978-1285190907 Chapter 12 Part 6

Chapter 12

Valuation: Cash-Flow-Based Approaches

12-49

in whole or in part.

Aggregate

Residual

Income:

$2,568/(0.0844) ………………………. $ 30,426 0.66689 20,291

Book Value of Common Equity, January 1, Year 16 ……………… 29,394

Total Value……………………………………………………………………….. $ 64,729

Half-Year Adjustment: $64,729 × [1 + (0.0844/2)] ………………… $ 67,461

aYear 16: $2,481 = 0.0844 × $29,394

Year 17: $3,050 = 0.0844 × $36,134

Year 18: $3,647 = 0.0844 × $43,210

Year 19: $4,274 = 0.0844 × $50,641

Year 20: $4,933 = 0.0844 × $58,443

Year 21: $5,624 = 0.0844 × $66,635

2. Valuation with 5% growth in earnings after Year 20

Present Value

Net Expected Residual Factor at Present

Year Income Income Income 8.44% Value

16 $6,740 $2,481 $4,259 0.92217 $ 3,928

17 $7,077 $3,050 $4,027 0.85040 3,425

18 $7,430 $3,647 $3,783 0.78421 2,967

19 $7,802 $4,274 $3,528 0.72317 2,551

20 $8,192 $4,933 $3,259 0.66689 2,173

Present Value of Residual Income for Year 16 to Year 20………. $15,044

Continuing

Value $8,602a $5,624 $2,978

Aggregate

Residual

Income:

$2,978/(0.0844 – 0.05) …………….. $86,570 0.66689 57,733

Book Value of Common Equity, January 1, Year 16 ……………… 29,394

Total Value……………………………………………………………………….. $102,171

Half-Year Adjustment: $102,171 × [1 + (0.0844/2)] ………………. $106,483

a $8,602 = $8,192 × 1.05

Chapter 12

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12-50

in whole or in part.

3. Valuation with 2.5% growth in earnings after Year 20.

Present Value

Net Expected Residual Factor at Present

Year Income Income Income 8.44% Value

16 $6,740 $2,481 $4,259 0.92217 $ 3,928

17 $7,077 $3,050 $4,027 0.85040 3,425

18 $7,430 $3,647 $3,783 0.78421 2,967

19 $7,802 $4,274 $3,528 0.72317 2,551

20 $8,192 $4,933 $3,259 0.66689 2,173

Present Value of Residual Income for Year 16 to Year 20………. $15,044

Continuing

Value $8,397a $5,624 $2,773

Aggregate Residual Income:

$2,773/(0.0844 – 0.025) …………… $46,684 0.66689 31,133

Book Value of Common Equity, January 1, Year 16 ……………… 29,394

Total Value ………………………………………………………………………. $75,571

Half-Year Adjustment: $75,571 × [1 + (0.0844/2)] ………………… $78,760

a$8,397 = $8,192 × 1.025

C. Residual ROCE Model

1. Zero growth after Year 20

Compre- Cum. Present Value/

hensive Implied Residual Share. Eq. Value Book

Year Income ROCE ROCE Growth Factor Ratio

16 $6,740 0.2293 0.1449 1.000 0.92217 0.1336

17 $7,077 0.1959 0.1115 1.229 0.85040 0.1165

18 $7,430 0.1720 0.0876 1.470 0.78421 0.1010

19 $7,802 0.1541 0.0697 1.723 0.72317 0.0868

20 $8,192 0.1402 0.0558 1.988 0.66689 0.0780

Continuing

Value

21 $8,192 0.1229 0.0385

0.0385/(0.0844) = 0.4562 2.267 0.66689 0.6897

Factor for Common Shareholders’ Equity on January 1, Year 13 …….. 1.0000

Value to Book Ratio …………………………………………………………………… 2.2056

Half-Year Adjustment: 2.2056 × [1 + (0.0844/2)] ………………………….. 2.2987

Value of Common Shareholders’ Equity: $29,394 × 2.2987 …………… $67,568

Chapter 12

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in whole or in part.

2. 5% growth after Year 20

Compre- Cum. Present Value/

hensive Implied Residual Share. Eq. Value Book

Year Income ROCE ROCE Growth Factor Ratio

16 $6,740 0.2293 0.1449 1.000 0.92217 0.1336

17 $7,077 0.1959 0.1115 1.229 0.85040 0.1165

18 $7,430 0.1720 0.0876 1.470 0.78421 0.1010

19 $7,802 0.1541 0.0697 1.723 0.72317 0.0868

20 $8,192 0.1402 0.0558 1.988 0.66689 0.0780

Continuing

Value

21 $8,602 0.1291 0.0447

0.0447/(0.0844 – 0.05) = 1.2994 2.267 0.66689 1.9645

Factor for Common Shareholders’ Equity on January 1, Year 13 …….. 1.0000

Value to Book Ratio …………………………………………………………………… 3.4804

Half-Year Adjustment: 3.4804 × [1 + (0.0844/2)] ………………………….. 3.6273

Value of Common Shareholders’ Equity: $29,394 × 3.6273 …………… $106,621

3. 2.5% growth after Year 20

Compre- Cum. Present Value/

hensive Implied Residual Share. Eq. Value Book

Year Income ROCE ROCE Growth Factor Ratio

16 $6,740 0.2293 0.1449 1.000 0.92217 0.1336

17 $7,077 0.1959 0.1115 1.229 0.85040 0.1165

18 $7,430 0.1720 0.0876 1.470 0.78421 0.1010

19 $7,802 0.1541 0.0697 1.723 0.72317 0.0868

20 $8,192 0.1402 0.0558 1.988 0.66689 0.0780

Continuing

Value

21 $8,397 1260 0.0416

0.0416/(0.0844 – 0.0250) = 0.7003 2.267 0.66689 1.0587

Factor for Common Shareholders’ Equity on January 1, Year 13 …….. 1.0000

Value to Book Ratio …………………………………………………………………… 2.5546

Half-Year Adjustment: 2.5746 × [1 + (0.0844/2)] ………………………….. 2.6624

Value of Common Shareholders’ Equity: $29,394 × 2.6827 …………… $78,259

D. Price-Earnings Ratio

One valuation scenario assumes no growth in earnings.

x = $6,602/0.0844

x = $78,223

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in whole or in part.

However, Exhibit 12.J projects earnings to grow at a 5.0% compound annual

rate during the next five years. Assuming that earnings will increase 5% a year

in perpetuity, the growth version of the P-E ratio yields a multiple of 30.5

[1.05/(0.0844 – 0.05)] and a purchase price of $201,361 million ($6,602 ×

30.5). Employing a more conservative growth rate of 2.5% yields a multiple of

17.3 [1.025/(0.0844 – 0.025)] and a purchase price of $114,215 ($6,602 × 17.3).

After the half-year adjustment, these values are as follows:

Zero Growth: $78,223 × [1 + (0.0844/2)] ……………… $ 81,524

5% Growth: $201,361 × [1 + (0.0844/2)] ……………… $209,858

2.5% Growth: $114,215 × [1 + (0.0844/2)] …………… $119,035

We might also use the price-earnings ratios of similar companies. The price-

earnings ratios of the four companies presented in the case are as follows:

Market Value Earnings Price-Earnings Ratio

Agee Robotics $ 6,915 $ 309 22.4

GI Handling Systems $ 20,000 $2,020 9.9

LJG Industries $102,667 $9,872 10.4

Gelas Corp. $ 41,962 $5,117 8.2

To select comparable companies, we should look to the profitability and other

characteristics of each firm.

Year 15 Data

GI Hand.

Holmes Agee Systems LJG Ind. Gelas

Sales………………………. $102,699 $4,241 $28,998 $123,034 $75,830

Net Income………………… $ 6,602 $ 309 $ 2,020 $ 9,872 $ 5,117

Assets……………….……… $ 45,513 $2,634 $15,197 $ 72,518 $41,665

Common Equity…………… $ 29,394 $1,551 $ 7,473 $ 38,939 $26,884

Market Value of Equity…… $ 46,876 $6,915 $20,000 $102,667 $41,962

Profit Margin for ROA……. 6.4% 7.3% 7.0% 8.0% 6.7%

Assets Turnover…………… 2.3 1.6 1.9 1.7 1.8

Return on Assets………….. 14.6% 11.7% 13.3% 13.6% 12.3%

Adjusted Leverage…………. 1.7 1.7 2.0 1.9 1.5

Return on Common Equity… 24.5% 19.9% 27.0% 25.4% 19.0%

Price/Earnings Ratio………. 7.1 22.4 9.9 10.4 8.2

Market-to-Book-Value

Ratio…………………… 1.6 4.5 2.7 2.6 1.6

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in whole or in part.

Based on its name and price-earnings ratio, Agee Robotics appears to be more

technology oriented than Holmes. The other three firms represent a better match

with respect to Holmes’ industry involvements. Holmes is similar in size to

Gelas. Holmes is most similar to LJG Industries in terms of profitability. After

the LBO, however, Holmes will have considerably more debt than Gelas and

LJG Industries. Thus, a price-earnings ratio less than 8–10 seems appropriate.

Applying various price-earnings multiples in the range for these two companies

to Holmes’ Year 15 earnings yields the following market values:

Earnings Multiple Market Value

$6,602 10.4 $68,661

$6,602 9.9 $65,360

$6,602 8.2 $54,136

This approach yields purchase prices in the $54 million to $69 million range.

E. Price-to-Book-Value Ratio

The residual ROCE valuation model in Part C above gives the values based on

the theoretical value-to-book-value ratio.

An alternative approach is to use the price-to-book-value ratios of comparable

companies. The price-to-book-value ratios of the four companies presented in

the case are as follows:

Market-to-

Company Market Value Book Value Book Ratio

Agee Robotics $ 6,915 $ 1,551 4.46

GI Handling Systems $ 20,000 $ 7,473 2.68

LJG Industries $102,667 $38,939 2.64

Gelas Corp. $ 41,962 $26,884 1.56

The relatively large price-to-book-value ratio of Agee Robotics reflects its

technology emphasis and probably more rapid growth. As discussed above,

Holmes is most similar to LJG Industries and Gelas with respect to profitability

and size. Applying a multiple of 2.64 to Holmes yields a market value of

$77,600 million ($29,394 × 2.64). Applying a multiple of 1.56 to Holmes yields

a market value of $45,855 ($29,394 × 1.56). The lower market value based on

Gelas’ market-to-book-value ratio reflects the weaker profitability and lower

risk of Gelas. Thus, LJG might be a better comparable firm in this case.

Applying a multiple of 2.64 implies that LJG Industries and Holmes will have

similar risk after the LBO. The faster total assets turnover of Holmes suggests

that it has less operating leverage risk than LJG Industries. However, Holmes

will have substantially more financial leverage risk than LJG Industries after the

LBO. Some reduction in the price-to-book-value ratio seems appropriate to

compensate for this additional risk.

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in whole or in part.

F. Summary of Valuations

Following are the valuations derived from various methods and sets of

assumptions (dollar amounts in millions):

Valuation Method Assumptions

$ 67,462 Present value of cash flows No growth after five years

$106,477 Present value of cash flows 5% growth forever

$ 78,759 Present value of cash flows 5% growth for five years

and then 2.5% growth

$ 67,461 Residual income No growth after five years

$106,463 Residual income 5% growth forever

$ 78,760 Residual income 5% growth for five years

and then 2.5% growth

$ 67,568 Residual ROCE No growth after five years

$106,621 Residual ROCE 5% growth forever

$ 78,855 Residual ROCE 5% growth for five years

and then 2.5% growth

$ 81,524 Price-earnings multiple No growth

$209,858 Price-earnings multiple 5% growth forever

$119,034 Price-earnings multiple 2.5% growth forever

$ 54,136 to

$ 68,661 Price-earnings multiple Comparable company

$ 45,855 to

$ 77,600 Market-to-book-value multiple Comparable company

The no-growth scenarios yield values in the $67–$81 million range. The 2.5%

growth scenarios yield values in the $79–$117 million range. The 5.0% growth

scenarios yield values in the $106–$206 million range. The need to manage cash

flow carefully after the LBO might result in some constraint on growth. We will

assume a purchase price of $80 million.

VI. Will the LBO Work at an $80 Million Purchase Price?

A. Inserting an $80 million purchase price into the balance sheet spreadsheet and

observing the effect on cash flows shows that Holmes will have virtually no

cash at the end of Year 17 and will have insufficient cash to service the debt in

Year 19 and Year 20. Exhibit 12.M shows the net cash required to service the

debt. The cash shortfall is summarized as follows:

Net Cash Flow: Year 16 Year 17 Year 18 Year 19 Year 20

Free Cash Flow Available

to Service Debt ……………… $8.6 $5.9 $6.2 $ 6.5 $6.9

Cash Flow to Service Debt .. (9.1) (9.3) (9.5) (9.7) (10.0)

Change in Cash ……………….. (0.5) (3.4) (3.3) (3.2) (3.1)

Cash, Beginning of Year …… 3.9 3.4 0.0 (3.3) (6.5)

Cash, End of Year ……………. $3.4 $0.0 $(3.3) $ (6.5) $(9.6)

Chapter 12

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12-55

in whole or in part.

Exhibit 12.M

Debt Service Requirements to Finance $80 Million Purchase Price

Projected

Year 16 Year 17 Year 18 Year 19 Year 20

Term Debt (0.50): $40 Million .. $ 7,683 $ 7,683 $ 7,683 $ 7,683 $ 7,683

Subordinated Debt (0.25):

$20 million ……………………… 3,540 3,540 3,540 3,540 3,540

Debt Service …………………………. $ 11,223 $ 11,223 $ 11,223 $ 11,223 $ 11,223

Interest on Debt:

Term Debt ………………………. $ 3,200 $ 2,841 $ 2,454 $ 2,036 $ 1,584

Subordinated Debt …………… 2,400 2,263 2,110 1,938 1,746

Total ………………………………. $ 5,600 $ 5,104 $ 4,564 $ 3,974 $ 3,330

Tax Rate …………………………. 0.375 0.375 0.375 0.375 0.375

Tax Savings ………………………….. $ 2,100 $ 1,914 $ 1,712 $ 1,490 $ 1,249

Net Cash Flow for

Debt Service ……………………. $ 9,123 $ 9,309 $ 9,511 $ 9,733 $ 9,974

Chapter 12

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12-56

in whole or in part.

B. Among the alternatives the acquirer might pursue to deal with the cash flow

shortage are the following:

1. Attempt to negotiate a lower purchase price.

2. Arrange for a balloon payment on the term loan or subordinated debt five

years or so after the purchase date so as to generate positive cash flow

during the next several years.

3. Issue zero coupon debt that does not require an annual cash payment for

interest.

4. Sell off fixed assets or other assets to generate cash flow.

Note that the projections of cash flow already assume that Holmes will

eliminate its dividend to conserve cash.