Valuation for acquisitions and mergers

FM taught you to value a share from its assets, earnings, dividends and free cash flows. AFM asks a harder question: what is the target worth to this particular bidder, once the two businesses are combined and the group's risk has changed? That question is the heart of area C and a natural subject for the Section A case study: a valuation, often of the combined company, followed by a discussion of the assumptions and a recommendation on the price to offer. This lesson assumes the FM methods (see the HPS FM notes on models for valuing shares) and the free cash flow technique in lesson B4, and concentrates on what is new: estimating growth, the three families of model in an acquisition, the effect of the deal on risk, and the illusion of value created by changing P/E ratios.

Which value are you looking for?

An acquisition involves several values, and you must know which one a requirement asks for.

The negotiating range lies between the standalone value and the value to the bidder; the price agreed decides how the synergies are shared. An unquoted target has no market price, so every value comes from a model, and a discount is normally made for the lack of marketability of its shares when it is compared with quoted companies.

Estimating growth

Every earnings and cash flow model needs a growth rate, and the study guide asks for near-term and continuing growth from internal and external measures.

Valuations are usually two-stage: a near-term period of higher growth, forecast year by year while a product is rolled out or synergies are realised, then a continuing (terminal) rate the business can sustain indefinitely.

For example, a company with a cost of equity of 10% has just paid a dividend of $0.20 and its share price is $4.20 ex dividend (illustrative figures). Market-implied growth = (4.20 × 0.10 − 0.20) ÷ (4.20 + 0.20) = 0.22 ÷ 4.40 = 5.0%. If it retains 40% of earnings and earns 12.5% on reinvested funds, internal growth is 0.40 × 12.5% = 5.0% too, so the market's view and the company's investment plans agree. Check: 0.20 × 1.05 ÷ (0.10 − 0.05) = $4.20.

Book value-plus models

Net asset value understates a profitable going concern because it leaves out the intangibles that earn the profits (FM). A book value-plus model starts from the net assets, restated to fair value where possible, and adds a value for those intangibles. One method is the calculated intangible value (CIV):

1. Find the return a typical company in the industry would earn on the target's tangible assets: industry return on tangible assets × the target's tangible assets.
2. Deduct it from the target's average pre-tax profit to find the excess return.
3. Take the excess return after tax, treat it as a perpetuity and divide by the cost of capital.

For example, a target has average pre-tax profit of $30 million and tangible net assets of $150 million; the industry earns 12% on tangible assets; tax is 25% and the cost of capital 10% (illustrative). Excess return = $30 million − 12% × $150 million = $12 million; after tax, $9 million; CIV = $9 million ÷ 0.10 = $90 million. The book value-plus value is $150 million + $90 million = $240 million.

These models suit asset-heavy businesses and give a floor for negotiation, but the CIV assumes the excess return lasts for ever and relies on an industry average that may not fit the target.

Market-based models

• P/E ratio: value = maintainable earnings × a suitable P/E. In an acquisition, decide whose P/E applies: the target's own, a sector average, or one adjusted for the growth and risk expected after the deal. Applying the bidder's higher P/E to the target's earnings assumes the bidder can make those earnings as valuable as its own; justify it, never assume it (see bootstrapping below).
• Enterprise value multiples: enterprise value (equity plus net debt) = EBITDA or revenue × a multiple from comparable companies or recent transactions. Useful where gearing differs, or, with revenue, where the target has no profits yet.
• Market to book and Tobin's q: market value compared with the book value, or the replacement cost, of the assets, to compare the target with similar companies.

Market models are quick and reflect current sentiment, but no two companies share the same growth, risk and accounting policies, and transaction multiples include the control premiums paid in other deals.

Cash flow models

A bidder buying control gains all the target's cash flows, so a cash flow model is usually the most complete. Free cash flow to the firm, discounted at the weighted average cost of capital (WACC), values the whole business, from which debt is deducted to value the equity; free cash flow to equity, discounted at the cost of equity, values the equity directly (lesson B4). The dividend valuation model suits a minority stake, not control.

The new step in an acquisition is the discount rate. If the deal changes the bidder's risk, its existing cost of capital no longer applies.

Changes in business and financial risk

Acquisitions are classified by their effect on the bidder's risk.

The Type III procedure uses the asset beta formula on the formulae sheet. With debt assumed risk-free (a debt beta of zero) it reduces to these steps:

The combined asset beta captures the new mix of businesses; regearing adds the financial risk of the new capital structure.

Worked example

Part 1 values a Type III acquisition with free cash flows; Part 2 shows the bootstrapping effect. All figures and rates are illustrative.

Part 1. Ikeja Logistics Inc, a quoted road haulier, plans to acquire Maitama Cold Chain Co, a quoted operator of refrigerated warehouses, a riskier business.

Ikeja will pay $390 million in cash for Maitama's equity, a 30% premium, borrowing all of it, and will take over Maitama's debt. Afterwards the combined company's gearing is expected to be 40% debt and 60% equity by market value, with a pre-tax cost of debt of 7.5%. The risk-free rate is 5%, the market return 11% and tax 25%; debt is risk-free. Free cash flows of the combined company, including synergies, are forecast at $146 million, $156 million and $166 million for years 1 to 3, then growing at 3% a year for ever.

Step 1: ungear. Ikeja: 1.00 × 1,200 ÷ (1,200 + 400 × 0.75) = 1,200 ÷ 1,500 = 0.80. Maitama: 1.50 × 300 ÷ (300 + 100 × 0.75) = 450 ÷ 375 = 1.20.

Step 2: combine. The businesses are worth $1,600 million and $400 million (equity plus debt). Combined asset beta = (0.80 × 1,600 + 1.20 × 400) ÷ 2,000 = (1,280 + 480) ÷ 2,000 = 0.88. Both companies have the same gearing, so weighting by equity values (1,200 and 300) gives the same answer.

Step 3: regear for 40% debt and 60% equity: βe = 0.88 × (60 + 40 × 0.75) ÷ 60 = 0.88 × 90 ÷ 60 = 1.32.

Step 4: cost of equity. ke = 5% + 1.32 × (11% − 5%) = 5% + 7.92% = 12.92%.

Step 5: WACC. After-tax cost of debt = 7.5% × 0.75 = 5.625%. WACC = 0.60 × 12.92% + 0.40 × 5.625% = 7.752% + 2.250% = 10.0%.

Step 6: value the combined company. Terminal value at the end of year 3 = 166 × 1.03 ÷ (0.10 − 0.03) = 170.98 ÷ 0.07 = $2,442.6 million.

Value of the combined company = 132.7 + 128.9 + 1,959.0 = $2,220.6 million.

Step 7: the gain to Ikeja's shareholders.

Two checks. The gearing assumption holds: debt of $890 million is 890 ÷ 2,220.6 = 40.1% of the combined value. And the gain reconciles: the combined company is worth $220.6 million more than the two businesses before ($2,000 million); Ikeja pays $390 million − $300 million = $90 million of that to Maitama's shareholders as a premium and keeps $130.6 million, about $0.33 on each of its 400 million shares.

Comment for the board. The deal appears to create value, but treat the result with care. The terminal value contributes 2,442.6 × 0.751 = $1,834.4 million, 83% of the total, so the answer rests on 3% growth for ever. At 2% continuing growth the terminal value is 166 × 1.02 ÷ 0.08 = $2,116.5 million, the combined company is worth $1,975.7 million and Ikeja's shareholders lose $114.3 million instead. Discounting Maitama's riskier cash flows at Ikeja's existing, lower cost of capital would have overstated the value further. The board should test the synergies built into the forecasts, and the growth assumption, before committing to a 30% premium.

Part 2: bootstrapping. Pategi Foods Inc has earnings of $60 million and 100 million shares, and trades on a P/E of 15: $9.00 a share, $900 million in total. Quatro Mills Co has earnings of $20 million and 40 million shares and trades on a P/E of 8: $4.00 a share, $160 million in total. Pategi offers 1 new share for every 2 Quatro shares, worth $4.50 a Quatro share, a premium of 12.5%. There are no synergies.

Pategi's earnings per share rise by 11% only because it has bought earnings at a P/E of 8 while the market values its own at 15. If the market applied Pategi's P/E to the combined earnings, $140 million of value would appear from nothing: this is the bootstrapping (or P/E) effect. Without synergies or better management of Quatro's assets, a rational market will value the group at about $1,060 million, a P/E of 13.25. Pategi's share price then falls to $1,060 million ÷ 120 million = $8.833, and its shareholders lose 100 million × ($9.00 − $8.833) = $16.7 million, which is exactly what Quatro's shareholders gain (20 million × $8.833 = $176.7 million, against $160 million): the premium has been paid with nothing to fund it. A rise in earnings per share is not a gain in value.

High-growth start-ups and loss-making companies

These are hard to value because today's earnings and cash flows are negative or meaningless and most of the value lies far in the future. The procedure is:

1. Understand the business model and market: how large the market could be, the share the company could win, and what drives revenue (customers, users, contracts).
2. Forecast to a steady state: model revenue growth, margins and the investment needed year by year until the business matures, which may take ten years or more, then apply a terminal value.
3. Allow for failure: use probability-weighted scenarios (success, moderate, failure) rather than a single forecast at a very high discount rate.
4. Cross-check with market evidence: revenue or other multiples from comparable companies, recent funding rounds and acquisitions.
5. Value the options: the right to expand, delay or abandon may be a large part of the value (lesson B2).

For a loss-making company, first ask why it makes losses. A sound business that is temporarily loss-making can be valued on the cash flows of a turnaround plan, including restructuring costs; one with no prospect of recovery is worth its break-up value. Unused tax losses may be worth something to a profitable bidder if the tax rules allow them to be used after a change of ownership.

Common mistakes

• Using the bidder's existing WACC for a target with different business risk, or for a deal that changes gearing.
• Putting a combined asset beta straight into CAPM without regearing, which gives the cost of equity of an ungeared company.
• Deducting only the bidder's original debt from the combined value, not the target's debt and the new borrowing.
• Applying the bidder's P/E to the combined earnings without justification, and calling the rise in EPS value creation.
• Discounting a terminal value at the end of year n with the year n + 1 factor, or using a continuing growth rate above long-term economic growth.
• Presenting one value without saying how sensitive it is to growth and synergies.

Exam technique

Before calculating, decide which value the requirement wants (the target alone, the target to the bidder, or the combined company) and say whether the deal is Type I, II or III, because that decides the discount rate. Number the beta steps, state each formula and show your weights. Value the combined company in one table with the terminal value on its own line, then bridge from the combined value to the gain for the bidder's shareholders. Finish with a sensitivity to growth or synergies and a recommendation on the maximum price: that is where the scepticism and commercial acumen marks are.

Study with AI

I am studying ACCA Advanced Financial Management (AFM), valuation for acquisitions
and mergers (sub-area C2). Give me a scenario in which a quoted company acquires a
company in a different industry for cash financed by debt, with both companies'
equity betas and gearing, the expected gearing afterwards, CAPM data and three
years of combined free cash flows. Ask me to find the combined WACC by ungearing and
regearing betas, then value the combined company and the gain to the bidder's
shareholders. Wait for my answer, then mark it step by step.

AI assistants can make arithmetic mistakes and can misstate the rules: check every answer against these notes before you rely on it.

Lecturer's note: Ask one question of every acquisition valuation: whose risk is being discounted? The cash flows belong to a new company that did not exist before, with a new mix of businesses and a new level of debt, so its cost of capital must be built from scratch: ungear to strip out each company's old financing, combine to get the new business risk, and regear for the new financing. A student who uses the bidder's existing WACC is valuing a company that will no longer exist.

Key points

• Distinguish the target's undisturbed value, its standalone value, its value to the bidder and the combined company's value; the price agreed decides how synergies are shared.
• Estimate near-term growth from the plan and continuing growth from internal (history, g = b × re) and external (market-implied, industry, economy) measures, never above the economy's long-term growth.
• Book value-plus models add intangibles, for example by the calculated intangible value; market models apply P/E or enterprise value multiples; cash flow models discount free cash flows.
• In a Type III acquisition, ungear both betas, combine the asset betas by value, regear for the new gearing and rebuild the WACC.
• Bootstrapping raises EPS when a high-P/E bidder buys a low-P/E target with shares, but creates no value without real synergies.
• Value start-ups with long forecasts to a steady state, probability-weighted scenarios, market cross-checks and real options; value loss-makers on a credible turnaround plan or their break-up value.

Quick check

1. A company has an equity beta of 1.40, equity worth $500 million and debt worth $200 million. Tax is 25% and debt is risk-free. What is its asset beta? (Figures are illustrative.)
2. A share trades at $3.15 ex dividend, the dividend just paid was $0.15 and the cost of equity is 12%. What growth rate does the market expect? (Illustrative rates.)
3. Company X (P/E 20, earnings $10 million) acquires company Y (P/E 10, earnings $5 million) for shares, with no premium and no synergies. If the market values the combined company correctly, what is its P/E?

Answers

1. βa = 1.40 × 500 ÷ (500 + 200 × 0.75) = 700 ÷ 650 = 1.08.
2. g = (3.15 × 0.12 − 0.15) ÷ (3.15 + 0.15) = (0.378 − 0.15) ÷ 3.30 = 0.228 ÷ 3.30 = 6.9%.
3. X is worth $10 million × 20 = $200 million and Y $5 million × 10 = $50 million. The combined $250 million ÷ combined earnings of $15 million gives a P/E of 16.7.