invic

Which of the following best describes projection risk in the estimation of the discount rate for private company valuations?

A) Management will always be overly optimistic to increase the acquisition price.

B) Projection risk results in higher discount rates.

C) If the availability of information from private firms is poor, the uncertainty of projected cash flows may increase.

---

Projection risk refers to the risk of misestimating future cash flows. Given the lower availability of information from private firms, the uncertainty of projected cash flows may increase.
However, management may not be experienced with projections and may underestimate or overestimate future prospects. The discount rate would then be decreased or increased accordingly. So management is not always overly optimistic and projection risk does not always result in higher discount rates.

invic

Which of the following best describes the use of size premiums when estimating the discount rate for private company valuations?

A) The treatment is similar to that for public firms.

B) When using data from comparable public firms, a distress premium may be inadvertently added in.

C) A size premium is subtracted when calculating the discount rate.

---

For private company valuations, a size premium is often added in when calculating the discount rate. This is not typically done for public firms. To get the size premium, the appraiser may use data from the smallest cap segment of public equity. This however may include a distress premium that is not applicable to the private firm.

invic

Which of the following best describes the use of size premiums when estimating the discount rate for private company valuations?

A) The treatment is similar to that for public firms.

B) When using data from comparable public firms, a distress premium may be inadvertently added in.

C) A size premium is subtracted when calculating the discount rate.

---

For private company valuations, a size premium is often added in when calculating the discount rate. This is not typically done for public firms. To get the size premium, the appraiser may use data from the smallest cap segment of public equity. This however may include a distress premium that is not applicable to the private firm.

invic

Using the following figures, calculate the value of the firm using the excess earnings method (EEM).

Working capital	$600,000
Fixed assets	$2,300,000
Normalized earnings	$340,000
Required return for working capital	5%
Required return for fixed assets	13%
Growth rate of residual income	4%
Discount rate for intangible assets	18%

A) $2,981,714.

B) $2,978,571.

C) $3,027,111.

---

The answer is calculated using the following steps.
Step 1: Calculate the required return for working capital and fixed assets.
Given the required returns in percent, the monetary returns are:
Working Capital: $600,000 × 5% = $30,000.
Fixed Assets: $2,300,000 × 13% = $299,000.
Step 2: Calculate the residual income.
After the monetary returns to assets are calculated, the residual income is that which is left over in the normalized earnings:
Residual Income = $340,000 − $30,000 − $299,000 = $11,000.
Step 3: Value the intangible assets.
Using the formula for a growing perpetuity, the discount rate for intangible assets, and the growth rate for residual income:
Value of Intangible Assets = ($11,000 × 1.04) / (0.18 − 0.04) = $81,714.
Step 4: Sum the asset values to arrive at the total firm value.
Firm Value = $600,000 + $2,300,000 + $81,714 = $2,981,714.

invic

Using the following figures, calculate the value of the equity using the capitalized cash flow method (CCM), assuming the firm will be acquired.

Normalized FCFE in current year	$3,000,000
Reported FCFE in current year	$2,400,000
Growth rate of FCFE	7.0%
Equity discount rate	16.0%
WACC	13.0%
Risk-free rate	3.5%
Cost of debt	10.5%
Market value of debt	$3,000,000

The value of the equity is:

A) $28,533,333.

B) $32,666,667.

C) $35,666,667.

---

To arrive at the value of the equity using the CCM, it can be estimated using the free cash flows to equity and the required return on equity (r):

Note that we grow the FCFE at the growth rate because the current year FCFE is provided in the problem (not next year’s FCFE). We use normalized earnings, not reported earnings, given that normalized earnings are most relevant for the acquirers of the firm. The relevant required return for FCFE is the equity discount rate, not the WACC.
An alternative approach to calculate the value of the equity would be to subtract the market value of the firm’s debt from total firm value. However, the FCFF are not provided so a total firm value cannot be calculated.

invic

The capitalized cash flow method (CCM) used in private firm valuation is most appropriate when:

A) there are many intangible assets to value.

B) stable growth is expected.

C) earnings are growing quickly in an initial period.

---

The CCM is a growing perpetuity model that assumes stable growth and is in effect a single-stage free cash flow model. It may be suitable when no comparables or projections are available and when stable growth is expected. The excess earnings method (EEM) is useful when there are intangible assets to value. The free cash flow method assumes high growth in an initial period followed by constant growth thereafter.

invic

Which of the following best describes the use of FCFF and FCFE when used in private firm valuation?

A) FCFE is usually favored if the firm is going to change its capital structure because the equityholders are usually the investors requesting the valuation.

B) FCFF is usually favored if the firm is going to change its capital structure because the WACC is less sensitive to leverage changes than the cost of equity.

C) FCFE is usually favored if the firm is going to change its capital structure because the cost of equity is less sensitive to leverage changes than the WACC.

---

Free cash flow to the firm (FCFF) can be used to value the firm as a whole and free cash flow to equity (FCFE) can be used for equity. FCFF is usually favored if the firm is going to significantly change its capital structure. The reason is that the discount rate used for FCFF valuation, the weighted average cost of capital (WACC), is less sensitive to leverage changes than the discount rate used for FCFE valuation, the cost of equity. Thus, the FCFF valuation will not vary as much as the FCFE valuation.

invic

Given the following figures, calculate the FCFF. Assume the earnings and expenses are normalized and that capital expenditures will cover depreciation plus 3 percent of the firm’s incremental revenues.

Current Revenues	$30,000,000
Revenue growth	6%
Gross profit margin	20%
Depreciation expense as a percent of sales	1%
Working capital as a percent of sales	15%
SG&A expenses	$3,800,000
Tax rate	30%

A) $927,400.

B) $1,785,400.

C) $1,245,400.

---

Pro forma Income Statement
Revenues	$31,800,000
Cost of Goods Sold	$25,440,000
Gross Profit	$6,360,000
SG&A Expenses	$3,800,000
Pro forma EBITDA	$2,560,000
Depreciation and amortization	$318,000
Pro forma EBIT	$2,242,000
Pro forma taxes on EBIT	$672,600
Operating income after tax	$1,569,400
Adjustments to obtain FCFF
Plus: Depreciation and amortization	$318,000
Minus: Capital expenditures	$372,000
Minus: Increase in working capital	$270,000
FCFF	$1,245,400

Pro forma Income Statement	Explanation
Revenues	Current revenues times the growth rate: $30,000,000 × (1.06)
Cost of Goods Sold	Revenues times one minus the gross profit margin: $31,800,000 × (1 − 0.20)
Gross Profit	Revenues times the gross profit margin: $31,800,000 × 0.20
SG&A Expenses	Given in the question
Pro forma EBITDA	Gross Profit minus SG&A expenses: $6,360,000 − $3,800,000
Depreciation and amortization	Revenues times the given depreciation expense: $31,800,000 × 0.01
Pro forma EBIT	EBITDA minus depreciation and amortization: $2,560,000 − $318,000
Pro forma taxes on EBIT	EBIT times tax rate: $2,242,000 × 0.30
Operating income after tax	EBIT minus taxes: $2,242,000 − $672,600
Adjustments to obtain FCFF
Plus: Depreciation and amort.	Add back noncash charges from above
Minus: Capital expenditures	Expenditures cover depreciation and increase with revenues: $318,000 + (0.03 × $31,800,000 − $30,000,000)
Minus: Increase in working capital	The working capital will increase as revenues increase: (0.15 × $31,800,000 − $30,000,000)
FCFF	Operating income net of the adjustments above

invic

Given the following figures, calculate the normalized EBITDA for a financial and strategic buyer.

Reported EBITDA	$4,500,000
Current Executive Compensation	$700,000
Market-Based Executive Compensation	$620,000
Current SG&A expenses	$6,300,000
SG&A expenses after synergistic savings	$5,600,000
Current Lease Rate	$300,000
Market-Based Lease Rate	$390,000

The normalized EBITDA for each type of buyer is:

Financial Buyer

Strategic Buyer

A) $4,190,000 $4,890,000

B) $4,670,000 $5,370,000

C) $4,490,000 $5,190,000

---

Both strategic and financial buyers will attempt to reduce executive compensation to market levels by $80,000 ($700,000 − $620,000). They will also have to pay a higher lease rate of $90,000 ($390,000 − $300,000). So the adjustment for both buyers to generate normalized EBITDA is $4,500,000 + $80,000 − $90,000 = $4,490,000.
However, only a strategic buyer will be able to realize synergistic savings of $700,000 ($6,300,000 − $5,600,000). So normalized EBITDA for a strategic buyer is $5,190,000 and for a financial buyer it is $4,490,000.

invic

An analyst values a private company using a price multiple based on recent sales of comparable assets. This approach to private company valuation is best described as the:

A) income approach

B) asset-based approach

C) market approach

---

Under the market approach, a firm is valued using price multiples based on recent sales of comparable assets. Under the income approach, a firm is valued according to the present value of its expected future income. Under the asset-based approach, the value of a firm is calculated as the firm’s assets minus its liabilities. (Study Session 12, LOS 43.d)