• Built Up Betas and the Cost of Equity

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Professor Crocker H. Liu Revised: December 27, 2004
Built Up Betas and the Cost of Equity
Objective: The objective of this assignment is to introduce students to how to calculate
beta using comparable companies. Not only is this approach the correct one to use in
general but is especially appropriate when a firm is either a private company or a
publicly traded company that has been trading only a short time or only infrequently. A
secondary goal is to show the impact that leverage (the use of debt) has on risk (beta).
Company: Mine Safety Appliances (Ticker: MSA, Website: http://www.msanet.com/)
You'd have to think long and hard to come up
with a name less sexy than "Mine Safety." Yet the
lack of sex appeal and minimal analyst exposure1
has not prevented Mine Safety from increasing its
earnings an average 26.2% per annum exceeding
that of the S&P and such Wall Street darlings as
Cisco and Intel (earnings decline an average of
19.1% per year).
Mining a rich vein of safety products for
hazardous workplaces, MSA is the largest company
in the world dedicated solely to producing a complete range of equipment and systems
for worker and plant protection in fire service, construction, chemical manufacturing,
military and mining. The Company's principal products include respiratory protective
equipment that is air-purifying, air-supplied and self-contained in design; instruments
that monitor and analyze workplace environments and control industrial processes;
thermal imaging cameras that enable firefighters and rescue workers to see through
smoke and darkness, and personal protective products including head, eye, face and
hearing protectors and fall protection equipment. On 11/3/2004, MSA announced
record 3rd quarter sales and earnings with growth
occurring primarily in the company's North American
segment, led by strong shipments of self-contained
breathing apparatus (SCBA) and thermal imaging
cameras (TICs) to the fire service market, and Advanced
Combat Helmets and gas masks to homeland security
and military markets. The company's broad range of
sophisticated new products are selling well, assisted by
higher government funding to support the fire service,
homeland security and the war on terrorism.”
Competitors (Publicly Traded): Abatix Corp (ABIX), DHB Industries Inc. (DHB), and
Lakeland Industries Inc (LAKE).
Only five analysts currently following the company in comparison to 36 analysts which follow Intel
(Nasdaq: INTC), or the 39 that follow Cisco Systems (Nasdaq: CSCO).
Item Assumption
Beta Use 60 months of the most recent data given in the “Returns”
worksheet to calculate the beta for each firm using the
SLOPE command in Excel.
Marginal tax rate Use the trailing twelve month (TTM) marginal tax rate for our
subject firm (Mine Safety Appliances).
Riskfree rate Use the 10 year Treasury bond as the appropriate
Debt Assume that MSA has an implied bond rating of AAA (based
on Altman’s EM-Z score) and a 10 year debt maturity. To
calculate the pre-tax cost of debt which you will use as the
discount rate to calculate the present value of the operating
lease (Value of Off-Balance Sheet Debt), add the 10 year
Treasury (located in the “Treasury Rates” worksheet) to the
Default Spread (located in the “Corporate Bond Spreads”
worksheet). Use the most recent debt outstanding for each
firm with respect to On Balance Sheet Debt.
Operating lease We will assume based on the operating lease payment for
Year 2008 of $2,657 that the Thereafter amount of $9,075
represents 4 additional years worth of operating leases with
the lease payment in each of the four years being an equal
Shares Outstanding Use the most recent shares outstanding for each firm
Equity Calculate the market value of equity (aka market cap) for
each firm using the most recent shares outstanding for each
firm multiplied by the price per share (given in the “Comps”
Risk premium (RM - rF) 5.5%
NA Set NA = 0 in the Financial Statements (Disclosure
Date of Analysis Assume that the date of your analysis is as of December 24,
Assignment: Download the MSA data from my website and use the downloaded
spreadsheet to answer the following questions (all work should be done on this
spreadsheet). The assumptions for each calculation are given on the preceding page.
Please highlight your answers in yellow in the worksheet templates provided:
1. Firm Betas (5 points): Calculate the betas for the comparable firms using either the
Regression option2 under Data Analysis in the Excel menu or the SLOPE command.
2. Total on Balance Sheet Debt (5 points): Calculate the total amount of On Balance
Sheet debt using the appropriate 10Q spreadsheet for each firm. In calculating the debt
for each comparable company, use the most recent figure given in the spreadsheet for
each firm. Assume that the book value of debt equals the market value of debt.
3. Market Value of Equity also known as Market Cap (5 points): Calculate the total
market value of equity using the appropriate 10Q spreadsheet for each firm and the
stock price for each firm located in the “Comps” worksheet.
4. Off Balance Sheet Debt (5 Points): Calculate the Present Value of Operating Leases.
5. Estimate the Beta for MSA using Comparables (70 points):
a. Method 1: Average the Betas and Debt/Equity and Then Unlever the Average Beta.
Calculate the levered beta for MSA using the “BuiltUp Beta - Method1” template.
Note that in re-leveraging the beta, the debt to equity ratio for MSA includes both on
balance sheet and off-balance sheet debt.
b. Method 2: Unlever the Beta for Each Comparable Firm and then Average the
Unlevered Betas. Calculate the levered beta for MSA using the “BuiltUp Beta –
Method2” template. Discuss whether the estimate of beta for MSA using the two
approaches is similar.
c. Method 3: Fundamental Beta: Rosenberg and Marather (1979) suggest that
fundamental information about a firm (the independent X variables) can be used
together with the historical levered beta (the Y variable) to obtain superior predictors
of future betas. Fundamental information that we use include the firm's dividend
yield, the coefficient of variation in operating income (standard deviation of operating
income divided by the mean of operating income), the size of the firm as measured
by its total assets, its debt/equity ratio (in book value terms), and its expected growth
rate in earnings per share. Using the data provided in the “Inputs for Fundamental
Beta” worksheet, use the Regression option under Data Analysis to calculate the
imputed levered beta for MSA. To calculate the levered beta for MSA you will need
to first calculate the X variables for MSA. More specifically, use the “MSA 10K”
worksheet to obtain the coefficient of variation of operating income (use 5 years
If you do not see the Data Analysis option under the Tools submenu in Excel, click on the Add-Ins option
under the Tools submenu then click on Analysis Toolpak and then click OK. You should now see the Data
Analysis option under the Tools submenu.
worth of data). Use the “MSA 10Q” in conjunction with the “Comps” worksheet to
obtain the dividend yield. Use the “MSA 10Q” to obtain the On Balance Sheet Debt
to Book Value of Shareholder Equity Ratio for the trailing twelve months. For the
constant average growth rate (CAGR), refer to the “Earnings Estimate (MSA)”
worksheet and use the MEAN Estimate of LT Growth Rate. For firm size (Total
Assets) use the “MSA 10Q”.
6. Estimate the Cost of Equity for Mine Safety Appliances (10 points): Calculate the cost
of equity for MSA under each of the three methods using the Capital Asset Pricing
Model (CAPM). The cost of equity is the discount rate that shareholders use to discount
back the cashflows they receive (dividends, stock buybacks, etc.). Use the 10 year
Treasury bond for the riskfree rate.
Please turn in a hard copy of your solutions together with your disk, which shows all
work on your spreadsheet. Since this is an individual effort, any student caught cheating
will be given an F on this assignment.

Use: 0.1024