**BFM – Fall 2023, Professor Annan Project 3 – Capital Structure**

**1) Submit solution by 11:59 pm on Wednesday,**

**11/29**

**2) Submit directly in Canvas Notes:**

1. This is a group assignment. You are permitted to seek guidance from other groups in understanding the concepts underlying this assignment, but **your group must work independently in the actual preparation of your report**. You must begin with a blank document.

2. **The report should be typed** (not handwritten). Make sure to include all the inputs for calculations. Numerical solutions, content and clarity of essay answers, attention to detail, and overall professionalism will all be considered in determining the grade.

3. The first page of your submission should be the filled-out PDF **cover page posted on Canvas** (see the projects folder). Since this time, you are submitting the report directly in Canvas, electronic signatures (i.e., just typed names) of the group members are sufficient (i.e., no need to scan the hand-signed cover page).

4. The report in the PDF format & the underlying Excel file with calculations should be submitted directly in Canvas like you have been doing for all assignments and exams. **The file name should include BFM, a space, and then your group’s name**. The time stamp of the email will be used to determine if the emailed version of the assignment was turned in on time.

5. This project will be graded on a 10-point scale. Your score on this project counts as 5 percent of your course grade.

You are going to estimate the weighted average cost of

capital (WACC) at the end of fiscal year 2022 for the following companies:

1)

Starbucks.com, Inc.

Stock traded on NASDAQ under the ticker

SBUX.

2)

Shake Shack Inc.

Stock traded on NYSE under the ticker SHAK.

Use

the EDGAR database on the SEC website[1] to

locate the most recent annual reports of these companies. Search by company

name and pick the right entity in the search results. SEC assigns a unique

CIK number (as an identifier) to each company. The CIKs for Starbucks and

Shake Shack are 0000829224 and 0001620533, respectively. In the list of

filings for each company, access the most recent annual report, 10-K.

Starbucks and Shake Shack filed these on 11/18/22 and 02/23/23.

**Question 1.** Based on the annual reports, on what day did the fiscal year 2022 end for each company?

Use Yahoo! Finance (finance.yahoo.com) to download stock prices of Starbucks and Shake Shack.

On the Yahoo Finance page of each company, select the tab “Historical Data.” The time period should be at least 5 years up to the end of the fiscal year 2022 of each company (identified in Q1). Select

“historical prices” and set the frequency equal to “monthly.” Press the “Apply” button. Once the page is refreshed, click the “download data” link.

Using the “adjusted close” prices, for each company, calculate the 60 monthly returns up to the end of the fiscal year 2022.

Hint. If the adjusted close price is equal to $100 on 9/1/2022 and $110 on 10/1/2022, then the stock return in that month equals:

110/100 − 1 = 0.1 = 10%.

Suggestion. Organize your spreadsheet in the following way. The first column should contain dates. The subsequent columns should contain adjusted stock prices, returns (computed from prices), etc. The secret of solving the project fast is in keeping the spreadsheet neat and clean.

Note. Compare prices reported in the monthly viewer with prices reported in the daily viewer to notice that the monthly viewer reports prices at the end of each month.

**Question 2.** What is the arithmetic average monthly stock return for each company during the 60-month period prior to the end of fiscal year 2022? (Note: the average should be computed over 60 monthly returns.) What about the geometric average return? Which stock has been a better investment if one cares only about the return (and not about the risk)? (Hint: Please keep in mind that the fiscal years may end on different days for each company. As such, the 60-month period for the return calculation may not be identical for the two stocks.)

**Question 3.** What is the standard deviation of monthly stock returns for each company in the same time period as in Question 2? Standard deviation of stock returns is a measure of volatility. The returns on which stock have been more volatile in the time period under consideration?

**Question 4.** Standard deviation of stock returns may be referred to as a measure of risk. There are two types of risks: idiosyncratic and systemic. What type of risk is captured by the standard deviation: idiosyncratic, systematic, both, or neither?

In Q2, you compared the two stocks based on the average realized return, without taking risk into consideration. The Sharpe Ratio is a measure for calculating risk-adjusted return. It is equal to the ratio of the excess return’s average (or expected) value and its standard deviation. We will calculate a simplified version of the Sharpe Ratio.

**Question 5.** For each stock, divide the arithmetic average monthly return (from Q2) by the standard deviation of monthly returns (from Q3). (In other words, at this point we are not calculating the excess return by subtracting the risk-free rate.) This is the (simplified) Sharpe Ratio. Which stock has been a better investment based on the (simplified) Sharpe Ratio comparison?

**Question 6.** Let X be a random variable distributed with mean 𝜇 and standard deviation 𝜎; one realization

7−𝜇 of X may be equal to 7. Then the z-score associated with this realization will be given by: 𝑧 =

. If 𝑧 ≈ 2,

𝜎 then 7 is about two standard deviations away from the mean of X. And the probability of obtaining X that far away from the mean (in either direction) is under 2.5%. Notice the similarity between the formula to the z-score and the Sharpe ratio. With this in mind, what are the approximate probabilities of obtaining Sharpe Ratios as large as those computed in Q5?

Traditionally, the return on a value-weighted index of traded stocks (e.g., S&P 500) is used to represent the return on the market. Use Yahoo! Finance to download monthly values of the S&P 500 index for at least the last 5 years.

**Question 7.** What is the arithmetic average monthly return (i.e., expressed as a per month rate) on S&P 500 during the time period used for Starbucks in Questions 2 & 3? What is the EAR associated with that monthly rate? How does it compare with the historical average return on large-company stocks in Table 1 (see below)? If there’s a difference, what explains it? (The reason we focus on large-company stocks in the table below is because the S&P 500 index consists of large-company stocks.)

Table 1: Average Annual Returns and Risk Premiums: 1926–2013

**Investment Average Return Risk Premium**

Large-company stocks

12.1%

8.6%

Small-company stocks

16.9%

13.4%

Long-term corporate bonds

6.3%

2.8%

Long-term government bonds

5.9%

2.4%

U.S. Treasury bills

3.5%

0.0%

For the historical risk-free rate, go to the website of Federal Reserve Bank of St. Louis (https://fred.stlouisfed.org/series/TB3MS), search for the “3-month Treasury bill secondary market rate,” and download the corresponding file. Make sure to download the file with monthly data frequency.

Note that the values reported in the downloaded file are 1) reported in percentage points and 2) annualized. Accordingly, the reported value of, say, 1.23 corresponds to the annualized interest rate of 1.23% (or 0.0123) in that month.

**Question 8a.** What is the arithmetic average risk-free return during the time period used for Starbucks in Questions 2 & 3? In this sub-question, please average over the 60 annualized rates and report the answer with four decimal places (e.g., 0.1234%). How does the computed average risk-free rate compare with the historical average return on U.S. Treasury bills in Table 1 (see above)? If there’s a difference, what explains it?

For the purpose of subsequent analysis, you want to calculate the monthly risk-free rate which corresponds to the reported annualized rate. Do so using the formula:

# Monthly Rate = (1 + Annualized Rate)1/12 − 1

**Question 8b.** Calculate the arithmetic average risk-free return during the same time period over the 60 monthly rates? Report the answer with four decimal places (e.g., 0.1234%). Next, annualize this number, i.e., report an EAR corresponding to that average monthly rate. **Extra credit:** Why is this value different from the one calculated in Q8a?

According to the capital asset pricing model (CAPM), the required return on equity is given by:

𝐸(𝑅𝑖)

= 𝑟𝑓 + 𝛽𝑖 ⋅ (𝐸(𝑅𝑀)

− 𝑟𝑓)

We want to estimate the

beta coefficient of each stock. To do so, calculate for each date:

a) the

excess monthly return on each stock equal

to the difference between (1) the monthly return on a stock and (2) the

monthly risk-free rate.

b) the

excess monthly return on the market portfolio

equal to the difference between (1) the monthly return on the S&P 500

index and (2) the monthly risk-free rate.

In this exercise, make sure

to use the monthly risk-free rates (as

opposed to the annualized rates).

The

beta coefficient can be obtained from a linear regression of (a) on (b). The

left-hand side variable (Y variable) in the regression is (a); the right-hand

side variable (X variable) is (b). Beta is the slope coefficient in this

regression, and the slope coefficient can be calculated using the Excel

function SLOPE.

**Question 9.** Using 60 monthly observations up to the end of 2022 fiscal year for each stock, what is the estimated beta for each of the two companies? Report your answer with 3 decimal places (e.g., 1.234).

**Question 10. **Be reminded that beta is a measure of a stock’s systematic risk. Which stock, Starbucks or Shake Shack, has more systematic risk based on your calculations in Q9? Tell an economic story of why you think this may be the case.

Now that you know equity betas of these companies, you can estimate the cost of equity (i.e., the required return on equity). Use the formula:

# 𝑟𝑖 = 𝑟𝑓 + 𝛽𝑖 ⋅ (𝐸(𝑅𝑀) − 𝑟𝑓)

where 𝛽𝑖 are equity betas estimated in Q8 for each company, [𝐸(𝑅𝑀) − 𝑟𝑓] is the historical market risk premium, and 𝑟𝑓 is the current risk-free interest rate.

For the historical market risk premium, use the 8.6% value from Table 1.

For the current risk-free interest rate, use the annualized 3-month Treasury bill rate at the end of fiscal year 2022 for each company.

**Question 11.** What is the estimated cost of equity for each of the two companies?

**Question 12.** Keeping in mind the Modigliani & Miller Proposition II, what could explain the difference in the cost of equity between these companies?

To calculate the market value of equity (E), we need to know the stock price and the total number of shares outstanding. Use Yahoo! Finance for stock prices. Since here we aren’t using prices to calculate returns, you should use the regular closing stock price (and not the adjusted one). The total number of shares outstanding at the end of fiscal for each company can be found in their 10-K reports.

** **

**Question 13.** What was i) the closing stock price (unadjusted), ii) the number of shares outstanding, and iii) the market value of common stock for each company on the date of its 2022 fiscal year end? (Note: if the market was closed on the date of the fiscal year end, use the closing price on the last day of trading prior to the date of the fiscal year end.)

Instead of calculating the market value of debt outstanding, use the book value of debt for each of the firms as a proxy for its market value of debt. This simplification assumes that the debt is trading relatively close to par value which is a reasonable approximation. Use the fiscal year 2022 balance sheet to determine the total value of interest-bearing debt* *(include leases). Inspect the liabilities section of the balance sheet of each company and cherry pick line items, which you think are relevant. Be clear about which line items you include as part of interest-bearing debt for each company.

**Question 14.** Based on the above-mentioned cherry-picking of line items, what is the value of debt at the end of fiscal year 2022 for each of the two companies?

𝐸

**Question 15.** Using your answers to Questions 13 & 14, calculate the capital structure weights:

and

𝐷+𝐸 𝐷

. For each of the two companies, what fraction of the firm’s financing is equity and what fraction is

𝐷+𝐸

debt?

As discussed in class,

the cost of debt can be difficult to calculate, especially if a corporation

has a lot of bonds outstanding with different yields to maturity (YTM), or

none at all. To approximate the cost of debt, calculate the average YTM on

debt that has the same bond rating as each corporation.

As of the end of fiscal year 2022, please assume the

following credit ratings for each company:

•

Starbucks: Baa2/BBB

•

Shake Shack: Aa2/AA

Table 2 (see below) lists

the corporate spreads as of January 2023.

Source =

https://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/ratings.html

The yield on a 10-year Treasury bond equals 1.50%. (Assume

10-year maturity for Starbucks’s and Shake Shack’s debt obligations as well.)

A

corporate spread is the difference in yield between a given bond rating and a

treasury security with the same maturity. For example, the yield on a 10-year

AAA bond is approximately equal to 1.

50% + 0.69% = 2.13%, where 0.63% is the AAA spread from Table 2 and

1.50% is the yield on a 10-year Treasury bond.

Table 2: Corporate spreads

Rating

Spread

Rating

SHAPE * MERGEFORMAT

Baa2/BBB

SHAPE * MERGEFORMAT

Spread

2.00%

Rating

Spread

Aaa/AAA

0.69%

B3/B-

7.37%

Aa2/AA

0.85%

Ba1/BB+

2.42%

Caa/CCC

11.57%

A1/A+

1.23%

Ba2/BB

3.13%

Ca2/CC

15.78%

A2/A

1.42%

B1/B+

4.55%

C2/C

17.50%

A3/A-

1.62%

B2/B

5.26%

What is this? This is a table that relates the interest coverage ratio of a firm to a “synthetic” rating and a default spread that goes with that rating. The link between interest coverage ratios and ratings was developed by looking at all rated companies in the United States. The default spreads are obtained from traded bonds. Adding that number to a riskfree rate should yield the pre-tax cost of borrowing for a firm.

**Question 16**. Using the bond rating and the bond information provided above, what is the approximate cost of debt for each of the companies?

Before calculating the WACC, you need the tax rate for each firm. Traditionally, that is done by looking at the historical tax rate that the firm has paid in the last few years. On the firm’s income statement, you can find the income tax expense and the pre-tax income (income before income taxes). You can calculate the tax rate by dividing the income tax expense by the pre-tax income.

For simplicity, let us assume that the marginal tax rate—for the purpose of WACC calculation—is equal to 21% for both companies.

**Question 17.** You are now ready to calculate the WACC. Calculate the WACC for each company using the information from the previous questions.

**Question 18. **Calculate the correlation of monthly stock returns between Starbucks and Shake Shack over the five-year period preceding the Starbucks’s 2022 fiscal year end. (Hint: it should be positive.)

To reduce the portfolio risk, we may add a stock with a low or negative correlation with other assets in the portfolio.

**Question 19. **Use your economic intuition to think of a public company in the U.S. that has a negative correlation of returns with either Starbucks or Shake Shack. Please:

A) specify the company’s name and ticker,

B) report the correlation of returns—should be negative—over the five-year period preceding the 201921 fiscal year end of either Starbucks or Shake Shack, and

C) explain the economic intuition which led you to believe that the correlation would be negative.

Hint: Use your economic intuition to identify a potential candidate, download its monthly stock returns from Yahoo! Finance, copy-paste them into the spreadsheet, calculate monthly returns, calculate the correlation, and check if it’s negative. If it’s positive, repeat until you find a company with a negative correlation.

[1] https://www.sec.gov/edgar/searchedgar/companysearch.html