# estimate an annual expected first-stage growth rate in dividends during stage 1, g1, AND the number of years, n, that you expect the g1 level of growth to persist.

**Assignment 2 – Submit One (1) Hard Copy per Team**

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Coca-Cola (KO) is the world’s largest producer of soft-drink concentrates, syrups, and juices. Its soft-drink brands include Coke, Diet Coke, Cherry Coke, Sprite, Tab, Nestea, and Barq’s. The firm sells about 59% of its concentrates and syrups to company-owned and independent bottlers in the United States and abroad, who distribute them to end users. Coca-Cola also makes fruit juices sold under names like Minute Maid.

**Follow the Two-Stage DDM method presented in class (including the Two-Stage DDM spreadsheet). If you need a further review, remember that you studied the Two-Stage DDM in your F371 text.**

**Answer the following question. You MUST show all of your calculation in the questions below is order to receive credit for any numerical answers. All five questions are worth 20 points each (5 x 20 = 100 points).**

**Two-Stage Dividend Discount Model**

**Q1.** The **First Step **in using the Two-Stage DDM is to **estimate an annual expected first-stage growth rate in dividends during stage 1, g1, AND the number of years, n,** that you expect the g1 level of growth to persist**. Two (2) popular methods for estimating g1 that were discussed in class are:**

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**(Method 1):**Form an estimate for g1, the growth rate in dividends based on the average annual historical growth in dividends over the past five (5) years. The assumption in this method is that the historical average growth rate in dividends over the past five years is a good estimate for g1 over the number of years of that you have assumed for stage 1.

**(Method 2):**Use the formula provide in the AAII article**“Methods for Valuing a Stock”**for estimating the**sustainable growth rate**in EACH of the past five years then take a simple average of these five annual sustainable growth estimates in order to arrive at a second estimate for g1. The assumption in this method is essentially that the historical average sustainable growth rate, which is essentially the expected sustainable growth rate in net income for a given level of ROE and a given retention ratio, is a good estimate for g1 (the growth rate in dividends). The sustainable growth rate formula assumes the capital structure remains constant and no new common stock is issued.

**Sustainable growth rate = ROE x retention ratio**

**Write a short paragraph **(at least three sentences) that** COMPARES and CONTRASTS** your two estimates for g1. Are the similar? Are they extremely different? Give your thoughts on why there are similarities or differences.

**You can also provide a subjective adjustment** to the average value estimates of g1 above based on any other information you feel is relevant (new products, increased competition, DuPont analysis, etc.). ** **

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**SELECT**the**one (1) single estimate**from Q1A and Q1B above that YOU believe is the**most appropriate value of g1**for valuing KO using the Two-Stage DDM. Further**, LIST**the**number of years, n,**you expect g1 to persist.**Provide a short paragraph**(at least three sentences) that**EXPLAINS**your reasoning for selecting these values of g1 AND n.

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***IMPORTANT: **A **Key Learning Point** here is that any estimate of the future growth in dividends will generally NEVER equal the actual growth that results after time passes. **All financial valuation estimates are subject to forecast error, which is also referred to as estimation risk.**

**Q2. ** The **Second Step** in using the Two-Stage DDM is to estimate an **annual required return on equity**, **Re**. While not absolutely necessary, for the purpose of this assignment you may assume that Re remains constant in stage 1 and stage 2. **Four (4) popular methods for estimating Re that were discussed in class are:**

**(Method 1):**Calculate the**arithmetic average**of realized historical annual returns over the past five (5) years. The assumption in this method is that the historical average annual return is a good estimate of future annual returns. This is not a law of nature. It is an assumption. To do this you will need to calculate annual total returns from the most recent 5-year period using**Monthly Historical Prices**. Calculate the annual total returns based on the**December-ending Adj Close***price found under Historical Prices on the**www.finance.yahoo.com**website.

*Annual Total Return = [Adj Close* Price December (t) – Adj Close* Price December (t-1)] / Adj Close* Price December (t-1)*

**Example:**

*Annual Total Return 2017 = [Adj Close* Price December 2017 – Adj Close* Price December 2016] / Adj Close* Price December 2016*

The Adj Close* price is adjusted for dividends and splits, so this price is all that you need to calculate a total return.

**(Method 2):**Use a factor return generating model such as the**CAPM**to estimate Re.

E(Re) = Rf + Beta x [E(Rm) – Rf]

As you know, the **CAPM requires an estimate Rf, Beta and an appropriate expected Market Risk Premium (MRP = E(Rm) – Rf). ** Once again, **more estimation risk!**

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**i) EXPLAIN your estimate of Rf**

ii) EXPLAIN your estimate of Beta

iii) EXPLAIN your estimate of the MRP = [E(Rm) – Rf)

***IMPORTANT: Keep in mind that you are estimating a value for Re the will hold forever (or at least over the life of the firm). As such, current values for Rf, Beta and MRP MAY NOT BE APPROPRIATE for the long-term. Consider the long-term average value for Rf, Beta and MRP**.

**(Method 3):**Use the**implied Re for a similar firm**derived from the**Constant Growth DDM (CGDDM).**

The CGDDM is written as P(0) = D(1) / (Re – g). To solve for an estimate of an implied Re, find the current price P(0) for a comparable firm, estimate the next dividend for that firm, D(1), estimate a growth rate (forever since this is the constant growth DDM) then solve for the implied Re that will generate P(0) given your assumptions for g and D(1).

**Re = [D(1) / P(0)] + g = Expected Dividend Yield + Expect Dividend Growth (forever)**

**Example:**

If you believe that Molson Coors Brewing (TAP) is in the same risk class as KO and that it will grow at 4% annually forever (extreme assumption), the current price is $90 per share and the current dividend is $1.63 per share then the implied Re is,

Re = [D(1) / P(0)] + g = $1.63/90 + .04 = 5.81%

***IMPORTANT:** You must select a firm that you believe is in the same risk class as KO. Realize also that your estimate of Re using this method also relies on your estimate of a growth value, g, that you expect will hold forever! **Once again, you cannot avoid estimation risk!**

**(Method 4)**Add a**3% – 4% equity risk premium (ERP) to the YTM on a KO long-term bond**that has at least 20 years to maturity. The rationale for this method is that the required return on equity must be greater than the required return on debt for any firm.**If KO does not have a 20-year bond outstanding, then add 3% to the YTM on a 20-year corporate bond with the same bond rating (i.e. A, AA, or AAA).**You must find the YTM on a KO**20-year bond**or the YTM on**a comparable corporate 20-year bond.**Realize that a risky 20-year corporate bond must have a YTM that is greater than the YTM on a risk-free 20-year Treasury bond.

**SELECT**the**one (1) single estimate**of Re from Q2A – Q2D above that YOU believe is the**most appropriate**for valuing KO using the Two-Stage DDM and**provide a short paragraph**(at least three sentences) that**EXPLAINS**your reasoning.

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**Websites for bond information:**

FINRA Bond Market Data

www.finra.org/marketdata

Click on Bonds

Click on Search

Click on Corporate in the Quick Search box

Type Coca Cola in the Issuer Name box

If no 20+ year bonds for KO are shown then try Pepsi

*You must find the YTM on a corporate bond with 20+ years to maturity and with a similar rating (A or AA). Do NOT use the YTM on a 20-year Treasury bond. Why?

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**Q3.** The **Third Step** is to estimate a second stage (also called the stable stage) growth rate in dividends**, g2**, for use in the Two-Stage DDM. This is the growth rate that you expect will continue “forever” in the second stage. Your estimate for**g2 should not be much greater than the expected future growth in the overall economy **(expected growth in GDP). Why? **LIST **your estimate for g2 and provide a short paragraph that **EXPLAINS **your reasoning AND the source of your estimate for long-term growth in GDP.

**Q4. **Using KO’s **current annual dividend** (most recent quarterly dividend x 4) as D(0) in the Two-Stage DDM, **LIST** your value (price per share) estimate for KO using the Two-Stage **DDM (provide a screen shot of your Two-Stage DDM spreadsheet).**

**Q5.** Perform **Sensitivity Analysis (SA)** on your estimated price per share in by varying **EACH** of your three (3) input parameters **(g1, g2 and Re)** by +/- 2.0 percent in .5 percent increments **while holding the other two parameters constant**. Provide two (2) short paragraphs (at least three sentences in each paragraph) that **LISTS** and **DISCUSSES** your results. That is, describe in words how your value estimates change as you change your growth and discount rate estimates. **Always remember that estimates are nothing more than estimates and subject to forecast error. This is why 1000 analysts can easily arrive at 1000 different estimates of value.**

*** LIST:** Write out the specific value.

***SHOW:** Provide a spreadsheet or hand-written copy of your calculations.

***EXPLAIN:** Provide verbal statement that supports your estimate(s).

***DISCUSS:** Describe your results in words. Do not simply just list your numerical results.

***JUSTIFY: **Provide sources of information, methods used to form assumptions and data used for estimating input variables.

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**Assignment 3 – Submit One (1) Hard Copy per Team**

**Continue your price per share estimation process for KO from Assignment 2.**

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**Use the FCFFM and RV spreadsheets and follow the Two-Stage FCFFM valuation method presented in class in order to answer the following questions. You MUST show all of your calculation in the questions below is order to receive credit for any numerical answers. All five questions are worth 20 points each (20 x 5 = 100 points).**

**Two-Stage Free Cash Flow to the Firm Model (FCFFM)**

**Q1. ** As in Assignment 2, estimate first-stage growth, **g1**, in the Two-Stage FCFFM AND the **number of years, n,** that you expect the **g1 level of growth in FCFF** to persist by looking at the historic growth in FCFF over the past five (5) years. You can use the recent 5-year growth as your estimate for g1 OR you may revise it based on any other information you feel is relevant (new products, increased competition, etc.). ** LIST** your estimate for g1 and number of years, n, you expect it to persist. Provide a short paragraph (at least three sentences) that **EXPLAINS **your reasoning.

**Q2.** Estimate KO’s WACC as the appropriate discount rate in the FCFF Model. This is relatively simple since the FCFF spreadsheet template will estimate a weighted average cost of capital for you! **You can use your best estimates for Re and YTM from Assignment 2 (unless points were deducted for these estimates in Assignment 2) as inputs for calculating the WACC for KO. ** **As you learned in F371, you should use market value weights for both debt and equity and not book value weights when calculating a firm’s WACC.** The problem here is that you do not have the time or resources to calculate KO’s market value of debt or the average YTM on that debt. **Therefore, make sure that you include the reported book value of debt as shown on the most current balance sheet statement as a proxy for the market value of debt. **Assume that KO’s WACC remains constant in stage 1 and stage 2. **LIST** your estimate for KO’s WACC.

**Q3.** Estimate second stage or stable stage growth, **g2**, in the FCFFM. **As in Assignment 2, your estimate for g2 should not be much greater than the expected future growth in the overall economy (growth in GDP) for a very long time. **Why? Stable stage growth need not be exactly the same in the DDM and FCFFM because dividends and free cash flow to the firm are two different series. They should, however, be relatively similar because dividends are paid from net income, which is an important component of FCFF.** LIST** your estimate for g2 and provide a short paragraph that **EXPLAINS** your reasoning.

**Q4. LIST** and and provide a short paragraph that **EXPLAINS** your estimate of KO’s**FCFF(0) **for use in the FCFM. **Be careful in this step.** Unlike using the current dividend as D(0) in the DDM, the current year’s FCFF may not be appropriate for using a base FCFF(0) value! Consider using the most recent **5-year average **FCFF value as your estimate for a base FCFF(0) **OR** a value based on the **5-year trend** in FCFF. Remember, your estimate of** FCFF(0) is the value on which you believe all future annual FCFF estimates are based **given your estimates of g1 and g2 (notice how many times the word “estimates” is used). You cannot avoid estimation risk!

**SHOW** your calculations and **LIST** your value (price per share) estimate for KO using the Two-Stage FCFFM.

***IMPORTANT:** There is nothing magic about using a 5-year historical averages as a starting point for estimating future values for input parameters. Using the most recent years of financial data does NOT prevent you from using additional historical financial information when forming your expectations about the future. You should realize, however, that if you simply use only the most recent annual statement (only one year of data), your estimates for future cash flows (particularly free cash flow) will be biased by the most recent one-year period. This is why you should consider using an average of recent time series of historical values for your base FCFF(0) estimate.