with expected EPS growth in sector for next 5 years What's the point of this equation? g = ROE x (1 – d) and solve for d=dividend payout ratio What happens in years 4 through 7? Does the Growth Assumption Make Sense? Expected EPS growth = (1 - expected dividend payout ratio) x expected ROE Last 4 quarterly dividends = Trailing 12 months EPS = Book val of common equity/share = Dividend payout ratio = ROE = Growth formula: EPS growth rate estimate = $ 3.43 $ 2.07 $ 43.17 165.7% 4.8% g = (1 − d ) * ROE -3.2% Modified Dividend Payout example: XOM (amounts in millions) Common Com stock Net income dividends repurchases 2008 $ 45,220 $ 8,058 $ 35,734 2007 $ 40,610 $ 7,621 $ 31,822 2006 $ 39,500 $ 7,628 $ 29,558 Total (3-yr) $ 125,330 $ 23,307 $ 97,114 Dividend payout ratios (conventional definition): 2008 17.82% 2007 18.77% 2006 19.31% Total (3-yr) 18.60% Com stock issuances $ 753 $ 1,079 $ 1,173 $ 3,005 Dividends Div / share OR Net _ income EPS Modified Dividend Payout Ratios (using various definitions): Dividends and repurchases only: Dividends 2008 96.84% 2007 97.13% Net 2006 94.14% Total (3-yr) 96.08% subtracting out stock issues: 2008 95.18% 2007 94.47% 2006 91.17% Total (3-yr) 93.69% + Re purchases _ income Dividends + Re purchases − Equity _ issuance Net _ income Dividend Discount Valuation - class examples Exxon Mobil (ticker: XOM) Application of Gordon constant growth model Input data: Most recent quarterly dividend Annualized dividend Assumed dividend growth rate Assumed cost of equity Value = $ 43.23 Closing price (03/23/20) = $0.870 $3.48 3.10% 11.40% $ 31.45 Thomson Reuters 2019 Dividends per share 3.43 Future Dividend growth rate based on 3 yr growth rate based on 5 yr growth rate Another straightforward use of constant growth formula: Solve for growth: Nominal GDP Growth Rate = Real GDP Grow P0= D1/(K-g) g= per year Any concerns? 2018 2017 2016 2015 2014 3.23 3.06 2.98 2.88 2.7 4.80% 𝐸𝑉 1 CAGR = 𝐺𝐴𝑉𝐺 = (𝐵𝑉)𝑁 − 1 4.90% wth Rate = Real GDP Growth Rate + Expected Inflation Rate 2020 3.10% Exxon Mobil (ticker: XOM) Application of nonconstant growth Input data: The valuation process for ALL e Most recent quarterly dividend Annualized dividend $3.48 Assumed dividend growth rate (yrs 1-3) 1.14% Assumed dividend growth rate (after yr 3) Assumed cost of equity Year Expected dividends P3 = Terminal value = 0 $3.48 Present values: dividends terminal value Current value = $ 40.98 1 $ 3.5197 $ 3.1595 1) 2) 3) 4) $0.870 2 $ 3.5598 $ 2.8685 3.10% 11.40% 3 $ 3.6004 $ 44.7228 $ 2.6043 $ 32.3499 Define forecast horizon. Construct a cash flow forecast Calculate the stock’s terminal Calculate the stock’s current v during the forecast horizon and 4 $ 3.7120 P3= D4/(K-g) Calculate the stock’s current value by adding the present values of the cash flows occurring Exxon Mobil (ticker: XOM) A 3-stage model that incorporates earnings growth & dividend growth as 2 separate components Input data: LT Expected EPS (2021) Expected dividend payout ratio (yrs 1 - 3) Expected EPS growth rate (yrs 1-3) Expected EPS growth rate (yr 4 only) Expected EPS growth rate (yr 5 only) Expected EPS growth rate (yr 6 only) Expected EPS growth rate (yrs 7+) Long-run expected ROE Long-run expected payout ratio Expected dividend payout ratio (yr 4 only) Expected dividend payout ratio (yr 5 only) Expected dividend payout ratio (yr 6 only) Assumed cost of equity Year 1 2 3 4 5 6 7 EPS DPS PV of DPS $2.44 $2.53 $ 2.27 $2.69 $2.78 $ 2.24 $2.96 $3.06 $ 2.22 $3.21 $2.96 $ 1.92 $3.42 $2.77 $ 1.62 $3.59 $2.50 $ 1.31 $3.70 $2.17 Terminal value at end of year 6 = PV of terminal value = Estimated value = 26.0958 13.6540 $ 25.23 $ 2.44 103.5% 10.15% 8.39% 6.63% 4.86% 3.10% 7.48% 58.6% 92.27% 81.03% 69.79% 11.40% rough estimate of current payout ratio roughly corresponds with expected EPS growth in sector f linear movement toward "long-run" linear movement toward "long-run" linear movement toward "long-run" assumed assumed consistent with long-run growth and ROE linear movement toward "long-run" linear movement toward "long-run" linear movement toward "long-run" with expected EPS growth in sector for next 5 years What's the point of this equation? g = ROE x (1 – d) and solve for d=dividend payout ratio What happens in years 4 through 7? Does the Growth Assumption Make Sense? Expected EPS growth = (1 - expecte ...
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find attached completed assignment

Dividend Discount Valuation - class examples
Home Depot (ticker: HD)
Application of Gordon constant growth model
Input data:
Most recent quarterly dividend
Annualized dividend
Assumed dividend growth rate
Assumed cost of equity
Value =
$ 333.83
Closing price (03/28/20) =

$1.500
$6.00
4.60%
6.48%

$ 190.55

Steet Inside

2019

Dividends per share

1.36

Future Dividend growth rate
based on 3 yr growth rate
based on 5 yr growth rate

Another straightforward use of constant growth formula:
Solve for growth:

Nominal GDP Growth Rate = Real GDP Grow
P0= D1/(K-g)
g=

5.77% per year

Any concerns?

2018

2017

2016

2015

2014

1.03

0.89

0.69

0.59

0.47

25.38%

𝐸𝑉 1

CAGR = 𝐺𝐴𝑉𝐺 = (𝐵𝑉)𝑁 − 1

23.68%

wth Rate = Real GDP Growth Rate + Expected Inflation Rate

2020
4.60%

Home Depot (ticker: HD)
Application of nonconstant growth
Input data:

The valuation process for ALL
Most recent quarterly dividend
Annualized dividend

$6.00

Assumed dividend growth rate (yrs 1-3)

4.60%

Assumed dividend growth rate (after yr 3)
Assumed cost of equity

4.60%
6.48%

Year
Expected dividends
P3 = Terminal value =

0
$6.00

Present values:
dividends
terminal value
Current value =
$ 333.83

1
$ 6.2760

$ 5.8941

1)
2)
3)
4)

$1.500

2
$ 6.5647

$ 5.7900

3
$ 6.8667
$ 382.0499

$ 5.6878
$ 316.4580

Define forecast horizon.
Construct a cash flow forecas
Calculate the stock’s termina
Calculate the stock’s current

during the forecast horizon and

4
$ 7.1825
P3= D4/(K-g)

Calculate the stock’s current value by adding the present values of the cash flows occurring

Date
Closing share price
3/28/2019
190.06
3/29/2019
191.89
4/1/2019
195.64
4/2/2019
194.31
4/3/2019
198.61
4/4/2019
200.45
4/5/2019
202.06
4/8/2019
203.55
4/9/2019
200.9
4/10/2019
199.43
4/11/2019
201.48
4/12/2019
203.85
4/15/2019
204.86
4/16/2019
204.47
4/17/2019
206.55
4/18/2019
205.66
4/22/2019
204.78
4/23/2019
206.05
4/24/2019
206.72
4/25/2019
206.5
4/26/2019
203.61
4/29/2019
202.16
4/30/2019
203.7
5/1/2019
198.8
5/2/2019
201.01
5/3/2019
200.56
5/6/2019
199.63
5/7/2019
194.77
5/8/2019
195.17
5/9/2019
194.58
5/10/2019
194.58
5/13/2019
190.34
5/14/2019
191.62
5/15/2019
191.76
5/16/2019
192.38
5/17/2019
192.58
5/20/2019
190.95
5/21/2019
191.45
5/22/2019
188.91
5/23/2019
192
5/24/2019
193.59
5/28/2019
191.55
5/29/2019
189.99
5/30/2019
191.08
5/31/2019
189.85
6/3/2019
189.57
6/4/2019
195.25
6/5/2019
196.69
6/6/2019
197.17
6/7/2019
197.3
6/10/2019
198.05
6/11/2019
198.01
6/12/2019
198.94
6/13/2019
202.35

Date
EPS
Jan-20
2.28
Oct-19
2.53
Jul-19
3.17
Apr-19
2.27

Share price and EPS

3.5
3

400
200
0

2.5
2
1.5
1
0.5share price
Closing
EPS

33444444444444444444444555555555555555555555566666666666666666
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22123458911111112222223123678911111122222223334567111111112222
89///////01256782345690///////034567012348901/////012347890145
//2222222//////////////2222222///////////////22222////////////
22000000022222222222222000000022222222222222200000222222222222
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