Week 5: Cost of Capital and Raising Capital (Ch. 13, 14)

Until now the discount rate or required return was simply given. This week shows where it comes from. If a company needs money to invest, it can use debt or equity. Debt has direct costs (interest); equity has indirect costs (the return investors require to provide equity). The combination is the firm's cost of capital, usually measured as the weighted average cost of capital (WACC). Chapter 14 then describes how firms actually raise capital: venture capital and private equity, IPOs, seasoned offerings, underwriting, underpricing, the costs of issuing and rights issues.

Required return versus cost of capital

(Book) The required return on an investment, the appropriate discount rate and the cost of capital are the same thing seen from different sides: the return investors require on the firm's securities is the cost to the firm of raising that capital. A project should earn at least what investors could earn in the financial markets on investments of similar risk.

Cost of equity: the dividend growth model approach

Example (Alpha): last dividend €2, growth 8% indefinitely, share price €30. D1 = 2 x 1.08 = €2.16; RE = 2.16/30 + 0.08 = 15.2%. Tutorial (Down and Out NV): dividend just paid €2.40, growth 5.5%, price €52: RE = 2.4 x 1.055/52 + 0.055 = 10.37%.

(Book) Advantages: simple to use and understand. Disadvantages: it only applies to firms that pay (steadily growing) dividends; the estimate is very sensitive to the growth rate (which must be estimated from historical growth or analyst forecasts); and it does not explicitly consider risk.

Cost of equity: the security market line (CAPM) approach

To estimate the cost of equity with the SML you need three things: the risk-free rate Rf, the market risk premium E(RM) - Rf and the company's beta (its systematic risk; see week 6).

Example (Alpha Air Freight): beta 1.2, market risk premium 7%, risk-free rate 6%: RE = 6% + 1.2 x 7% = 14.4%. Tutorial (Landsväg AG): beta 0.85, market risk premium 8%, T-bills 5%: RE = 0.05 + 0.85 x 0.08 = 11.8%. With the dividend growth model (last dividend Skr1.60, growth 6%, price Skr37): RE = 1.60 x 1.06/37 + 0.06 = 10.58%. When two methods give different estimates, a reasonable best estimate is their average: (11.8% + 10.58%)/2 = 11.19%.

(Book) Advantages of the SML approach: it explicitly adjusts for risk and can be used for firms without steady dividend growth. Disadvantages: both the market risk premium and beta must be estimated, and estimates based on the past may not reflect the future.

Cost of debt and cost of preference shares

Tutorial (Filer Manufacturing): two bond issues: face value £70m at 93% of par with YTM 7.68%, and £55m at 104% of par with YTM 7.17%. Market values: 0.93 x 70 = £65.1m and 1.04 x 55 = £57.2m, total MV_D = £122.3m. Weights 0.5323 and 0.4677. After-tax cost of debt (tax 28%): RD(1 - T) = (1 - 0.28) x (0.5323 x 7.68% + 0.4677 x 7.17%) = 5.36%.

Weighted average cost of capital (WACC)

To compute the WACC you need the cost of equity, the after-tax cost of debt and the capital structure (weights).

• Amount of equity E: number of shares outstanding x share price (market value).
• Amount of debt D: market price of a single bond x number of bonds outstanding (market value).
• V = E + D is the combined market value; E/V + D/V = 100%. These percentages are the capital structure weights and can be read like portfolio weights. Market values are used, not book values.

Example: debt-equity ratio 0.5, cost of equity 29.2%, cost of debt 10%, tax 28%. D/E = 0.5 means E/V = 1/1.5 = 2/3 and D/V = 1/3. WACC = 2/3 x 29.2% + 1/3 x 10% x (1 - 0.28) = 21.87%.

Example (Catty Style): 1.4 million shares at €20; risk-free rate 8%, market risk premium 7%, beta 0.74. Debt: total face value €5 million quoted at 93% of face value, priced to yield 11%. Tax 34%.

• E = 1.4m x €20 = €28m; D = 0.93 x €5m = €4.65m; V = €32.65m.
• E/V = 28/32.65 = 85.76%; D/V = 14.24%.
• RE (SML) = 8% + 0.74 x 7% = 13.18%. RD = YTM = 11%.
• WACC = 0.8576 x 13.18% + 0.1424 x 11% x (1 - 0.34) = 12.34%.

Tutorial (Sixx AM): target D/E 0.65, RE 15%, RD 9%, tax 35%. D/V = 0.65/1.65 = 0.3939 and E/V = 1/1.65 = 0.6061. WACC = 0.6061 x 15% + 0.3939 x 9% x 0.65 = 11.40%. Tutorial (Filer): E = 11m x £68 = £748m; D = £122.3m; V = £870.3m; E/V = 0.8595 and D/V = 0.1405. RE = 4.1 x 1.06/68 + 0.06 = 12.39%. WACC = 0.8595 x 12.39% + 0.1405 x 5.36% = 11.40%. Tutorial (Mullineaux): 60% equity, 5% preference shares (RP 6%), 35% debt (RD 8%), tax 28%, WACC 10.72%. Solving 10.72% = 0.60RE + 0.05 x 6% + 0.35 x 8% x 0.72 gives RE = 14.0%. Note: only the costs of debt and equity (and preference shares) enter the WACC, not the costs of other inputs such as leased bikes or raw materials.

(Book) The WACC can also be used for performance evaluation: economic value added (EVA) compares a firm's operating profit with the charge for the capital employed (capital x WACC).

Divisional and project costs of capital

Many project cash flows have risks distinctly different from those of the overall firm. If a firm uses its single WACC for all accept-reject decisions, it will tend to incorrectly accept risky projects and incorrectly reject less risky projects. In the SML graph (Rf = 7%, market risk premium 8%, firm WACC 15% at beta 1): project A with beta 0.6 and expected return 14% lies above the SML (required 7% + 0.6 x 8% = 11.8%) and should be accepted, but it is below the WACC and would be wrongly rejected. Project B with beta 1.2 and expected return 16% lies below the SML (required 16.6%) and should be rejected, but it is above the WACC and would be wrongly accepted.

Pure play approach: use a WACC that is unique to a particular project, based on companies in similar lines of business (pure plays). Betas: Alcatel-Lucent 1.44, L'Oréal 0.45, SAP 0.56, Siemens 1.51, Daimler 1.25, Philips Electron 0.92, Renault 1.64, Volkswagen 0.40. If Renault wants to build a division for business IT products, it should use the beta of SAP (0.56), not its own (1.64); with its own beta the project might be incorrectly rejected. (Book) The difficulty is finding a truly comparable pure play firm.

Subjective approach: projects are placed in risk classes and an adjustment factor is added to or subtracted from the firm's WACC (here 14%):

A high-risk project A with an expected return above the firm's WACC of 14% but below 20% is (correctly) rejected. The subjective approach still makes some errors, but fewer than using one WACC for everything.

Flotation costs

If a firm accepts a new project, it may need to issue (float) new bonds and shares. The costs of doing so are flotation costs: underwriting fees, legal fees and registration fees, for example paid to investment banks. Costs of issuing shares in practice include professional fees (lawyers and accountants), commissions and fees of underwriters, clerical and administrative costs, filing fees with the regulator (such as the SEC) and marketing costs. Selling a large amount of bonds quickly also costs money for investors (price concessions).

Example (Tripleday Printing SA): target debt-equity ratio 100% (E/V = D/V = 0.5); new printing plant in Lyon costs €500,000; flotation costs 10% for new equity and 2% for a 30-year bond. fA = 0.5 x 10% + 0.5 x 2% = 6%. True cost = 500,000/(1 - 0.06) = €531,915: if 6% of €531,915 (€31,915) is paid as flotation costs, the company raises exactly €500,000. In the NPV analysis the investment is €531,915 instead of €500,000. (Book) The flotation costs are added to the investment, not to the discount rate, and they are relevant because new financing must be raised for the project.

Private equity and venture capital

Private equity is equity financing for non-public companies (small; shares not traded). Banks are generally not interested in lending to start-ups, especially those with no assets other than an idea, run by entrepreneurs without a track record, with high risk and high search costs. Such firms look for venture capital (VC), an important part of the private equity market. Example: OpenAI raised about $6.5 billion in 2024 at a valuation of around $150 billion, the largest venture round of all time.

Venture capital refers to financing new, often high-risk start-ups; it usually comes before (larger) private equity financing. Individual venture capitalists (business angels) invest their own money. Venture capital firms pool funds from individuals, pension funds, insurance companies, large corporations and university endowments. Venture capitalists know that many new companies will fail, but the ones that succeed can provide enormous profits. The public image of early-stage financing comes from television shows such as Dragons' Den. (Book) VC is expensive: a venture capitalist typically demands 40% or more of the equity, board seats and preference shares, and access relies heavily on personal networks.

Business example (Betterment): an online investment company that raised $105 million in five rounds from 13 investors: a seed round (2010), Series A $3m (2010), Series B $10m (2012), Series C $32m (2014) and Series D $60m (2015), with venture funds such as Menlo Ventures and Bessemer Venture Partners.

The process of issuing securities

Alternative issue methods: capital can be raised through public issues or a private placement (shares sold directly to a few large investors). Public issues are either a general cash offer (shares offered to the public at large) or a rights issue (new shares offered to existing shareholders, usually at a discount). Types of equity offering: an initial public offering (IPO) is the first sale of stock by a private company to the public; a seasoned equity offering (SEO) is a sale of additional stock by a company that is already public.

Examples: Snap Inc. (Snapchat) prepared an IPO in 2017 that could value it at $25 billion or more; the Dutch online retailer Coolblue postponed its IPO because of investor uncertainty. The number of US IPOs fell from 486 in 1999 to 31 in 2008 and fluctuated around 100 to 275 afterwards; on Euronext Amsterdam activity peaked in 2021. Facebook's IPO (2012) valued the company around $100 billion, with Mark Zuckerberg holding about 28.4%.

IPO and capital increase: after an IPO the shares traded on the exchange consist of new shares (a capital increase: new equity for the company) and old shares sold by existing shareholders (only the shareholder composition changes); other old shares remain with the old owners (no change). Without a capital increase an IPO brings no new capital to the company, only cash to the old shareholders (as in the Bojangles' IPO from week 1).

Going public versus staying private: being private avoids disclosure, regulation and short-term market pressure; large late-stage private funding (Pinterest, Airbnb) reduced the need to go public. Firms can also go back private (Elon Musk's 2018 tweet about taking Tesla private at $420, 'funding secured', led to an investigation).

Underwriting

(Book) Dutch auction example: Rial plc sells 400 shares; bids are 100 at £16, 100 at £14, 200 at £12, 100 at £12 and 200 at £10. The highest price at which all 400 shares are sold is £12, so all winning bidders pay £12; bids at £12 or better total 500 shares, so each receives 80%. Google's IPO (19 August 2004) used a Dutch auction, valued the six-year-old company at about $23 billion, raised $2,718,281,828 (the digits of e), and paid only 2.8% in fees instead of the usual 4% or more.

Green shoe option (overallotment option): a clause in the underwriting agreement allowing underwriters to buy up to an additional 15% of shares at the offering price, used if demand exceeds expectations and the stock trades above the offer price; it helps to stabilise the initial share price. The name comes from the Green Shoe Manufacturing Company, the first to use it. (Book) Other features: lock-up agreements (insiders cannot sell for usually 180 days after an IPO) and the quiet period (communication limited to factual matters around the IPO). Key terms in rights issues: standby underwriting (the underwriter guarantees to buy any shares not taken up by investors), the standby fee (paid for that guarantee) and the oversubscription privilege (existing shareholders may buy unsubscribed shares).

IPOs and underpricing

Average initial returns differ widely across countries: for example the Netherlands 10.2%, Germany 24.2%, UK 16.1%, US 16.8%, Japan 40.2%, Greece 50.8%, India 88.5% and China 137.4%. In the US, first-day returns were extremely high in the 1999 to 2000 dot-com period (64.5% on average) and more moderate otherwise (7.3% in the 1980s, 14.8% in 1990 to 1998, 12.2% in 2001 to 2012). Key takeaway: underpricing is larger for small companies than for large companies. (Book) Explanations include the winner's curse (uninformed investors get more of the bad issues), compensation for risk, and underwriters' interest in successful issues.

SEOs and firm value

The costs of new issues

Six types of cost (see flotation costs): spread or underwriting discount (difference between the price the issuer receives and the offer price), other direct costs (filing fees, legal fees, taxes), indirect costs (management time), abnormal returns (the drop in share price at the announcement of an SEO), underpricing (in IPOs) and the green shoe option (the cost to the issuer of letting underwriters buy extra shares at the offer price).

Key takeaway: relative costs of IPOs and SEOs are smaller for large companies (economies of scale). For SEOs total direct costs fall from about 13% for the smallest US issues to about 3% for the largest; UK rights issues and open offers show the same pattern. An SEO is typically cheaper in percentage terms than an IPO.

Dilution

(Book) Dilution of proportionate ownership happens when new shares are sold to the public; a rights issue lets existing shareholders avoid it. Dilution of value (market value or EPS) occurs if the new money is invested in negative-NPV projects; a mere fall in book value per share is not a problem in itself.

Rights issues

In a rights issue (rights offering) existing shareholders receive rights (an option to buy new shares at a fixed subscription price within a limited time). Only current owners are eligible; if exercised, they get more shares and keep their ownership percentage; if not, the rights expire (or can be sold). Each shareholder receives one subscription right (SR) per share, but usually needs several rights to buy one new share. The right acts like a short-term option. In Europe rights issues are more common than general cash offers.

Business example: Atlético de Madrid issued 750,000 new shares at €61.90 (about €45 million) in a seasoned offering; existing shareholders had pre-emptive rights to buy one new share for every four held, but the majority shareholders committed not to exercise their rights so that the Wanda Group could acquire a 20% stake.

Example (Arcelor Mittal): an investor owns 100 shares at $10; a 2-for-5 rights issue (2 new shares for every 5 held) at $6. Portfolio before: $1,000. The investor receives 100 rights and can buy 40 new shares for 40 x $6 = $240. After exercising: 140 shares worth $1,240, so the price per share becomes 1,240/140 = $8.86 and the value of a right = 10 - 8.86 = $1.14. Without using the rights: 100 x 8.86 + 100 x 1.14 = $1,000. The use of the rights is irrelevant for wealth: with 5 shares (wealth $50) you receive 5 rights; after the issue your shares are worth 5 x 8.86 = $44.30 plus rights worth 5 x 1.14 = $5.70 (the slide rounds to $6.70), together $50. If you sell the rights: $44.30 in shares plus about $5.70 in cash. If you use them: pay 2 x $6 = $12 and own 7 shares worth 7 x 8.86 = $62.00; minus the $12 of own cash that is again $50.

Share price pattern: the share trades 'cum rights' until the rights start trading; then it trades ex rights and the price drops by the value of the right. The rights trade separately until the new shares are issued.

Example (O. Bama Company): subscription ratio 4:1 (one new share for four old), current price $32, issue price $25, 8 million shares. (1) New price = (4 x 32 + 1 x 25)/5 = $30.60; value of a right = 32 - 30.60 = $1.40. (2) New shares: 8m/4 = 2 million. (3) Main shareholder H. Illary owns 30% (2.4m shares), has no cash and wants to buy as many shares as possible by selling part of her rights. (a) Her 2.4m rights are worth 2.4m x 1.40 = $3.36m. Each new share effectively costs $25 plus 4 rights of $1.40 = $30.60 (the new share price: key insight). She can buy 3.36m/30.60 = 109,803 new shares, using 439,212 rights, and sells the remaining 1,909,803 rights for $2,745,103.20, which pays for the new shares (109,803 x $25 = $2,745,075). (b) Her stake becomes 2,509,803/10,000,000 = 25.1% (before 30%, and 24% if she had done nothing). (c) Wealth before: 2.4m x $32 = $76.8m. After: 2,509,803 x $30.60 = $76,799,971.80 plus $28.20 cash (rounding) = $76.8m. Her wealth is unchanged.

Exercise (T.Rump company): 400,000 old shares at $20; 200,000 new shares at $11. New price = (400,000 x 20 + 200,000 x 11)/600,000 = $17; value of a right = 20 - 17 = $3 (N = 2 rights per new share: (17 - 11)/2 = 3).

Tutorial exercises: Jefferson Refining: new shares at £21 plus 3 rights, price £23: TERP = (3 x 23 + 21)/4 = 22.50, value of a right = £0.50. The Motor Plant raises £21.4m at £12 per share with 2.6m shares outstanding: new shares = 21.4m/12 = 1.783m; rights per new share = 2.6/1.783 = 1.46. Precise Machining: TERP £46, price £53, 7m shares, raising £70m: with N = 7m/(70m/S) = S/10, solving 46 = (N x 53 + S)/(N + 1) gives S = £27.06. Wuttke Corp. raises $3m with 400,000 shares at $40, subscription price $20 and a 4% underwriter spread: net proceeds $19.20 per share, new shares 156,250, N = 2.56, TERP = (2.56 x 40 + 20)/3.56 = $34.38, value of a right $5.62; an investor with 5,000 shares who sells the rights receives about $28,090. D.L. Jones & Co. received £20.80 per share on 25,000 shares while the underwriter sold 23,700 shares at £22: the underwriter bought the whole issue, so this was a firm commitment underwriting. Jones & Co., funded by individual investors to finance new ideas, is a form of venture capital.