How to calculate the IRR – a manual

How to calculate the IRR – a manual. Harvard Business Case: “Butler Capital Partners and Autodistribution:

Putting Private Equity to work in France”

PE & VC SeminarSummer Term 09

Prof. Dr. Ted AzarmiPractical Tool

Christine Scheef

1PE & VC Seminar – Christine Scheef

Introduction

• Harvard Business Case: “Butler Capital Partners and Autodistribution: Putting Private Equity to work in France”

• Analysis based on several assumption• Autodistribution able to realize its expansion strategy• Accurate forecast of sales and acquisitions for the next seven years• Interest rates constant over time

Key question:What is the internal rate of return (IRR) for the investment in Autodistribution, a French company in the automotive parts after market???


Introduction

• Several ways to calculate the IRR:• Discounted Cash Flow Methods

• Weighted average cost of capital (WACC) method• Adjusted present value (APV) method• Total cash flow (TCF) method• Flow to Equity method

• Multiples

• Differences of DCF methods• WACC and TCF assume a constant capital structure• APV does not depend on the debt to equity ratio ratio can change over time


Agenda

1. WACC approach1.1 Revenue1.2 EBITDA1.3 EBIT1.4 Free cash flow (FCF)1.5 Weighted-average-cost-of-capital (WACC)1.6 Enterprise value1.7 Equity value1.8 Internal rate of return (IRR)

2. Multiples2.1 EV/EBIT of peer group2.2 EV/EBIT of Autodistribution acquisition

3. Conclusion


1. WACC method

• MethodExpected future cash flow is discounted by the WACC. WACC is the weighted average of cost of equity and cost of debt according to the debt-to-equity ratio.

• Enterprise value (growing perpetuity)

• Assumption• Debt-to-equity ratio constant over time• Growth rate appropriately estimated by investor

• Pros• Precise calculation

• Cons• A lot of data input needed• Result depends heavily on the accuracy of the estimation


1.1 Revenue

Given for the calculation• Organic sales growth and sales from acquisitions• Sales in 1998 are 5,400m FFr.

see historical financial information (total net turnover in 1998)

Formulas

Revenue is the income that a company receives from its normal business activities, usually from the sale of goods and services to customers.

Revenuet = salest + sales from acquisitionst

Salest = salest-1 * (1+ growth ratet )


1.1 Revenue

Example for 1999• Sales = 5,400m * (1 + 0.02) = 5,509m• Revenue = 5,509m + 378m = 5,887m

(in Thousand of FFr) 1998 1999 2000 2001 2002 2003 2004 2005 2006

Organic sales growth 2.0% 3.9% 3.7% 3.5% 3.0% 2.5% 2.5% 2.5%

Sales 5,400,532 5,508,543 6,116,593 6,946,863 7,889,805 8,911,560 9,932,250 11,074,100 12,070,400

Sales from acquisitions 378,457 582,407 676,137 762,195 778,440 871,750 701,900 706,600

Sum revenue 5,887,000 6,699,000 7,623,000 8,652,000 9,690,000 10,804,000 11,776,000 12,777,000


1.2 EBITDA

Formula

Given for the calculation• EBITDA as a percentage of the revenue

Example for 1999• EBITDA value = 5,887m * 0.075 = 441,525

EBITDA – Earnings before interest, taxes, depreciation and amortization Measures cash earning without accrual accounting, canceling tax effects and effects of different capital structures.

EBITDA valuet = revenuet * EBITDA ratet

(in Thousand of FFr) 1998 1999 2000 2001 2002 2003 2004 2005 2006

Sum revenue 5,887,000 6,699,000 7,623,000 8,652,000 9,690,000 10,804,000 11,776,000 12,777,000

EBITDA 7.500% 7.750% 7.975% 8.225% 8.625% 8.700% 8.825% 8.925%

EBITDA value 441,525 519,172 607,934 711,627 835,762 939,948 1,039,232 1,140,347


1.3 EBIT

• Implication for Private Equity firms: The PE firm evaluates a change in the capital structure of the target company (through a leveraged-buyout). The PE firm first evaluates the EBIT of the target company and then, determines the optimal use of debt and equity.

Formula

EBIT – Earnings before interest and taxesMeasure of company’s fundamental earnings potential

Operating revenue– Operating expenses – cost of goods sold – administrative expenses – depreciation and amortization – extraordinary expenses= EBIT

EBITDA– depreciation and amortization– extraordinary expenses= EBIT


1.3 EBIT

Given for the calculation• Depreciation rate as a percentage of revenue• Extraordinary expenses

Example for 1999• Depreciation value = 5,887,000 * 0.012 = 70,644

• EBIT = 441,525 – 70,644 – 5,000 = 365,881

Depreciation valuet = revenuet * depreciation ratet

1998 1999 2000 2001 2002 2003 2004 2005 2006

Summe revenues 5,887,000 6,699,000 7,623,000 8,652,000 9,690,000 10,804,000 11,776,000 12,777,000

EBITDA value 441,525 519,172 607,934 711,627 835,762 939,948 1,039,232 1,140,347

Depreciation 1,20% 1,23% 1,23% 1,23% 1,23% 1,23% 1,23% 1,23%

- Depreciation value 70,644 82,398 93,763 106,420 119,187 132,889 144,845 157,157

- Extraordinary expenses 5,000 8,000 9,000 10,000 11,000 12,000 13,000 14,000

EBIT value 365,881 428,775 505,171 595,207 705,575 795,059 881,387 969,190


1.4 Free cash flow (FCF)

Free cash flow is the cash flow available for distribution among all the security holders of a company, including debt holders and equity holders.

Net income (EBIAT)+ Depreciation– Change in net working capital– Capital expenditure– Acquisitions= Free Cash Flow

• According to the discounted cash flow method, the firm’s intrinsic value is equal to the present value of all future FCF and the proceeds from an eventual sale.

Formula

Accounting for the consumption of capital is the main differences betweennet income and FCF

• Net income uses depreciation, expenses are smoothed over maturity.• FCF uses last period’s net capital purchase.


1.4.1 EBIAT

Given for the calculation of EBIAT (Earnings before interest after taxes)• Tax rates as a percentage of EBIT value

Example for 1999• Taxes = 365,881 * 0.4 = 146,352

• EBIAT = 365,881 – 146,352 = 219,529

Taxest = EBITt * tax ratet

1998 1999 2000 2001 2002 2003 2004 2005 2006

EBIT value 365,881 428,775 505,171 595,207 705,575 795,059 881,387 969,190

Tax rates 40% 36.70% 36.70% 36.70% 36.70% 36.70% 36.70% 36.70%

- Taxes 146,352 157,360 185,398 218,441 258,946 291,787 323,469 355,693

EBIAT 219,529 271,414 319,773 376,766 446,629 503,272 557,918 613,497

EBIATt = EBITt – taxest


1.4.2 Net working capital

Formula

Assumption• NWC is relatively stable as long as the financing (current liabilities) are stable

and no investments in inventory (current assets) are made. • With these constraints, the NWC can only change by the amount of generated

revenues (current assets).

Net working capital (NWC) represents the operating liquidity available to a company. It is often measured in days and can be interpreted as the average number of days that the capital is invested in the operating cycle.

NWCt = current assetst – current liabilitiest


1.4.2 Net working capital

Given for the calculation of the change in net working capital• Net working capital in days

Example for 1999•

• Change in NWC = 887,082 – 749,927 = 137,155

Change in NWCt = NWCt-1 – NWCt

1998 1999 2000 2001 2002 2003 2004 2005 2006

NWC in days 55 55 55 55 55 55 55 55

Summe revenues 5,887,000 6,699,000 7,623,000 8,652,000 9,690,000 10,804,000 11,776,000 12,777,000

Average NWC 749,927 887,082 1,009,438 1,148,671 1,303,726 1,460,137 1,628,000 1,774,466 1,925,301

Change in NWC 137,155 122,356 139,233 155,055 156,411 167,863 146,466 150,836


1.4 Free cash flow

Further items given for the calculation of the FCF• Capital expenditure• Acquisitions multiple of the current sales from acquisitions

Example for 1999

• Acquisitions = 0.275 * 378,457 = 104,076

Net income (EBIAT) 219,529 See slide 10+ depreciation + 70,644 See slide 8– Change in NWC - 137,155 See slide 12– Capital expenditure - 60,000 Given– Acquisitions - 104,076 See below= Free cash flow - 11,058

Acquisitionst = acquisitions multiplet * sales from acquisitionst


1.4 Free cash flow

1998 1999 2000 2001 2002 2003 2004 2005 2006

EBIAT 219,529 271,414 319,773 376,766 446,629 503,272 557,918 613,497

+ Depreciation value 70,644 82,398 93,763 106,420 119,187 132,889 144,845 157,157

- Change in NWC 137,155 122,356 139,233 155,055 156,411 167,863 146,466 150,836

- Capital expenditure 60,000 68,000 77,000 88,000 99,000 110,000 121,000 132,000

Acquisition multiple 0.275x 0.275x 0.300x 0.300x 0.350x 0.350x 0.350x 0.350x

- Acquisitions 104,076 160,162 202,841 228,659 272,454 305,112.5 245,665 247,310

Free Cash Flow (FCF) -11,058 3,294 -5,538 11,473 37,951 53,186 189,632 240,509

The derived FCFs are the same for any valuation method. In the following, the discount factor, here the weighted-average-cost-of-

capital (WACC) is calculated in detail.


1.5 Weighted average cost of capital

Formula

Assumption• Capital structure remains stable over time

Autodistribution pursues an ongoing acquisition program, financed by debt assumption reasonable


Weighted average cost of capital (WACC) is a valuation method. It is the rate that a company is expected to pay on average to all its security holders. The WACC is calculated as a weighted average of each component of the capital structure and indicates whether an investment is profitable.

1.5.1 Cost of debt

Given for the calculation• BNP offer includes 3 types of loans (HBC exhibit 16)• BNP offer includes a 9.5 % warrant in the subordinated loan

for simplification, the effect of the warrant is not taken into account

Example for Tranche A: Coupon payment = 1,100 * (0.046 – 0.0025) = 47.85

Cost of debt = 111.925 / 2,050 = 5.46%


size coupon adjustment coupon adjusted term Coupon payment

Tranche A 1,100 4.60% -0.25% 4.35% 7 years 47.85

Tranche B 350 5.10% -0.25% 4.85% 8 years 16.975

Subordinated loan 600 8.10% -0.25% 7.85% 10 years 47.1

Sum 2,050 111.925

Cost of debt is composed of the different rates of interest paid. The interest rate includes the risk free rate plus a premium for the risk of default.

1.5.2 Cost of equity

Formula

Key assumptions of the CAPM (all investors are…)• Rational and risk avers• Aim to maximize economic utility• Are price takers• Have no transaction costs• Can lend and borrow unlimited at the risk free rate• Have the same information


Capital Asset Pricing Model (CAPM) is a theoretical model to determine the appropriate required rate of return of an asset. Investors require a higher return for holding a more risky asset.

Cost of equity = risk free rate + beta * equity risk premium


Given for the calculation of the equity beta of Autodistribution (AD)• Information about comparable companies (HBC exhibit 19)• Equity β of each firm has to be adjusted for differences in leverage

Example for Genuine: unleveraged β = 0.69 * 5,385 / (705 + 5,385) = 0.61


Beta measures an asset’s sensitivity to systematic risk (non-diversifiable risk). In the CAPM, the beta is the defining factor in rewarding for systematic risk.

Comparable companies Genuine AutoZone Pep Boys O'Reilly Discount Keystone Universal Part Source Partco Fine List

Net debt (D) 705 538 877 169 156 -10 21 17 55 227

Equity value (E ) 5,385 4,578 917 967 381 272 10 10 286 187

Equity β 0.69 1.05 0.68 0.78 0.62 0.66 1 -0.5 0.5 0.73

unleveraged β 0.61 0.94 0.35 0.66 0.44 0.69 0.32 -0.19 0.42 0.33

unleveraged β = equity β * equity / (debt + equity)


• Average unleveraged β of comparable firms: 0.46 used as industry average relatively low, proofs that the automotive parts after market is more likely to be a counter cycle business.

Assumption• Capital markets across industrialized countries are homogenous Comparable companies used for the calculation are from the UK and US

Equity beta of Autodistribution (AD)• Average unleveraged industry β is used• equity βAD = unleveraged industry β * (debt + equity) / equity

= 0.46 * (2,050 + 1,405) / 1,405 = 1.12



Equity risk premium• Difference between a French stock market index (e.g. CAC40) and the risk free

rate for that time (2006).• Taken from historical data, the equity risk premium is 0.075.

Risk free rate• 30-year French government bond with 4.88% • Taken from the BNP preliminary term sheet proposal (HBC exhibit 16)

CAPMCost of equity = risk free rate + beta * equity risk premium

= 0.0488 + 1.12 * 0.075= 13.31 %


1.5 Weighted average cost of capital

Given for the calculation• Initial capital structure imposed by the deal

• Debt of 2,050m FFr.• Equity of 1,405m FFr.

• Tax rate of 36.70 % (constant over time)• Cost of equity = 13.31% (see slide 20)• Cost of debt = 5.46% (see slide 16)


debt + equity = 3,455m FFr.

1.6 Enterprise value

Formula

Calculation • Assumption of a growing perpetuity from 2006 on• The terminal value varies with the assumption about the future growth rate

Example for 3% growth rate


Growth rate 3.0% 5.0% 5.5% 6.0%

WACC 7.465% 7.465% 7.465% 7.465%

Terminal Value 5,548,501 10,246,033 12,914,768 17,405,535

Enterprise value reflects the market value of the whole business. It is the sum of claims of all security holders, including debt and equity holders etc.

1.7 Equity value

Formula

Given for the calculation• Additional debt and debt imposed by the deal• 9.5% dilution because of the warrant in the subordinated loan

Example for 3% growth rate• Equity value without dilution = 5,548,501 – 910,000 – 2,050,000 = 2,588,501• Equity value = 2,588,501 * (1-0.095) = 2,342,594


Equity value is the enterprise value minus the net debt. It accounts for all the equity ownership interest in a firm including the value of unexercised stock options and securities convertible to equity.

Equity value = (enterprise value – net debt) * (1 – dilution)

1.8 Internal rate of return

Formula

Time n equal to 7 years (time 1999 – 2006)

Example for 3% growth rate


Internal rate of return (IRR) is the annualized effective compounded return rate that can be earned on the invested capital. It is a measure to compare the profitability of investments.

1.8 Internal rate of return

Growth rate 3.0% 5.0% 5.5% 6.0%

WACC 7.465% 7.465% 7.465% 7.465%

Enterprise Value 5,548,501 10,246,033 12,914,768 17,405,535

- additional debt 910,000 910,000 910,000 910,000

- deal debt 2,050,000 2,050,000 2,050,000 2,050,000

Equity value without dilution 2,588,501 7,286,033 9,954,768 14,445,535

Equity value 2,342,594 6,593,860 9,009,065 13,073,209

Investment 1,405,000 1,405,000 1,405,000 1,405,000

IRR 7.58% 24.72% 30.40% 37.53%


Final Table with the calculation of the IRR

The IRR varies strongly according to the growth rate chosen. Butler Capital Partners has to decide which growth potential they see in

Autodistribution from 2006 on.

Agenda


1. WACC approach

2. Multiples

2.1 EV/EBIT of peer group

2.2 EV/EBIT of Autodistribution acquisition

3. Conclusion

2. Multiples

• MethodFinancial ratio of the company is multiplied by an industry-specific multiple. Multiples based on the enterprise value reveal the rating of a business independently of its capital structure.

• Formula (e.g. for EBIT multiple)

• Pros• Easy calculation• Few input needed

• Cons• No precise calculation


Enterprise value (EV) = EV/EBIT multiple * EBITT

2.1 EV/EBIT of peer group

Given for the calculation• Industry specific EV/EBIT multiple: 16.6x

» Peer group consists of US and UK firms with different sizes• EBIT of Autodistribution in 2006: 969,190 FFr.

Calculation• Enterprise value = 16.6 * 969,190 = 16,088,556 FFr.


Enterprise Value 16,088,556

- additional debt 910,000

- deal debt 2,050,000

Equity value without dilution 13,128,556

Equity value 11,881,343

Investment 1,405,000

IRR 35.66%

2.2 EV/EBIT of Autodistribution acquisition

Given for the calculation• EV/EBIT multiple of the acquisition of Autodistribution in 1998

• EBIT of Autodistribution in 2006: 969,190 FFr.

Calculation• Enterprise value = 11.11 * 969,190 = 10,767,048 FFr.


Enterprise Value 10,767,048

- additional debt 910,000

- deal debt 2,050,000

Equity value without dilution 7,807,048

Equity value 7,065,378

Investment 1,405,000

IRR 25.95%

Agenda


1. WACC approach

2. Multiples

3. Conclusion

3. Conclusion

• Choice of the appropriate valuation method is important• Both methods lead to different internal rates of return (IRR)• Determination of the enterprise value is crucial

• Within each method, accurate assumptions must be made

• Difficulties• WACC: Choice of the appropriate growth rate after 2006 • Multiples: Selection of the accurate industry specific multiple


3. Conclusion


Multiples• Peer group consists of US and UK firms with different sizes.• After the expansion, AD is a large player with eventually no comparably sized

companies.

WACC method• Butlers has to assume a growth rate after 2006 of 5.5% in order to reach their goal

of an IRR of 30%. • Market will grow with 2-3% • In 2006, AD has finished its expansion strategy AD grows no longer with

purchases instead AD has to grow internally to reach the 5.5%.

Peer multiple is less accurate, acquisition multiple should be usedIRR (multiple) = 25.95%

Very ambitious goal; can only be reached with internal improvements

Documents

How to calculate the IRR – a manual