5.2 Valuing a Business

Overview

Stock valuations are the result of a combination of Discounted Free Cash Flows (FCF), comparables multipliers, and transactions.

Discounted Cash Flows

Discounted cash flows use the present value of FCF forecast ~5 years into the future. FCFs are calculated as follows.

FCF = Earnings before Interest and Taxes (EBIT) – Taxes Paid – Working Capital Increases – Changes in Other Assets

Comparables

This method uses data from companies in the same industry as the firm being valued. In doing this, the methodology uses multipliers. The best multiplier is:

EV/EBITDA = Enterprise Value / Earnings Before Interest, Taxes, Depreciation, and Amortization

where EV = [[# of shares outstanding x market price/share] + [interest-bearing debt outstanding]]

You take the EBITDA of the target firm being evaluated and multiply it by the EV/EBITDA for its comparable to get the target firm’s EV. To get the value of the target firm’s equity, subtract interest-bearing debt outstanding from the calculated EV. Finally, divide the equity by the number of shares outstanding to get the comparable price per share.

You can repeat this process using other comparable firms and then average the calculated prices to get a comparable-based stock price. Also, you can use other ratios, such as EV to cash flow, and so on.

Transactions

Acquisitions of firms in the same industry as the target firm also give us an indication of the stock price for the target firm. To use this method, compare the stock price of the acquired firm prior to the announcement of the acquisition to the final price paid. This comparison is the premium paid. This premium can then be applied to the current stock price of the target firm to get a transaction-based stock price.

All three methods may be combined by giving the stock prices calculated under each weight. The sum of these weights is 100%. You choose how you weigh each. That said, discounted cash flows should carry a higher weight because the method is more rigorous. As always, it all depends!

Wilson Aviation

You have read the Wilson Aviation case. Now, please answer questions in the case using the Excel template below. The template already contains all the data you need to complete your work.

Wilson Aviation: Valuing a Business
Alfonso F. Canella Higuera
October 18, 2021
Daniel Rouse was a fixture at the Deerfield Airport in central California. Daniel, now 50
years old, had started working there when he was in high school, continued working there through
college at Cal Poly in San Luis Obispo, and continued using the airport, flying his Cessna there
during visits from southern California, where he was working as an engineer for Boeing.
Daniel had just taken an early retirement package and decided to go home. So, one day, he
flew his Cessna back, tied it down, and never looked back at southern California again. He renovated
his parents’ home, some two miles from Deerfield Airport, and stayed there for good. He loved the
area, the weather, the scenery, the laid-back atmosphere, and, yes, the access to the airport. Oh, and
everyone knew Daniel and appreciated him!
The weeks passed after his arrival and Daniel grew restless. He had worked long and hard
at Boeing and it was difficult to change gears. He wanted something to do and was wondering what
it would be. That evening, while hanging out at the airport’s restaurant, he was offered the purchase
a business that sold aircraft controls to Boeing. Daniel could only remark “the apple doesn’t fall far
from the tree, does it?”
The firm’s owner, Harlan Wilson, 78, had known Daniel for decades and loved him like a
son. Seeing that Daniel had moved to the area for good, Harlan, also a Cal Poly alum, had 5 children
but they were not interested in engineering or flying or moving to Central California or running a
business. And since his 12 grandchildren were his heirs, he had to sell the firm to help fund their
college educations. So, it made sense to see if Daniel, whom Harlan trusted implicitly, would
continue the business and keep it locally owned. Daniel’s engineering experience at Boeing certainly
helped smooth the transition to a new owner.
And so it was. Daniel was very receptive and Harlan offered to give him the firm’s financials
so Daniel could figure out a purchase price. Harlan had a notion of the price of his firm (an even
million) but he hadn’t run the numbers. He wouldn’t run them anyway; Harlan knew that Daniel’s
honesty was as long as a summer day and he knew they’d work out a fair price without bringing in
an appraiser.
Harlan knew Daniel might not have the money required to buy the business outright. He
understood, rightly, that a lot of Daniel’s net worth was tied up in retirement accounts that would
trigger a large tax bill if they were cashed out. So, Harlan threw in a sweetener: “I’ll keep 50% of
the equity in the business and you can pay me 5% on it for the first 5 years. At the end of those 5
years, buy me out for what we calculate the 50% is worth today.”
The proposal was clever – Harlan would earn a sure 5% on his money, which was clearly
higher than he could expect on his Treasury investments. Also, with the extra equity, Daniel could
borrow at a lower rate from the bank as the firm would have little debt. It was a win-win.
Daniel accepted and they wrote the terms of the agreement on the restaurant’s paper table
covering. After signing on the terms, Daniel and Harlan walked over to Wilson Aviation’s offices
so that Harlan could give him the financials.
The next day, Daniel sat down and started going through Wilson Aviation’s financials. These
financials would help him generate the free cash flow projections (FCF) that he could then present
value to get the enterprise value (EV) of Wilson Aviation. To remind himself of the entire process,
he wrote on the dry erase board in his office what he needed to do:
1. Calculate the weighed average cost of capital (WACC):
a. Estimate the appropriate cost of debt and the amount of debt for Wilson after the
purchase and the tax rate to be applied
b. Estimate the cost of equity for a firm like Wilson Aviation; this would require using
the Capital Asset Pricing Model (CAPM)
c. To use the CAPM, Daniel would need to estimate Wilson’s beta (ß), which is the
firm’s covariance of returns relative to the overall stock market. Daniel would also
need the 10-year Treasury rate as a stand in for the risk-free rate and the stock
market’s historical returns over and above the risk-free rate (this was called the
market premium)
2. Forecast the firm’s income statement for the next 5 years
3. Use the results from the income statement to forecast the firm’s balance sheet and use the
numbers generated to calculate the working capital for each year
4. Generate the FCF as follows:
a. Get the Income Before Taxes from the income statement
b. Add to these the interest paid by adding the Bank Loan, Current Portion of Long
Term Debt (CPLTD), and Long Term Debt (LTD) together and multiplying that by
the debt interest rate used in the WACC calculation
c. The sum of Income Before Taxes and the interest paid is now equal to Earnings
Before Interest and Taxes (EBIT)
d. Subtract the actual taxes paid from EBIT to get Earnings before Interest and After
Tax (EBIAT)
e. Subtract the increases from year to year of Working Capital from EBIAT
f. Subtract the increases from year to year of Other Assets from EBIAT (this is a proxy
of capital expenditures)
g. Once the two subtractions are done, you are left with the FCF
h. Use the perpetuity formula to calculate the terminal value (TV); in this case, apply a
long term growth rate of 2.5% as a higher growth rate was not appropriate and would
also high too high an EV
i. Use the NPV function of Excel with the WACC as the discount rate to get the present
value of the FCF
j. Subtract the 2020 values for Bank Loan, CPLTD, and LTD to get the dollar value of
equity
Daniel started from the top by commencing to calculate Wilson Aviation’s WACC.
Because Wilson was privately owned by Harlan, it had no stock price data. So, Daniel would have
to start from scratch. The formula for the WACC is:
[% Debt x Cost of Debt x (1 – tax rate)] + [% Equity x Cost of Equity]
Page 2 of 7
work:
Daniel had done some research since his retirement and had some notions of what would
% Debt = 25%
Cost of debt = 4.9%
Tax rate = 21%
% Equity = 75% (basically, it was 1 – % Debt)
Cost of Equity = ???
He needed to come up with a way to calculate the cost of equity for Wilson. Since it wasn’t
traded, he had no beta (ß) to plug into the Capital Asset Pricing Model (CAPM) that allows analysts
to come up with an expected return on equity:
Cost of Equity = Risk-Free Rate + [Beta x Market Premium]
He had checked out the internet and found out the following:
Risk-Free Rate = 2.0% (10-year Treasury)
Market Premium = 6.0% (a historical average that varied based on what years were averaged)
Beta = ???
Daniel needed to get a beta but how? He emailed his old professor at Cal Poly as he suspected
that he might know. The professor replied that Wilson Aviation had two major competitors in its
industry, Maxwell and Barston, and they had public data that could be used to back into the
industry’s average beta. He gave the data to Daniel, who then put together the table below:
Component
Net Income (M$)
Earnings per share (EPS)
# of shares (M)
Price per share
Market Value – Equity (M)
Market Value – Debt (M)
Market Value – Total (M)
– % Debt
– % Equity
Beta (levered)
Beta (unlevered)
Average Beta (unlevered)
Maxwell
17.22
4.20
14.00
20
20
0.60
Barston Notes
9.70
4.50
Net Income / EPS
11.50
# of shares x price per share
7
7
Debt as a per cent of Total MV
Equity as a per cent of Total MV
0.66 as reported in Value Line
Beta (levered) x % Equity
Average of the two Beta (unlevered)
The unlevered beta was the risk associated with the industry. Daniel needed to take that
unlevered beta and relever it to make it specific to Wilson Aviation. To do this, he put together
another table:
Page 3 of 7
Values for Wilson:
% Debt
% Equity
Beta (relevered)
Risk free rate
Market risk premium
Expected equity return (CAPM)
Expected cost of debt
Tax rate
Weighed average cost of capital (WACC)
25.0%
2.0%
6.0%
4.9%
21.0%
It was now all coming together! Daniel could take the unlevered beta and divide it by Wilson
Aviation’s % Equity to get the Beta (relevered). He would then use it in the CAPM to get the
Expected Equity Return using the CAPM. That was the last piece of the puzzle as the already had
all the other factors at hand. He filled in the numbers and when he looked at the WACC, he couldn’t
help but realize that Harlan’s proposed return on his equity wasn’t far off.
This bit of news comforted Daniel. He feared that over time Harlan had been losing the firm
grip he had on his business but now he realized that the old man was as sharp as ever. He was now
convinced that the firm had been in good hands all along and that he would be buying a solid
enterprise with good products, a solid service program, and a pipeline of new controls that would
keep the firm busy for at least a decade if not more.
With the WACC calculated, Daniel turned to forecasting the firm’s income statement.
Harlan had given him the firm’s 2020 financials and between the two of them they came up with an
estimate for the growth of the firm’s two revenue streams: parts sales and service. They also came
up with an estimate of the future growth of the various expense line items.
Harlan told Daniel that the service program showed not only higher revenues but also higher
margins. Daniel said that that was also the case at Boeing, where service was the cash cow for the
business and aircraft and parts sales were almost there to support the service business unit.
That all said, both recognized that both revenue streams relied on the firm’s investment in
research and development (R&D). Looking at the forecasts, they both realized that R&D was
becoming the largest line item in the expenses. It all made sense. In some firms, R&D can reach
20% of revenue and these firms were the ones that had the most success in their markets.
Accompanying the R&D expenses in dollar amounts were salaries and benefits. Both agreed that
the future of the firm was based on its human capital and that to keep the best you had to pay well
and offer good benefits. Not many people would move to central California to live and to get them
to do so, you had to offer them an incentive in their pay package.
Based on his discussions with Harlan, Daniel put together the following income statement
forecast for Wilson:
Page 4 of 7
Income Statement (in ‘000 $)
Growth rates:
Parts Sales
Service Program
Parts Sales
Service Program
Total Operating Revenues
Actual
2020
2,223
2,142
4,365
Salaries and benefits
Research and development
Service expense
Sales and Administrative
Depreciation/amortization
Total Operating Expenses
995
922
565
437
374
3,293
Income before taxes
Income tax expense/(benefit)
Net Income
1,072
225
847
2021
2022
Projected
2023
2024
2025
5.0%
6.0%
5.0%
6.5%
5.0%
6.5%
5.0%
6.5%
5.0%
6.5%
Notes
Increase at a
yearly rate of
4.5%
7.0%
5.0%
4.0%
4.0%
For the income statement, the math was straightforward, for example:
2021 Parts Sales = 2020 Parts Sales x (1 + 2021 Part Sales growth rate)
2021 Salaries and benefits = 2020 Salaries and benefits x (1 + Salaries and benefits growth rate)
2021 Income tax expense = 2021 Income before taxes x 21%
With income statement all done, Daniel put together the forecast balance sheet for Wilson:
Cash and investments
Accounts receivable
Inventory and supplies, net
Other
Current Assets
Other
Total Assets
Balance Sheet
1,934
1,249
1,045
192
4,420
5,932
10,352
Bank Loan
Payables
CPLTD
Other
Current Liabilities
LTD
Equity
Total Liabilities & Equity
4,049
248
44
93
4,434
1,877
4,041
10,352
Working Capital
4,035
Increase at a
yearly rate of
12.0%
10.0%
9.0%
3.0%
Increase at
5.0%
Plug account
Increase at a
yearly rate of
5.0%
1.0%
3.0%
Exclude Bank Loan
It was all now starting to take shape. The income statement forecast allowed Daniel to see
how the firm would be faring going forward. The bottom line for the income statement was robust
and, most importantly, it was feeding the Equity account in the balance sheet. The formula for the
Equity was:
2021 Equity = 2020 Equity + Net Income
Page 5 of 7
The LTD account formula was also straightforward:
2021 LTD = 2020 LTD – 2021 CPLTD
This was because the CPLTD was taken out of LTD and paid out in 2021, thus reducing the
LTD account. That made sense. The Bank Loan, the last debt account, was a balancing account and
consisted of:
Bank Loan = Total Assets – Payables – CPLTD – Other – LTD – Equity
The Bank Loan, if positive, was a working capital loan that allowed Wilson to fund itself
properly. The amount was calculated correctly and the balance sheet balanced – that is, total assets
equaled total liabilities plus equity. If the Bank Loan was negative, the absolute value of it was just
cash.
All the other line items in the balance sheet had their allocated yearly growth rates and they
grew at a good pace as the firm was growing. Finally, the working capital was calculated. Daniel
was careful NOT to include the Bank Loan in the calculation:
Working Capital = Current Assets – Payables – CPLTD – Other
Daniel knew that he had to forecast the balance sheet in part to see how the firm’s accounts
would be faring in the coming years but mostly because he needed the change in working capital
from year to year to generate the FCF.
With the income statement and balance sheet looking good, Daniel then set up the FCF table
to calculate the EV and the value of the equity:
Free Cash Flow Valuation
(in ‘000 $)
Income before taxes
+ Interest
= Income before interest and taxes (EBIT)
EBIAT
– Change in Working Capital
– Change in Other assets
Free Cash Flow (FCF)
PV of FCF = EV
– Existing Debt
= Value of equity
2021
2022
2023
2024
2025
TV
Growth rate
2.5%
He applied the 2.5% growth rate to the perpetuity governing the Terminal Value (TV)
calculation:
Terminal Value = 2025 FCF x (1 + TV growth rate)^2/(WACC – TV growth rate)
Page 6 of 7
He understood that the (1 + TV growth rate) term had to be squared because implicit in the
formula was a discounting of the terminal value by one period. So, if he didn’t square it, the TV
would be as of the end of 2025 and not as of the end of 2026, as he had it laid out in his table. Daniel
knew that Excel would treat the cell after 2025 as 2026 and made this adjustment.
Daniel calculated the FCF as well as the TV. He applied the NPV function to them using the
WACC as the discount rate. He got the EV and then subtracted the value of the 2020 debt. He had
finally gotten the value of the equity of Wilson Aviation!
Harlan would hold 50% of it and Daniel would give him half the value of the calculated
equity to hold the other 50%. It was a pretty sweet deal for both!
Case Questions
Use the Wilson Aviation template to calculate the following:
1.
2.
3.
4.
WACC
Forecast Income Statement and Balance Sheet, including Working Capital
FCF
EV and value of the Equity
Remember to show all your formulas to ensure that you can get partial credit. If you show
only a numerical answer and it is not correct, you will not be eligible for partial credit.
Page 7 of 7
Component
Net Income (M$)
Earnings per share (EPS)
# of shares (M)
Price per share
Market Value – Equity (M)
Market Value – Debt (M)
Market Value – Total (M)
– % Debt
– % Equity
Beta (levered)
Beta (unlevered)
Average Beta (unlevered)
Values for Wilson:
% Debt
% Equity
Beta (relevered)
Risk free rate
Market risk premium
Expected equity return (CAPM)
Expected cost of debt
Tax rate
Weighed average cost of capital (WACC)
Maxwell
30.00
5.00
27.00
155
0.55
50.0%
5.5%
6.1%
8.0%
21.0%
Barston Notes
25.00
4.00
Net Income / EPS
21.75
# of shares x price per share
144
Debt as a per cent of Total MV
Equity as a per cent of Total MV
0.65 as reported in Value Line
Beta (levered) x % Equity
Average of the two Beta (unlevered)
Income Statement (in ‘000 $)
Growth rates:
Parts Sales
Service Program
Parts Sales
Service Program
Actual
2020
2021
Projected
2022
2023
2024
2025
3.0%
4.0%
3.0%
5.0%
4.0%
5.0%
4.0%
5.0%
2,481
1,087
Total Operating Revenues
3,568
Salaries and benefits
Research and development
Service expense
Sales and Administrative
Depreciation/amortization
790
750
533
271
450
Total Operating Expenses
2,794
Income before taxes
Income tax expense/(benefit)
Net Income
Cash and investments
Accounts receivable
Inventory and supplies, net
Other
774
163
611
Balance Sheet
1,911
1,103
922
102
Current Assets
Other
Total Assets
4,038
5,451
9,489
Bank Loan
Payables
CPLTD
Other
2,900
200
33
75
Current Liabilities
LTD
Equity
Total Liabilities & Equity
3,208
1,860
4,421
9,489
Working Capital
4.0%
5.0%
Notes
Increase at a
yearly rate of
4.5%
5.5%
5.5%
4.5%
4.0%
Increase at a
yearly rate of
4.0%
4.0%
2.0%
2.0%
Increase at
3.0%
Plug account
Increase at a
yearly rate of
Exclude Bank Loan
2.0%
2.0%
2.0%
Free Cash Flow Valuation
(in ‘000 $)
Income before taxes
+ Interest
2021
2022
2023
2024
2025
TV
= Income before interest and taxes (EBIT)
EBIAT
– Change in Working Capital
– Change in Other assets
Free Cash Flow (FCF)
PV of FCF = EV
– Existing Debt
= Value of equity
Growth rate
2.0%
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