AFM 274

AFM 274: Introduction to Corporate Finance
Tingting Wu
HH-386B TTh 2:30-4pm

Participation - 10%
MT #1 - 30%
MT #2 - 35%
MT #3 - 25%

0 | Introduction

0.1 | Outline

1 | Capital Structure (how should a firm finance its operations)

2 | Payout Policy (how much cash should firms pay out to shareholders) (how should it be paid - dividends vs repurchases)

3 | Valuations (how financing decisions affect investment decisions) (how firms finance equity and debt)

4 | Raising Money (how firms issue equity and debt)

5 | Short-term financing (working capital management)

Recurring themes

1. Efficient Market Hypothesis
2. Conflict of Interest (agency problems)
3. No-arbitrage principle (same return + same risk = same price)

Balance Sheet

• Current Assets (cash, AR, inventory)
• Fixed Assets (buildings, machinery, land)
• Current Liabilities (AP, Unearned Revenue)
• Long Term Debt (corporate bonds, bank loans)
• Shareholders’ Equity

Key Issues

• Capital budgeting (which fixed assets to invest in)
• Capital structure (how to finance fixed assets)
• Working capital management (managing current assets / liabilities)
• Payout policy (how how and how to return money to shareholders)

0.2 | Review

TVOM

FV of present cash flow

$$F{V}_h=PV(1+r{)}^h$$

PV of future cash flow

$$PV=\frac{C_h}{(1+r{)}^h}$$

PV of series of cash flows

$$PV=C_0+\frac{C_1}{1+r}+\frac{C_2}{(1+r{)}^2}+\cdots +\frac{C_N}{(1+r{)}^N}=\sum _{n=0}^N\frac{C_n}{(1+r{)}^n}$$

Perpetuity

$$PV=\frac{C}{r}$$

Growing perpetuity

$$PV=\frac{C}{(r-g)}$$

Annuity

$$PV=C\times (\frac{1}{r})[1-\frac{1}{(1+r{)}^N}]$$

Growing annuity

$$PV=\frac{C_1}{r-g}[1-(\frac{1+g}{1+r}{)}^N]$$

Notes

• All PV formulas assume first period is one period from today
• Assumes $r$ is given as a per period rate
• If there are $k$ periods per year:

$$r=\frac{APR}{k}$$ $$EAR=(1+r{)}^k-1$$ $$r=(1+EAR{)}^{1/k}-1$$

Examples

1. PV

$$PV=\frac{1000}{(1.07{)}^5}$$

2. FV

$$PV=100\times (1+\frac{0.05}{12}{)}^{12\times 6}$$

Instrument Valuation

1. Stock

$$r=\frac{APR}{k}=\frac{0.08}{4}=0.02$$ $$PV=\frac{C_1}{r-g}=\frac{1}{0.02-0.005}+1$$

2. Bond

$$r=(1+EAR{)}^{1/2}-1=(1.0816{)}^{1/2}-1=0.04$$ $$C=\frac{1000\times 0.07}{2}=35$$

Bond = Annuity (coupons) + Lump Sum (principal)

$$PV=C\times (\frac{1}{r})[1-\frac{1}{(1+r{)}^N}]+\frac{C}{(1+r{)}^N}$$ $$PV=\frac{35}{0.04}[1-\frac{1}{(1.04{)}^{16}}]+\frac{1000}{(1.04{)}^{16}}$$

Arbitrage

No-arbitrage principle: same future cash flows + same risk = same price (no free lunch)

1. Bonds Solution 1: replicate the cash flow Government bond: $t=1\to 1000\times 0.1=100$ $t=2\to 100+1000=1100$

Same thing as: $t=1\to 1\times 97=97$ $t=2\to 11\times 95=1045$

$$PV=97+1045=1142$$

Solution 2: calculate the discount rate $r_1=\frac{100}{97}-1=0.03$ $r_2=\frac{100}{95}-1=0.05$

$$PV=\frac{100}{1.03}+\frac{1100}{1.05}\approx 1142$$

Risk, Portfolio Theory, CAPM

Total risk = market (systematic) risk + diversifiable (idiosyncratic) risk

Capital asset pricing model (CAPM)

$$E(R_j)+r_f+\beta [E(R_M)-r_f]$$

• $j$ = risky security
• $M$ = market portfolio (contains all risky securities, completely diversified, only has market risk)

Cost of Capital

$$V=D+E$$

• $D$ = debt value with return $r_D$
• $E$ = equity value with return $r_E$
• $V$ = firm’s value

If an investor owns all debt and all equity, its expected return is: Asset cost of capital / Unlevered cost of capital / pretax weighted average cost of capital (WACC)

$$r_U=(\frac{E}{E+D})r_E+(\frac{D}{E+D})r_D$$

Asset beta (unlevered beta)

$${\beta }_U=(\frac{E}{E+D}){\beta }_E=(\frac{D}{E+D}){\beta }_D$$

Weighted average cost of capital (assuming $r_D=r$)

$$r_{wacc}=(\frac{E}{E+D})r_E+(\frac{D}{E+D})r_D(1-{\tau }_c)$$

• ${\tau }_c$ = corporate tax rate
• $r$ = interest rate
• $r(1-{\tau }_c)$ = effective after-tax interest rate
  • Interest payment is tax deductible
  • The government is subsidizing ${\tau }_C$ of every dollar because it “would have gone to taxes”

Market efficiency = investors can’t earn higher than market returns without taking on extra market risk

• Corporate financial managers shouldn’t try to cook the books
• Managers cannot deliberately sell overvalued securities
• Market prices reflect a lot of information

1 | Capital Structure

17 | Capital Structure in Perfect Capital Markets

Background

Capital Structure = firm’s mix of financing instruments

$$V=D+E$$

• Does it matter how you slice this pie? Can you slice the pie to maximize $V$?
• Modigliani-Miller say in a perfect capital market, it doesn’t

Cost of Capital review Dividend growth model:

$$\begin{array}{rl}{P}_0& =\frac{D_0(1+g)}{r_E-g}=\frac{D_1}{r_E-g}\\ r_E& =\frac{D_1}{P_0}+g\end{array}$$

CAPM

$$R_E=r_f+{\beta }_E[r_M-r_f]$$

Asset cost of capital

$$r_U=(\frac{E}{E+D})r_E+(\frac{D}{E+D})r_D$$

Extends to more complex cases - with preferred shares $P$:

$$r_U=(\frac{E}{E+D+P})r_E+(\frac{D}{E+D+P})r_D+(\frac{P}{E+D+P})r_P$$

Leverage = using borrowed money (increases expected returns and risk)

1. PV of equity:

$$PV=\frac{7.5m}{0.05}=150m$$

2. PV of equity vs debt

Asset	Value
Firm	$7.5m$
Debt	$4m\times 0.05=200k$
Equity	$7.5-0.2=7.3m$
Annual interest from debt is 200k forever

$$P{V}_D=\frac{200k}{0.05}=4m$$ $$P{V}_E=\frac{7.3m}{0.05}=146m$$

Perfect capital market assumptions

1. Investors (retail) and firms (institutions) can trade the same set of securities at competitive market prices equal to the present value of their future cash flows (no arbitrage)
2. There are no taxes, transaction costs, or issuance costs associated with security trading (no taxes)
3. A firm’s financing decisions do not change the cash flows generated by its investments, nor do they reveal new information about them (no info leakage)

MM Proposition I

MM (Modigliani-Miller) Proposition 1 (Perfect Capital Markets) In a perfect capital market, the total value of a firm is equal to the market value of the total cash flows generated by tis assets and is not affected by its choice of capital structure

$$V^U=V^L$$

• $V^U$ = value of unlevered firm
• $V^L$ = values of identical levered firm

Examples

Example 1: Firm U: $V^U$ = $100m, Perpetual cash flow = $10m Firm L (same cash flow): $r_D$=5%, $D^L$ = $50m

• Annual debt payment = $50m x 5% = $2.5m
• Cash flow left for equity holders = $10m-$2.5m = $7.5m

MM Proposition 1 implies that $E^L$ = $50mSuppose$E^L$=$45m, not $50m

	Cashflow Today	Perpetual Return
Buy 2% of U’s equity	100m x 2% = (2,000,000)	10m x 2% = 200,000
Buy 2% of L’s equity	45m x 2% = (900,000)	7.5m x 2% = 150,000
Buy 2% of L’s debt	50m x 2% = (1,000,000)	2.5m x 2% = 50,000

Arbitrage: short row 1, long row 2, 3

• In fact, the no-arbitrage principle (hedge funds will take advantage) guarantees MM1

	Cashflow Today	Perpetual Return
Buy 2% of L’s equity	60m x 2% = (1,200,000)	7.5m x 2% = 150,000

Arbitrage: long row 1, short row 2, 3

• Problem: It’s harder to take a short position on a company’s debt (same as borrowing from them)

Observations

• MM is based on the no arbitrage principle
• A key assumption is that individuals can borrow as cheaply as corporations
  • They borrow on margin, with the stock as collateral
  • Firms borrow using illiquid assets as collateral (and get charged high rates)
• The same arguments apply to more complex cash flows (they don’t need to be perpetual)

Example 2: Original Capital Structure: All Equity

• Number of shares = 1,000
• Share price = $10
• Market value of shares = $10,000

Assume EBIT (earnings before interest and tax), EPS (earnings per share), ROE (return on equity) differ across economic states on a uniform distribution

$$r_u\approx ROE=0.15$$

Now the company takes a leveraged recapitalization (share buy-back, EBIT same)

• Number of shares = 500
• Share price = $10
• Market values of shares = $5000
• Market value of debt = $5000 (by MM1, 10,000-5,000)

$$r_u=\frac{1}{2}(0.2)+\frac{1}{2}(0.1)=0.15$$

Takeaway:

• Levered firms have more expected return but also more risk
• MM argument: this doesn’t matter, because investors can replicate the payoffs from the alternative capital structure using ‘homemade leverage’ (borrowing on margin)
• Basically MM1 still holds

MM Proposition II

Motivation

• We have seen that leverage increases expected return and risk
• Pretax WACC is the same regardless of how a firm is financed (15% = 15%) - this is an implication of MM1

MM II: The cost of capital of levered equity increases with the firm’s market value debt-equity ratio:

$$r_E=r_U+\frac{D}{E}(r_U-r_D)$$

• $r_U$ = cost of capital
• $r_E$ = cost of equity
• $r_D$ = cost of debt

Capital Budgeting and WACC

Weighted average cost of capital

$$r_{wacc}=(\frac{E}{E+D})r_E+(\frac{D}{E+D})r_D(1-{\tau }_c)$$

• ${\tau }_c$ = corporate tax rate
• $r(1-{\tau }_c)$ = effective after-tax interest rate

Now

• In perfect capital markets, there are no taxes, so $r_{wacc}=r_U$
• This implies that WACC is independent of capital structure
• If the risk of a new project equals the risk of the firm’s assets, the firm’s WACC can then be used as the discount rate for that project

Problem:

1. WACC

$$WACC=\frac{E}{E+D}{r}_E=\frac{D}{E+D}+r_D=\frac{1}{2}(0.08)+\frac{1}{2}(0.16)=0.12$$

2. Equity > Debt

$$0.12=\frac{3}{5}{r}_E+\frac{2}{5}(0.0725)$$ $$r_E=\frac{0.12-\frac{2}{5}(0.0725)}{\frac{3}{5}}=0.15$$

New problem

$$E=30BD=10B{r}_E=0.09r_D=0.04$$

1. Calculate $r_U$

$$r_U=\frac{3}{4}(0.09)+\frac{1}{4}(0.04)=0.0775$$

2. Issues new equity 10B, debt = 0

$$r_E=r_U$$

3. Does WACC change

$$\text{No}$$

Levered and Unlevered Beta Asset beta (unlevered beta) doesn’t change with capital structure

$${\beta }_U=(\frac{E}{E+D}){\beta }_E=(\frac{D}{E+D}){\beta }_D$$

Change in capital structure results in a change in equity beta

$${\beta }_E={\beta }_U+\frac{D}{E}({\beta }_U-{\beta }_D)$$

Publix

$${\beta }_U=\frac{1}{3.8}(1.51)+\frac{2.8}{3.8}(0.15)=0.507$$

Kroger

$${\beta }_U=\frac{1}{1.395}(0.69)+\frac{0.395}{1.395}(0)=0.4946$$

(to get $\frac{D}{D+E}$ given $\frac{D}{E}$, assume $E=1$)

Net Debt

• Assets on a firms balance sheet include cash and investments in risk-free securities; these reduce the value of a firm’s assets (eg. when cash is spent)
• They have the opposite effect of leverage: cash and investments are effectively negative debt
• Net debt = debt - cash - investments in risk-free securities

Example

$$E=143.6BD=24.6B{\beta }_E=1.15Cash=60.38B$$ $$EV=143.6B+24.6B-60.38B=107.82B$$ $$\text{Net Debt}=24.6B-60.38B=-35.78$$ $${\beta }_U=\frac{143.6}{107.82}(1.15)-\frac{35.78}{107.82}(0)=1.53$$

(we assume the debt is risk-free because we can pay it off with the cash)

Two Common Fallacies

1. ”Increasing leverage increases EPS” but also risk
2. ”Issuing shares leads to dilution” but also gives the company cash inflows

18 | Debt and Taxes

Introduction

• Relax perfect capital market assumptions: companies have to pay corporate tax
• Interest payments are tax deductible, this benefits debt financing

Ex: EBIT = $100/yr,$\tau_c=40%$, annual after-tax cash flow to shareholders?

$$100-40=60$$

Ex: $12 interest / year

$$\text{Taxable Income}=100-12=88$$ $$\text{Taxes}=0.40\times 88=35.20$$ $$\text{Debtholders get}=12$$ $$\text{Shareholders get}=88\times (1-0.4)=52.80$$ $$\text{Total Cash Flow}=12+52.80=64.80$$

What if there was no leverage? Additional Cash Flow from Leverage = $64.80 - $60 = $4.80 Notice that: 40% tax rate x $12 interest = $4.80 (Tax Shield)

Effective interest paid by shareholders = $60-$52.80 = $7.20Noticethat:$12 x (1 - 40%) = $7.20

The Interest Tax Shield (levered firms) All equity

$$EBIT(1-{\tau }_c)$$

Levered

$$\underset{\text{Available to shareholders}}{\underbrace{(EBIT-\text{Interest Paid})(1-{\tau }_c)}}+\underset{\text{Paid to debtholders}}{\underbrace{\text{Interest Paid}}}$$

Rearranging

$$\underset{\text{Cash flows to investors without leverage}}{\underbrace{EBIT(1-{\tau }_c)}}+\underset{\text{Interest tax shield}}{\underbrace{\text{Interest Paid}\times r_c}}$$

MM 1 (Corporate Tax)

$$V^L=V^U+PV(\text{Interest Tax Shield})$$

Valuing the Interest Tax Shield

Example: Firm borrows $100m for 5 years at r = 4%, ${\tau }_c=35\%$, what is PV of Interest Tax Shield? Annual interest = $100M x 4% = $4M Annual tax shield = $4M x 35% = $1.4M Ordinary Annuity:

$$PV=1.4M(\frac{1}{0.04})(1-\frac{1}{1.04^5})=6,232,551$$

Special case: firm issues debt $D$ and keeps it constant in perpetuity

• Borrows at interest rate = $r_D$
• Interest tax shield each year = ${\tau }_c\times r_D\times D$

$$PV(\text{Interest tax shield})=\frac{{\tau }_c\times r_D\times D}{r_D}={\tau }_C\times D$$

Recall: pretax WACC

$$r_U=(\frac{E}{E+D})r_E+(\frac{D}{E+D})r_D$$

After-tax WACC:

$$\begin{array}{rl}{r}_{wacc}& =(\frac{E}{E+D})r_E+(\frac{D}{E+D})r_D(1-{\tau }_C)\\ & =\underset{\text{Pretax WACC}}{\underbrace{(\frac{E}{E+D})r_E+(\frac{D}{E+D}{r}_D)}}-\underset{\text{Decrease from interest tax shield}}{\underbrace{(\frac{D}{E+D})r_D{\tau }_c}}\end{array}$$

Recap:

$$\text{Interest tax shield}=\text{Interest}\times {\tau }_c$$

MM1 (Corporate tax):

$$V^L+V^Y+PV(ITS)$$

With PERPETURAL Debt $\bar{D}$ (not applicable if given equity cost of capital)

$$PV(ITS)=\bar{D}\times {\tau }_C$$

Example:

$$FCF=\$4.25mg=4\%r_E=10\%r_D=6\%{\tau }_C=35\%\frac{D}{E}=0.5V(ITS)=?$$ $$PV(ITS)=V^L-V^U$$ $$r_L=WACC=\frac{1}{1.5}(10\%)+\frac{0.5}{1.5}(6\%)(1-35\%)=7.97\%$$ $$r_U=\frac{1}{1.5}(10\%)+\frac{0.5}{1.5}(6\%)=8.67\%$$ $$V^L=\frac{FC{F}_1}{(WACC-g)}=\frac{4.25M}{(7.97\%-4\%)}=107.14M$$ $$V^U=\frac{FC{F}_1}{(r_u-g)}=\frac{4.25M}{8.67\%-4\%}=91.07M$$ $$PV(ITS)=V^L-V^U=107.14M-91.07M=16.07M$$

Alternatively

$$PV(ITS)=\frac{[(107.14\times \frac{0.5}{1.5})\times 6\%\times 35\%]}{(8.67\%-4\%)}$$

A Leveraged Recapitalization

Recapitalization = changing capital structure Leveraged Recapitalization = issuing debt to repurchase shares

Ex: Physical assets = $128,000,Equity=$128,000, Shares = 10,000

$$\text{Share Price}=P_U=\frac{128,000}{10,000}=12.8$$

Post-Announcement Balance Sheet

Assets		Liabilities & Equity
Cash	0	Debt	0
Physical Assets	128,000	Equity	142,400
Interest Tax Shield	40,000 x 36% 14,000
Total Assets	142,400	Total L&E	142,000

Existing shareholders reap the rewards, because the share price goes up

$$\text{Share Price}=\frac{142,000}{10,000}=14.24$$ $$\text{Shares Outstanding}=10,000-\frac{40,000}{14.24}=7,191$$ $$\text{Share Price}=\frac{\text{Equity}}{\text{\# Shares}}=\frac{142,000}{7,191}=19.74$$

Optimal Capital Structure with Taxes

D/E ratio varies a lot across industries

19 | Financial Distress, Managerial Incentives, Information

Introduction

• Financial Distress = firm can’t make payment to creditors
  • Stock-based insolvency = value of firm’s assets < what it owes creditors
  • Flow-based insolvency = firm’s cash flows < required payments
• Default = firm fails to make a payment
• Bankruptcy = debt holders are given legal rights to take ownership of the firm’s assets

What happens in financial distress?

• Doesn’t always mean termination
  • For flow-based insolvency, the firm can raise more money
• Asset restructuring
  • Selling off assets
  • Cutting back R&D and capital spending
  • Merging with another firm
• Financial restructuring
  • Cutting dividends
  • Issuing new securities
  • Negotiating with creditors
  • Exchanging debt for equity
  • Filing for bankruptcy

Bankruptcy Law

In a legal bankruptcy, firms choose between liquidation or reorganization

• Liquidation = terminate the firm, sell assets, distribute proceeds to creditors
• Reorganization = keep the firm, issue new securities to replace old ones
• In Canada, we use
  • Bankruptcy and Insolvency Act (BIA) for small firms
  • Companies’ Creditors Arrangement Act (CCAA) for larger firms

Bankruptcy is a legal and time-consuming process

• Firms sometimes try to negotiate with creditors rather than filing for bankruptcy (a workout)
• Alternatively, firms reach first agreement on reorganization with main creditors, then file for bankruptcy to pressure any hold outs from creditors (prepackaged bankruptcy)

Direct vs Indirect Costs

• Direct costs = legal costs associated with formal bankruptcy or workout (3-4%) of pre-bankruptcy total asset value
• Indirect costs = much larger (lost sales, tarnished brand reputation, loss of key personnel, and damaged supplier relationships)

Costs of Financial Distress

In general, costs of financial distress are borne by the shareholders

Ex: Firm is worth $250k or $180k with $P(0.5)$, $\beta =0,r=4\%$ (i) Suppose the firm is all-equity financed with 10,000 shares. What is the share price?

$$E(V)=0.5(250,000)+0.5(180,000)=215,000$$ $$V=\frac{215,000}{1.04}=206,731$$ $$P=\frac{206,731}{10,000}=20.67$$

(ii) Suppose the firms borrows $200k after a year and uses it to buy back shares

Payoff	Good	Bad
Assets	250k	180k
Equity	250k - 200k = 50k	180k - 180k = 0
Debt	200k	180k

$$PV(E)=\frac{(50,000)(0.5)+0(0.5)}{1.04}=24,038.46$$ $$PV(D)=\frac{200,000(0.5)+180,000(0.5)}{1.04}=182,692.31$$ $$V=D+E=206,731$$

In Perfect Capital Markets, $V^L=V^U$

$$\text{\# remaning shares}=10,000(\frac{E}{D+E})=10,000(\frac{24.038}{206,731})=1,163$$ $$\text{Share price}=\frac{24,038}{1,163}=20.67$$

Share price stays the same - could’ve just calculated this value without calculating $PV(E)$

(iii) How does (ii) change if there are bankruptcy costs of $30k?

Payoff	Good	Bad
Assets	250k	180k
Bankruptcy	0	30k
Equity	50k	0
Debt	200k	180k - 30k =150k

$$PV(E)=\frac{50,000(0.5)+0(0.5)}{1.04}=24,038.46$$ $$PV(D)=\frac{200,000(0.5)+150,000(0.5)}{1.04}=168,269.23$$ $$V=E+D=192,308$$ $$\text{\# remaining shares}=10,000(\frac{24,038}{192,308})=1,250$$ $$\text{Share price}=\frac{24,038}{1,250}=19.23$$

Takeaway: Equity holders bear the bankruptcy costs

$$PV(BC)=\frac{30,000(0.5)}{1.04}=14,423.08$$ $$\text{Loss in value of equity}=(20.67-19.23)(10,000)=14,423$$

The Tradeoff Theory

Tradeoff theory = firms weigh the benefits of debt (from interest tax shields) against costs of financial distress

$$V^L=V^U+PV(\text{interest tax shield})-PV(\text{financial distress costs})$$

Factors affecting the PV of financial distress costs

• Probability of financial distress
• Size of costs once the firm is in financial distress
• Appropriate discount rate

Agency Costs and Benefits

Agency costs = costs arising from conflicts of interest between the firm’s stakeholders

Example: High-risk firm

$$E(\text{Pay-off})=0.1(100)+0.9(0)=10$$ $$NPV=\frac{10}{1.5}-10=-3.33$$

Payoff	Good (10%)	Bad (90%)
Asset	100	0
Debt	50	0
Equity	50	0

$$\text{Debt NPV}=\frac{0.1(50)+0.9(0)}{1.5}-10=-6.67$$ $$\text{Equity NPV}=\frac{0.1(50)+0.9(0)}{1.5}-0=3.33$$

Takeaway: Equity holders can only go to 0, debt holders can go negative

Example: Debt Overhang

Payoffs	Good	Bad
Assets	60	60
Debt	50	50
New Equity	10	10
Original Equity	0	0

$$NPV=\frac{60}{1.1}-30=24.54$$ $$NPV(D)=\frac{50}{1.1}-0=45.45$$ $$NPV(\text{New Equity})=\frac{60-50}{1.1}-30=-20.90$$ $$NPV(\text{Old Equity})=\frac{0}{1.1}-0=0$$

Management entrenchment = separation of ownership and control, where managers make decisions which benefit themselves at the expense of investors Management entrenchment theory = managers use low leverage in order to avoid the discipline imposed by debt and to enhanced job security by avoiding financial distress

Asymmetric Information

Asymmetric information influences managerial decisions about capital structure

• Credibility principle = claims in someone’s self interest are only believable if they are backed up by actions that would be too costly to take if the claims were untrue
• Signaling theory of debt = leverage can be used as a way for managers to credibly convey information about the firm’s prospects to investors in capital markets
• Adverse selection = buyers of a good are less informed about the quality of the good than sellers, or vice versa
  • Used car sellers know more, and the existence of bad cars hurts good cars
  • Announcements of new equity issues are bad news (need more money)
  • Stock prices tend to rise in advance of announcements of new equity issues but then fall post-announcement
  • Firms can manage these by timing new equity issues when information asymmetry is relatively low (just after earnings announcements)
• Pecking order hypothesis = Mangers prefer to fund new investments using retained earnings first, then debt, then equity only if absolutely necessary

2 | Payout Policy and Valuations

20 | Payout Policy

Background

Payout policy = how firms choose to distribute FCF to equity holders Cash dividends / share repurchases = the firm buys back stock (open-market repurchase or tender offer) Stock dividend = distribution of stock (eg. 10% stock dividend = investors receive 1 extra share for every 10 they own) Stock split = large stock dividend (more than 25% under TSX rules)

Cash Dividends

Dividends usually paid quarterly

• Declaration date = board declares a payment on the record date
• Payment date = dividends sent to shareholders
• Ex-dividend date = first day when stock trades without dividend (record date - 1)

Dividend Policy in Perfect Capital Markets

Example 1

Policy 1: dividends = CF Ex: At $t=0$, managers know the firm will be liquidated at $t=2$. FCF of $110k$ at $t=1$ and $121k$ at $t=2$. $r=0.1$ and $10k$ shares outstanding. Calculate share price in 2 ways: Method 1: CF

$$V=\frac{110k}{1.1}+\frac{121k}{1.1^2}=200k$$ $$P=\frac{200k}{10k}=20$$

Method 2: Dividends

$$Div(t=1)=\frac{110k}{10k}=11$$ $$Div(t=2)=\frac{121k}{10k}=12.1$$ $$P=\frac{11}{1.1}+\frac{12.1}{1.1^2}=20$$

Policy 2: Pay higher dividend ($14 / share) at $t=1$ Can the firm pay $14 dividend at t = 1?

$$140k-110k=30k$$

How much equity financing do we need, and when should it be issued? 30k, on the ex-dividend date for the t = 1 dividend so the old shareholders get the t = 1 dividend instead of the new one How much do we promise equity holders at t = 2?

$$30k\times 1.1=33k$$

What is the dividend to old equity holders at t = 2?

$$121k-33k=88k$$

What is the new share price on the ex-dividend date but right before the new equity issuance?

$$\frac{88k}{10k}=8.8$$ $$P_{ex-div}(t=1)=\frac{88}{1.1}=8$$

How many shares should be issued?

$$\frac{30k}{8}=3750$$

What is the share price after new equity issuance?

$$\frac{\frac{121k}{1.1}}{10k+3750}=8$$

What is the share price at t = 0 if the market knows this plan?

$$\frac{[\frac{140k}{1.1}+\frac{88k}{1.1^2}]}{10k}=20$$

Policy 3: use 100k to repurchase shares instead of paying a dividend at $t=1$ What is the share price immediately before the first buyback at t = 1?

$$P_{t=1}=\frac{110k+\frac{121k}{1.1}}{10k}=22$$

How many shares are bought back at t = 1?

$$\frac{110k}{22}=5k$$

What is the share price immediately after the first buyback at t = 1?

$$P=\frac{\frac{121k}{1.1}}{10k-5k}=22$$

Is the share price different if the firm chooses to sell or not? Sell:

$$PV=\frac{22}{1.1}=20$$

Don’t sell:

$$PV=\frac{\frac{121k}{5k}}{1.1^2}=20$$

Takeaway: When you choose to sell / not sell is irrelevant to share price

• Shareholders will not pay more for a firm if the shareholder can either replicate or undo the dividend decision through homemade dividends
  • If you want more CF, sell shares
  • If you want less CF, buy shares
• MM Dividend Irrelevance: In perfect capital markets, holding fixed the investment policy of the firm, the firm’s choice of dividend policy is irrelevant

Suppose the firm sticks with policy 1, but an investor who owns 50 shares prefers policy 2

	$t=1$: 111k	$t=2$: 121k
Policy 1	11	12.1
Policy 2	14	8.8

What is the investor’s cash flow under policy #1?

$$Di{v}_{t=1}:11⟹11\times 50=550$$ $$Di{v}_{t=2}:12.1⟹12.1\times 50=605$$

What is the investor’s cash flow under preferred policy #2?

$$t_1:14\times 50=700$$ $$t_2:8.8\times 50=440$$

How much additional cash flow does the investor want at t = 1?

$$t_1:\Delta =700-550=150$$

How can the investor create this additional cash flow? Sell shares at $t=1$ What is the share price after the dividend at t = 1? Only one CF left:

$$P_{t=1}^{ex-div}=\frac{12.1}{1.1}=11$$

How many shares should the investor sell on the ex-dividend date?

$$\frac{150}{11}=13.64$$

CF ends up being the same:

$$t=1:11(50)+11(13.64)=550+150=700$$ $$t=2:(50-13.64)\times 12.1=440$$

Alternatively, suppose the firm switches to policy #2 and an investor who holds 30 shares prefers policy #1

$$t_1=14/\text{share},t_2=8.8/\text{share}$$

What is the investor’s cash flow under policy #2?

$$t_1:30\times 14=420$$ $$t_2:30\times 8.8=264$$

What is the investor’s cash flow under preferred policy #1?

$$t_1=30\times 11=330$$ $$t_2:30\times 12.1=363$$

How much less cash flow does the investor want at t = 1?

$$420-330=90$$

How should the investor get rid of this additional cash flow? Re-invest 90 in the firm What is the share price after the dividend at t = 1?

$$P_{t=1}^{ex-div}=\frac{8.8}{1.1}=8$$

How many shares should the investor buy on the ex-dividend date?

$$\frac{90}{8}=11.25$$

CF ends up being the same:

$$t=1:30(14)-11.25(8)=330$$ $$t_2:(30+11.25)(8.8)=363$$

Example 2

FCF = 2.5m, Shares = 200k, r = 10%, dividends only next year increased by $7.50

What is the stock price under the current dividend policy? Firm value

$$2.5m\times \frac{1}{0.1}\times \frac{1}{200k}=125$$

Dividend value

$$2.5m\times \frac{1}{200k}\times \frac{1}{0.1}=125$$

How much new funding is required?

$$7.5\times 200k=1.5m$$

How much perpetual return do the new shareholders require from t = 2?

$$1.5m\times 0.1=150k$$

How much cash flow do original shareholders now expect to receive?

$$t=1:2.5m+1.5m=4m$$ $$t=2:2.5m-150k=2.35m$$

What is the new share price on the ex-dividend date for the special dividend but right before the new equity issuance?

$$2.35m\times \frac{1}{200k}\times \frac{1}{0.1}=117.5$$

How many shares will be issued?

$$\frac{1.5m}{117.5}=12,766.96$$

What is the new share price and firm value after the equity issuance? Dividends / share

$$\frac{2.5m}{200k+12k}=11.75$$

Share price

$$\frac{11.75}{0.1}=117.50$$

Firm value

$$117.50(200k+12k)=25m$$

What is the share price and firm value at t = 0 assuming the market is aware of this plan?

$$t=1:4m$$ $$t=2:2.35m$$ $$V=\frac{4m}{1.1}+\frac{1}{1.1}(\frac{2.35m}{0.1})=25m$$ $$P_0=\frac{25m}{200k}=125$$

Timeline

• $t=0$ - firm announces special dividend, share price remains $125m
• Ex dividend for $t=1$:
  • Share price drops to $117.50, since those who buy don’t get the special dividend
  • On ex-div, firm issues new shares, share price remains the same
• Payment for $t=1$ - Firm pays $4m($20 / share) special dividend to original shareholders
• $t=2$ and after: Firm pays $2.5m($11.75 / share) to all shareholders

Effects of Personal Taxes

If dividend income tax rate (${\tau }_d$) > capital gains tax rate $({\tau }_g)$, investors would prefer share repurchases > dividends

• Lower taxes and higher firm value
• Optimal dividend policy would be to not pay dividends
• Long-term trend favored repurchases, recent changes favor dividends
• General rule: firm should never issue shares to pay it back as a dividend - this destroys value

Notation

• $P_0$ = original purchase price
• $P_{cum}$ = cum-dividend price
• $P_{ex}$ = ex-dividend price
• $Div$ = dividend
• ${\tau }_t$ = dividend income tax
• ${\tau }_g$ = capital gains tax

Average investor should be indifferent between selling before vs selling after

$$P_{cum}-(P_{cum}-P_0){\tau }_g=P_{ex}-(P_{ex}-P_0){\tau }_g+Div(1-{\tau }_d)$$ $$\Delta P=P_{cum}-P_{ex}=[\frac{1-{\tau }_d}{1-{\tau }_g}]$$

Therefore

$${\tau }_d={\tau }_g⟹\Delta P=Div$$ $${\tau }_d>{\tau }_g⟹\Delta P<Div$$ $${\tau }_d<{\tau }_g⟹\Delta P>Div$$

Example: Selling before VS on ex-dividend date VS with price drop

$$P_0=10P_{cum}=20Div=2.5{\tau }_d=40\%{\tau }_g=25\%$$

Sell before

• Proceeds: $P_{cum}=20$
• Dividend: $0$
• Capital gains tax: $(20-10)0.25=2.5$
• Dividend tax: $0$ After-tax cash: $20-2.5=17.5$

$\Delta P=3$

• Proceeds: $P_{ex}=20-3=17$
• Dividend: $2.5$
• Dividend tax: $(17-10)0.25=1.75$
• Capital gains tax: $2.5(0.4)=1$

After-tax cash: $17+2.5-1.75-1=16.75$

$\Delta P=1$

• Proceeds: $P_{ex}=20-1=19$
• Dividend: $2.5$
• Dividend tax: $(19-10)0.25=2.25$
• Capital gains tax: $2.5(0.4)=1$
• After-tax cash: $19+2.5-2.25-1=18.25$

$\Delta P=2$

• Proceeds: $P_{ex}=20-1=18$
• Dividend: $2.5$
• Dividend tax: $(18-10)0.25=2$
• Capital gains tax: $2.5(0.4)=1$
• After-tax cash: $18+2.5-2-1=17.5$

Effective Dividend Tax Rate: additional tax per dollar if after-tax capital gains is received as a dividend instead

$$\Delta P=Div\times \frac{1-{\tau }_d}{1-{\tau }_g}$$

• ${\tau }_d^{\ast }>0$ - better to pay capital gains / buy back shares
• ${\tau }_d^{\ast }<0$ - better to pay dividends

The Clientele Effect

Clientele	Stocks
High tax bracket	Zero-to-low payout
Low tax bracket	Low-to-medium payout
Tax-exempt	Medium to high payout
Corporations	High payout

Payout vs Retention of Cash

A firm which retains cash can invest in either in new projects or in financial assets. When should it invest in each?

• If new NPV > 0 projects are available, invest
• If they’re not, consider paying out the cash or investing in financial assets

MM Payout Irrelevance: In perfect capital markets, if a firm invests its excess cash in financial securities, the firm’s choice of payout vs. retention is irrelevant and does not affect the initial value of the firm.

Ex: A firm has $1m of excess cash. Consider only corporate taxes

• If the firm pays as a dividend and shareholders invest in 3% T-bills, they will have $1.03m
• If the firm retains the cash and pays a dividend after one year, the shareholders will have less, because the firm pays taxes on interest it receives

$$1m(1+0.03(1-{\tau }_c))$$

Effective tax disadvantage:

$${\tau }_{retain}^{\ast }=[1-\frac{(1-{\tau }_c)(1-{\tau }_g)}{(1-{\tau }_i)}]$$

• ${\tau }_c$ = corporate tax rate
• ${\tau }_g$ = personal tax rate on capital gains
• ${\tau }_i$ = personal tax rate on interest income

Ex: ${\tau }_c=26.50\%,{\tau }_i=53.53\%,{\tau }_g=26.76\%,{\tau }_{retain}=-15.84\%$. Corporation earns $100k each year If payout: Investors receive

$$100k(1-53.53\%)=46,470$$

Tax Paid

$$100k-46,470=53,530$$

If retain: Tax paid: Corporate tax + Capital gains (on everything else)

$$100k(26.5\%)+100k(1-26.5\%)(26.76\%)=46,169$$

After-tax income

$$100k-46,169=53,831$$

Difference between tax paid = ${\tau }_{retain}^{\ast }\times$ (amount received by investors)

$$53,530-46,169=7,361=-15.84\%\times 46,470$$

Why retain cash?

• More flexibility for positive NPV projects
• Cushion against bankruptcy and financial distress
• High-tech and biotech (Microsoft, Pfizer, Cisco Systems, Apple, Intel)

Asymmetric Information

Dividend signaling hypothesis: weakly good

• Changes in dividends lag behind changes in retained earnings (firms don’t cut dividends during temp bad times; don’t increase during temp good times)
• Special dividends = sign that firm is doing well

Share repurchases: weakly good

• Means the firm thinks shares are undervalued

Stock dividends and splits

• In perfect capital markets, they have no effect

21 | Capital Budgeting and Valuation with Leverage

Background

In AFM 272, we treated each project like an independent, all-equity firm

If financing decisions do matter, there are 3 basic approaches

1. adjusted present value (APV)
2. weighted average cost of capital (WACC)
3. flow-to-equity (FTE)

WACC

Example 1: PV of project?

$$\text{Net Debt}=320-20=300$$ $$\frac{D}{V}=\frac{E}{V}=\frac{300}{300+300}$$ $$r_{wacc}=\frac{1}{2}(10\%)+\frac{1}{2}(6\%)(1-40\%)=6.8\%$$ $$PV=\frac{C}{r}[1-\frac{1}{(1+r{)}^n}]=\frac{18}{6.8\%}[1-\frac{1}{(1+6.8\%{)}^4}]=61.25M$$ $$NPV=61.25M-28M=33.25M>0$$

Example 2: D/E = 1.5, $r_{wacc}=7\%$. Increase FCF by $6 million in year 1, and this amount is expected to grow at 2.5% per year forever.

$$PV=\frac{6M}{(7\%-2.5\%)}=133.33M$$ $$NPV=133.33M-120M=13.33M$$ $$D=PV\times \frac{D}{V}=133.33\times \frac{1.5}{2.5}=80M$$ $$E=133.33M-80M=53.33M$$ $$\text{New equity issuance}=E-NPV=53.33-13.33=40$$ $$\text{\$120m cost - \$80m debt issued = \$40m new equity issued}$$

Adjusted Present Value

Avco Example

APV Approach

$$V^L=V^U+PV(ITS)$$

Example: Find the value of the RFX project (Recall: Cost = 28; FCF = 18 (year 1 to 4); D/V = .5; Rd = 6%; Re = 10%; Tc = 40%; WACC = 6.8%)

Setup

$$CF:ITS=D_{t+1}\times R_d\times {\tau }_c$$ $$\frac{D_0}{V_0}=\frac{D_1}{V_1}=\cdots =\frac{D_4}{V_4}$$ $$APV=V_n+PV(ITS)$$

Calculations

$$r_U=\frac{1}{2}(10\%)+\frac{1}{2}(6\%)=8\%$$ $$NPV=\frac{18}{0.08}\times [1-\frac{1}{1.08^4}]=59.6$$

Brute forcing $V_{0,1,2,3,4}$

$$V_0=V_n+PV(ITS)=59.6+1.29=61.25$$ $$D_1=V_0\times \frac{D}{V}=61.25\times 0.5=30.63$$ $$IT{S}_1=30.63\times 6\%\times 40\%=0.74M$$ $$V_1=18M\times \frac{1}{6.8\%}\times [1-(\frac{1}{1.068^3})]=47.41$$ $$D_1=V_1\times \frac{D}{V}=23.71M$$

Calculate the rest

$$V_2=32.63,D_2=16.32$$ $$V_3=16.85,D_3=8.43$$ $$V_4=0,D_4=0$$

Calculate ITS

$$PV(ITS)=\frac{D_0\times R_d\times {\tau }_c}{(1+r)}+\cdots +\frac{D_4\times R_d\times {\tau }_c}{(1+r{)}^4}=1.63M$$ $$APV=V^L=59.62+1.63+61.25=122.5$$ $$NPV=61.25-28=33.25$$

FBN Example

Calculate APV given $r_D=5\%,r_E=14\%,{\tau }_c=40\%$. Recall: Cost = $120;FCF=$6mil; g = 2.5%; D/E = 1.5; WACC = 7%

$$APV=V_U+PV(ITS)$$ $$r_U=\frac{1}{2.5}(13\%)+\frac{1.5}{2.5}(5\%)=8.2\%$$ $$V_U=\frac{6}{8.2\%-2.5\%}=105.26$$

We know $V_L=133.33M$ - let’s confirm it

$$D_0=V_L\times \frac{3}{5}=80$$ $$PV(ITS)=\frac{80\times 5\%\times 40\%}{8.2\%-2.5\%}=28.07$$ $$V_L=105.26+28.07=133.33M$$

If $V_L^{t=0}$ is unknown, then

$$\begin{array}{rl}{V}_L& =V_U+PV(ITS)\\ & =105.26+\frac{V_L\times \frac{3}{5}\times r_D\times {\tau }_C}{8.2\%-2.5\%}\\ & =105.26+\frac{0.012V_L}{8.2\%-2.5\%}\\ V_L& =133.33M\end{array}$$

Flow-to-Equity

Free cash flow

$$FCF=EBIT\times (1-{\tau }_c)-\text{Capex}+\text{Depreciation}$$

Free cash flow to Equity (FCFE) = FCF left over after adjusting for, after-tax interest payments, additional borrowing, or debt repayments

$$FCF{E}_t=FC{F}_t-r_D{D}_{t-1}(1-{\tau }_c)+(D_t-D_{t-1})$$

• where net borrowing at date $t=D_t-D_{t-1}$
• like WACC, commonly used when a company has a targeted D/V

Avco RFX example (Recall: Cost = 28; FCF = 18 (year 1 to 4); D/V = .5; Rd = 6%; Re = 10%; Ru = 8%; Tc = 40%; WACC = 6.8%)

Year 0

$$\begin{array}{rl}FC{F}_{t=0}& =FC{F}_{t=n}-r_d\times D_{t-1}\times (1-{\tau }_c)+(D_0-D_{t-1})\\ & =-28-0+(30.6230-0)\\ & =2.6230\end{array}$$

Year 3

$$\begin{array}{rl}FC{F}_{t=3}& =18-6\%\times 16.3174\times (1-40\%)+(8.4270-16.3174)\\ & =9.5222\end{array}$$

Finding PV(FCFE)

$$2.62+\frac{9.97}{1.1}+\frac{9.75}{1.1^2}+\frac{9.52}{1.1^3}+\frac{9.27}{1.1^4}=33.25M$$ $$NPV=\text{increase in E}=33.25M$$

APV and Other Leverage Policies

Target Interest Coverage Ratio Suppose the firm keeps interest payments at fraction $k$ of FCF, and the tax shield is discounted at $r_u$

$$\begin{array}{rl}PV(ITS)& =PV({\tau }_c\times k\times FCF)\\ & ={\tau }_c\times k\times PV(FCF)\\ & ={\tau }_c\times k\times V^U\end{array}$$

Implies

$$V^L=V^U\times (1+{\tau }_c\times k)$$

Acvo RFX example: $V^U=59.62M$, plans to pay 20% of FCF as interest

$$V^L=59.62\times (1+0.4\times 0.2)=64.39M$$

Predetermined Debt Levels

$$\frac{D{r}_D{\tau }_c}{r_D}={\tau }_c\times D$$ $$V^L=V^U+{\tau }_c\times D$$

3 | Raising Capital

23 | Raising Equity Capital

Introduction

initial public offering (IPO) seasoned equity offering (SEO)

Equity Financing for Private Firms

Sources of equity financing

• Angel investors
• Venture capital (VC) firms
  • A VC is one of the GPs who runs the firm on behalf of the LPs
  • VCs have board seats
  • LPs are more diversified
• Private equity (PE) firms
• Institutional investors (endowments, foundations, pension funds)
• Sovereign wealth funds (SWFs) are government-controlled money
  • Are the largest LPs in PE firms
  • Financed by resource revenues (usually oil)
  • Largest SWF is Norway’s government pension fund ($1.3T)
• Corporate investors (Google, Meta, etc)

Preferred stock: typically sold to outside investors, senior in liquidation and dividend payment

Pre-money valuation: value of existing shares at new price Post-money valuation: value of all shares (new + previously existing)

Pre-money valuation

$$\text{Pre-money}=0.67\times 13,713,439=9.188M$$ $$\text{Post-money}=0.67\times (13,713,439+2,686,567)$$

Exit strategies

• IPOs
• Being bought by another firm

Initial Public Offerings

Advantages: liquidity Disadvantages: regulatory (OSC, SEC)

IPOs are managed by investment banks (underwriters)

• Primary offering = new shares
• Secondary offering = existing shares

Types of IPOs

• Best-efforts basis: small IPOs, underwriter just tries to sell at the best possible price
• Firm commitment basis: large IPOs, underwriter guarantees the entire firm will be sold
  • Most common type
• Auction IPO: investors invited to submit bids

IPO has lead underwriter and syndicates

1. Obtain approval
2. Preliminary prospectus sent to regulator and investors
3. Regulator evaluates and specifies changes
4. Underwriters estimate a price range
5. Market demand assessed through a road show
6. Underwriters determine final offer price based on total demand (book building)
7. Final prospectus contains price, number of shares offered, etc, and must be approved

Selling period

1. Syndicates agree not to sell for less than offering price
2. Lead underwriter can buy shares to stabilize downward pressure (usually illegal outside of IPO protection period)
3. If shares are unsold after a period (eg. 30 days), the syndicate breaks up, and members can sell shares for whatever price
4. Lockup period (eg. 180 days) = pre-existing shareholders can’t sell shares
5. Underwriters

Managing risk

1. Setting relatively low price: in the 1990s US, first-day closing price > opening price in 75% of cases
2. Over-allotment allocation (greenshoe option): underwriters can sell up to 15% more shares than original to control price (short position)
   1. If the share price rises, they will sell more
   2. If the share price falls, they will buy to close their short position, which will bring price back up
   3. Naked short position = selling more than they can cover

Other forms of IPO support

• Reverse greenshoe: underwriters can sell shares back to the firm at offer price
• Stabilizing bids: underwriters can post bids in the market agreeing to buy at the offer price
• Penalty bids: If the buyer sells shares before a specific period expires, they incur a financial penalty

Underpricing is a common occurrence

• Underwriters want to minimize the risk of the issue being withdrawn
• Winner’s Curse: Highest bid ends up losing value

IPO Scandals

• Spinning: underwriters were found to have allocated “hot” IPOs to the personal brokerage accounts of favoured clients such as senior executives of a different firm in exchange for future investment banking business
• Laddering: requiring the purchase of additional shares in the aftermarket in return for participation in IPOs

Seasoned Equity Offerings

SEO = publicly traded firm offers new shares

• Cash offer = firm offers new shares to any new investor
• Rights offer = new shares offered first to existing shareholders

Rights offer protection to current shareholders against new equity being sold at a low price

• Offer to buy at the subscription price
• If invertors are entitled to the right, the stock is rights-on
• Otherwise, the stock is ex-rights
• Rights offers usually use standby underwriting - a firm commits to buy the unsubscribed portion of the issue

Suppose a firm has 10 million shares which are trading at $15 per share. The firm wants to raise $50 million via a rights offering. Let the subscription price be set at $10 per share. How many rights are needed to buy one share?

Number of new shares:

$$\frac{50m}{10}=5m$$

Number of rights issued

$$\text{10m (1 per original share)}$$

Number of rights required to buy 1 new share

$$\frac{\text{10m rights}\times \text{1 new share}}{\text{x rights}}=\text{5m new shares}$$ $$\text{2 rights = 1 share}$$

How much is one right worth?

$$V=\$15\times 10m+\$10\times 5m=200m$$

Ex-rights price is like a weighted average

$$P_{ex}=\frac{V}{10m+5m}=\frac{200}{15}=13.33$$ $$R=P_{on}-P_{ex}=15-13.33=1.67$$

What are the rights-on and rights-off prices?

$$P_{on}=15$$ $$P_{ex}=13.33$$

What if the subscription price is $5 instead of $10? How many new shares?

$$\frac{50m}{5}=10m$$

How many rights is a share worth?

$$10m\times \frac{1}{x}=10m⟹x=1$$

What are the rights-on and rights-off prices?

$$P_{on}=15$$ $$V=15\times 10m+5\times 10m=200m$$ $$P_{ex}=\frac{200m}{10m+10m}=10$$ $$Right=P_{on}-P_{ex}=15-10=5$$

Subscription price	$10	$5
IF RIGHTS EXERCISED
Number of shares	$3$	$3$
Price per share	$13.33$	$10$
Cost of exercise	$-10$	$-5$
Total value	$3(13.33)-10=30$	$3(10)-5=25$
IF RIGHTS SOLD
Number of shares	$2$	$2$
Price per share	$13.33$	$10$
Value of shares	$2\times 13.33=26.67$	$2\times 10=20$
Rights sold	$2$	$2$
Price per right	$1.67$	$5$
Value of sold rights	$2\times 1.67=3.33$	$2\times 5=10$
Total value	$26.67+3.33=30$	$20+10=30$

Rights Formulas Notation

• $R$ = price of one right (ignores the time value)
• $S$ = subscription price
• $P_{on}$ = rights-on share price
• $P_{ex}$ = ex-rights share price
• $N$ = number of rights needed to buy one share

Exercising $N$ rights and paying $S$ to get one ex-rights share gives a payoff of $P_{ex}-S$, so the appropriate value of one right is

$$R=\frac{P_{ex}-S}{N}$$

Assuming $P_{on}=P_{ex}+R$, we can also write

$$R=\frac{P_{on}-S}{N+1}$$

SEOs are generally bad news because of the pecking order hypothesis (internal financing > debt > equity)

Costs of new equity issues

• Floatation costs (costs of issuing new equity)
  • Direct costs: reported in the prospectus, spread and administrative expenses, filing fees, accounting and legal fees, etc.
  • Indirect costs: not reported in the prospectus, time, underpricing, green shoe option, price drop in SEOs
• Prompt-offering prospectus (POP) system allows large firms to file annual statements with the OSC regardless of whether or not they issue securities in a given year, then use a shorter prospectus to speed up SEOs
• Self registration is a similar US system

24 | Debt Financing

General Background

Debt markets are larger than equity markets

• New issues of public debt follow the same procedures as new equity issues (prospectus, registration with OSC, etc)
• Indenture = formal contract between bond issuer and trust company which represents the bondholders interests in the case of default and ensures that the terms of indenture are followed
• Face value of $1k, maturity < 30 years, coupons semi-annually (in NA)

Corporate public debt - unsecured means higher interest rate

• Notes (shorter)
• Debentures (longer)
• Mortgage bonds (secured by house)
• Asset-backed bonds (secured by assets)

Private debt / bank loans

• Term load
• Revolving line of credit

Private placement = bond issue sold to small group of investors (institutions, pension plans)

• Usually has higher interest rate

International bonds can be categorized into

• Domestic bonds: issued domestic, denominated domestic
• Foreign bonds: issued by foreign, denominated domestic
• Eurobonds: not denominated in domestic currency
• Global bonds: offered for sale in several markets at once

Debt Covenants

Debt covenants = restrictions specified in the debt contract

• New debt
• Dividends and repurchases
• Levels of working capital
• Transfer or sale of assets
• Corporate investments
• M&A
• Repurchase debt at a specific price

Repayment Provisions

$$P=\frac{CPN}{YT{M}_n}[1-\frac{1}{(1+YT{M}_n{)}^n}]+\frac{FV}{(1+YT{M}_n{)}^n}$$

Example: Quarterly bond, $r=8\%,r_f=6\%,P=1000,n=10$

$$EAR=\frac{6\%}{4}=1.5\%$$ $$CPN=1000\times \frac{8\%}{4}=20$$ $$P=\frac{20}{0.015}[1-\frac{1}{1.015^{(4\times 10)}}]+\frac{1000}{1.015^{(4\times 10)}}$$

Callable bond = like an option

• Bonds can be fully callable or partially callable
• Call price = price the issuer can buy the bond for
• Call-protected = when the issue cannot exercise the option for a specified amount of time (eg. 5y)
• Re-investment risk = the issue will be brought back in an environment of low interest rate
• Callable bonds are traded at a lower price and have higher yield

Why issue?

• No advantage or disadvantage
• Superior interest rate predictions
• Financial flexibility
• Reduced interest rate risk
  • If rates increase, value drops (not as much as a non-callable bc higher coupon)
  • If rates fall, value rises (not as much as a non-callable bc call feature)
  • Bond yields and prices are inversely related

Ex: Value of a callable bond at a call date PAR = $1k, Coupon rate = 7.5% (APR) paid semi-annually, 10y to maturity

$$CPN=1000\times \frac{7.5\%}{2}=37.5$$

Case 1: YTM = 4% - firm will call

$$ESR=\frac{4\%}{2}=2\%$$ $$PV=\frac{37.5}{0.02}[1-\frac{1}{1.02^{2\times 10}}]+\frac{1000}{1.02^{2\times 10}}=1268$$

Call price = $1k (exercise call) Case 2: YTM = 10% - firm won’t call

$$ESR=\frac{10\%}{2}=5\%$$ $$PV=\frac{37.5}{0.05}[1-\frac{1}{1.05^{2\times 10}}]+\frac{1000}{1.05^{2\times 10}}=844$$

Call price = $844 (buy from market) Callable price is always the lower one!

YTM (Maturity) = standard market yield (assuming no call) YTC (Call) = standard yield (assuming call)

Ex: Yield on Callable Bonds

$$CPN=\frac{100}{2}-50$$ $$YTM=1158=\frac{50}{R}[1-\frac{1}{(1+R{)}^{10}}]+\frac{1000}{(1+R{)}^{10}}$$ $$YTC=1158=\frac{50}{r}[1-\frac{1}{(1+r{)}^4}]+\frac{1050}{(1+r{)}^4}$$

Make Whole Call and Sinking Funds

• Make whole call provision = call price determined by remaining PV of coupons + FV (at market rates)
• Sinking fund = Issuer makes regular payments over the life of the bond into a fund administered by the trustee. Trustee then uses the money to repurchase bonds

Convertible Bonds

Convertible bond = bond which can be converted at then bond holder’s option into a fixed number of common shares

• Conversion ratio = number of shares the bond can be converted into
• Conversion price

$$\frac{\text{Par value of bond}}{\text{Converstion ratio}}$$

• Conversion premium

$$\text{Conversion price - Stock Price}$$

Ex: $40/share,$1k par, Conversion ratio = 20 Conversion price = $40Conversionpremium=$40 - $50=-$10 (do not convert)

Convertibles are callable by the issuer. If they call, the holder can choose to convert rather than selling the bonds back (force conversion)

Conversion price is usually set 10-30% above the stock price. Value depends on

Straight bond value

• Bond issue with total amount $F$ owned at maturity $T$
• At $T$ the firm is obligated to pay $F$ to bondholders, but if it default, bondholders receive $V_T$
• At $T$, bondholders receive $\min (F,V_T)$

Conversion value

• $N$ existing shares, if all bonds convert there will be $N_c$ new shares
• Convertible owners have

$$[\frac{N_c}{N+N_c}]\times V$$

Price of a warrant cannot be negative

When should an issuer force conversion?

• Management should call as soon as convertible bond = call price
• Managers usually wait until convertible bond >>> call price
  • Required notice periods
  • Clauses preclude the issuer from calling
  • Firms with high dividends might pay interest rather than new dividends

Why issue convertibles?

1. Matching cash flows: issues securities with cash flows that match the firm
   1. Young, risky, growth firms are cash constrained and benefit from lower coupons
   2. There will be high dilution, but whatever
2. Risk synergy: hard to assess the risk of the issuer
   1. There’s a hedge if you converge or not
3. Mitigation of agency costs: shareholders vs debtholders
   1. Convertibles reduce the ability of shareholders to take risky projects and screw over bondholders
4. Backdoor equity: asymmetric information
   1. If management knows current shares are undervalued, it will be unwilling to issue equity
   2. Convertible reduces interest cost and doesn’t issue equity

26/27 | Short-Term Financing

Introduction

Operating cycle = length of time between when a firm originally acquires inventory and when it receives payment for finished product Cash cycle = length of time between when firm pays for inventory and end of operating cycle

$$\text{Cash Conversion Cycle (CCC) = Inventory days + A/R days - A/P days}$$ $$\text{Inventory Days}=\frac{\text{Inventory}}{\text{Average daily COGS}}$$ $$\text{A/R days}=\frac{\text{Accounts Receivable}}{\text{Average daily sales}}$$ $$\text{A/P days}=\frac{\text{Accounts Payable}}{\text{Average daily COGS}}$$

Working Capital Management

Breaking even on your initial investment isn’t enough - you need to account for TVOM

Trade Credit: “x/y net z”

• x% discount for payment within y days, or full amount owed after z days

Ex: 2/10 net 45 for a sale price of $500 Customer either pay $490 on day 10 or $500 on day 45 If the customer pays on day 45, that’s the same as borrowing $490 at a rate of

$$\frac{10}{490}=2.401\%$$

over 35 days. Thus, the EAR is

$$1.02041^{365/35}-1=23.452\%$$

Why trade credit?

1. Access to better information on credit quality
2. Collateral
3. Price discrimination

Float = time between when bill is paid vs when cash is received

• Collection float = customer pays bill - firm uses funds
  • Mail float (cheques)
  • Processing float (process and deposit)
  • Availability float (bank makes funds available)
• Disbursement float = firm makes payment - there is cash outflow

Receivables management - which credit policy?

• Credit standards = will credit be granted to any customers or just low risk ones?
• Credit terms = length and time of discount
• Collection policy = how to deal with late payments

Ex: 2/10 net 30 terms would increase sales by 20%, with 50% paying in 10 days, 30% paying in 30 days, 20% paying in 50 days. 100 sales daily, per sale revenue = $500,expenses=$400. r = 4, do we grant credit?

If credit not granted,

$$\text{Gross margin}=100(500-400)=10k$$

If credit granted

$$\text{Daily sales}=100\times 1.2=120$$ $$\text{COGS}=400\times 120=48k$$ $$\text{Revenue}=\frac{(0.5\times 120)(490)}{1.04^{10/365}}+\frac{(0.3\times 120)(500)}{1.04^{30/365}}+\frac{(0.2\times 120)(500)}{1.04^{50/365}}=59,246$$ $$\text{Gross Margin}=59,246-48,000=11,246$$

Aging schedule = table classifying the firm’s accounts according to how long they’ve been outstanding Stretching payables = deliberately paying late, or paying the discount price after eligible (UNETHICAL)

Calculate the EAR on a decision to forgo the discount on a trade credit agreement of 1/10 net 60, with the full amount of $1,818. That is, the customer will pay the supplier on day 60.

$$\text{Discoutned price}=1,818\times (1-0.01)=1,799$$ $$\text{Forgone discount}=1,818\times 0.01=18.18$$ $$\text{50-day rate}=\frac{18.18}{1,799}=1.01\%$$ $$EAR=(1+1.01\%{)}^{365/50}-1=7.61\%$$

Inventory management

• Acquisition costs (price paid for inventory)
• Order costs (cost pf placing order)
• Carrying costs (storage, insurance, lost inventory + opportunity of funds tied up in inventory)

Cash management

• Transaction balance: amount of cash needed to pay bills
• Compensating balance: amount that the bank requires in an account
• Precautionary balance: amount of cash needed to manage risk

Short-Term Financing Alternatives

Matching Principle = short-term requirements should be financed with short-term debt (<1 year), long-term needs should be financed with long-term debt

• Permanent working capital = amount of working capital needed to cover a firm’s ongoing operations
• Temporary working capital = portion of working capital due to transistory factors (seasonal sales, temporary shocks)

Aggressive financing policy = permanent working capital with short-term debt

• Advantage: cheaper
• Disadvantage: refinancing + bankruptcy risk

Conservative financing policy = temporary working capital with long-term debt

• Advantage: less risk
• Disadvantage: periods of excess cash invested at lower interest rates

Bank Loans

Bank loans = single, end-of-payment loan (interest, then lump sum)

• Interest can be fixed or vary with benchmark rate (prime rate)

Line of credit = lends the firm any amount up to a maximum at any time

• Legal obligation terms that are re-negotiated annually
• Revolving line of credit = happens every 2-3 years

Bridge loan = short-term loan supplied by a bank while a firm arranges long-term financing

Commitment fee = small fee on unused part of the LOC

Example: maximum amount is $10 million, simple interest rate is 7%, commitment fee is 0.5%. Suppose the firm borrows $6 million at the start of the year and then repays it at the end of the year. What is the total cost of the loan?

$$\text{Commitment fee}=(10-6)\times 0.5\%=20k$$ $$\text{Interest}=6\times 7\%=420k$$ $$\text{Total cost}=20k+420k+440k$$

Other Sources of Short-Term Funds

Loan origination fee = percentage deducted from loan at outset, resulting in higher effective interest rate

Example: consider a $1 million loan for 6 months at an annual percentage rate of 10% with a 1% loan origination fee. What is the EAR of the loan? Loan origination fee = $1\%\times (1m)=10k$ Usable loan = $1m-10k=990k$ Firm must pay interest on full $1M

$$\text{Interest}=1m\times \frac{0.1}{2}=50k$$ $$ESR=\frac{(\frac{10\%}{2})\times 1m+1m}{900k}-1=6.06\%$$ $$EAR=(1+ESR{)}^2-1=1.0606^2-1=12.49\%$$

Compensating balance = firm doesn’t have access to the full principal of the loan

Example: Calculate the EAR for a $2,000 (principal amount) one-year bank loan with an APR of 6%, compounded annually. The principal amount includes a compensating balance requirement of 10%. (Note that no interest on the compensating balance is paid to the borrower) Amount borrowed = $2k(1-10\%)=1.8k$ Interest = $2k\times 6\%=120$

$$EAR=\frac{\text{interest charged}}{\text{amount borrowed}}=\frac{120}{1800}=6.67\%$$

Commercial paper = unsecured short-term debt issued by corporations

Example: If a firm issues 60 day commercial paper with a face value of $1 million and it receives $985,000, what effective annual interest rate is the firm paying?

$$\text{Effective 60-day rate}=\frac{1m}{985k}-1=1.52\%$$ $$EAR=(1.0152{)}^{365/60}-1=9.6\%$$

Secured loan = loan collateralized by a short-term asset like inventory or A/R

Inventory as collateral

• Floating lien = all of it
• Trust receipt loan = specific inventory items are held and stored
• Warehouse agreement = inventory is used as collateral and stored in a warehouse (escrow)

RAX wants to borrow $5 million for one month. Using its inventory as collateral, it can obtain an 9% (APR with monthly compounding) loan. The lender requires that a warehouse arrangement be used and the warehouse fee is $30,000, payable at the end of the month. RAX estimates it will save $20,000 in storage costs due to the warehouse arrangement. Calculate the effective annual rate (EAR) of this loan for RAX.

$$\text{Monthly interest}=5m\times \frac{9\%}{12}=275k$$ $$\text{Warehouse fee - Storage savings}=30k-20k=10k$$ $$EMR=\frac{37.5k+10k}{5m}=0.95\%$$ $$EAR=(1+0.0095{)}^{12}=12.01\%$$