Capital Structure, Mergers & Acquisitions, and Leasing: A Comprehensive Guide

Posted on May 22, 2024 in Economy

Chapter 17: Capital Structure: Limits to Debt

17.5 Signaling

Investors view debt as a signal of firm value:

• If a firm has a high level of debt, investors will think that the firm has high anticipated profits.
• If a firm has a low level of debt, investors will think that the firm has low anticipated profits.

The firm’s capital structure optimization: Marginal benefit of debt = Marginal cost of debt.

Firms with high anticipated profits have lower expected bankruptcy costs; hence, they want to have more debt.

If managers want to fool investors:

• The more valuable firms will want to issue more debt than less valuable firms. The cost of extra debt increases with the amount of debt, which will prevent less valuable firms from issuing more debt than the more valuable firms.

The Free Cash Flow Hypothesis

The Free Cash Flow Hypothesis states that:

• An increase in dividends should benefit the stockholders by reducing the ability of managers to pursue wasteful activities.
• An increase in debt will reduce the ability of managers to pursue wasteful activities more effectively than dividend increases.

The Pecking-Order Theory

The Pecking-order Theory states that “firms prefer to issue debt rather than equity if internal finance is insufficient.” The order of capital for an investment project: internal funds, followed by new debt issue, then new equity issue.

1. If a manager believes that equity is overpriced, they will want to issue more equity.
2. If a manager believes that equity is underpriced, they will want to use an alternative source of financing.

Result: The market sees an equity issue as a signal that equity is overpriced, which results in the drop of the share price. The same is true for debt but to a lesser degree.

If bonds are overpriced (i.e., the yield is too low because the market underestimates the true probability of bankruptcy), the manager wants to issue debt. This results in a downward shift in the belief about the well-being of the firm, which leads to the drop of the share price.

Chapter 30: Mergers and Acquisitions

ΔV = V_AB – (V_A + V_B). The synergy can be determined by the discounted cash flow model:

• Value of Firm B to firm A is: V_B* = V_B + ΔV
• The NPV from the merger for firm A is: NPV = V_B^* – Cost to Firm A of the acquisition.

Example of a Merger with Common Stock

Alternative solution:

Since shareholders of firm A gain $100-$80=$20, the share price = $20/100=$0.20 from $700/100=$7 per share to $7+$0.20=$7.20 per share. That is, the after-merger share price will be P_AB=$7.20. Since shareholders of firm B must receive $280, we should give them N shares so that N*$7.20=$280; thus, N=280/7.20=38.88 shares.

About Synergy

A firm will use stocks if synergy is small and cash if synergy is high:

• Implication 1: A cash offer may signal a high synergy level to the market and lead to an increase in the acquirer’s stock price.
• Implication 2: A cash offer may signal a high synergy level to the target firm and lead to an increase in the price demanded by the target.

Cash vs. Common Stock

• Implication 1: Using stock as a method of payment sends a “bad” signal to the market and results in the drop in the acquirer’s share price.
• Implication 2: Using stock as a method of payment sends a “bad” signal to the target and results in a higher price demanded by the target firm.

Chapter 22: Leasing

• A lease is a contractual agreement between a lessee and a lessor.
• The agreement establishes that the lessee has the right to use an asset and, in return, must make periodic payments to the lessor.

The Basic Types

• Operating Leases: Usually not fully amortized, requires the lessor to maintain and insure the asset, and the lessee has the option to cancel the contract before the expiration date.
• Financial Leases: The lessor does not provide maintenance or service, the lease is fully amortized, the lessee usually has the right to cancel before the expiration date, and financial leases can’t be canceled.
• After-Tax Cost of Debt: This is the discount rate to use because lease payments and tax shields are riskless cash flows.

NPV Analysis of Buy vs. Lease

• Leasing: NPV of Leasing = Cost of machine – , r: after-tax cost of debt.
• Buy: NPV = -cost of machine + , using a financial calculator for and entering N=5; I/Y=5; PMT=5,825, CPT PV.

Chapter 19: Dividends

Dividend policy is irrelevant. Investors do not need dividends to convert shares to cash; they will not pay higher prices for higher dividend payouts. They use homemade dividends.

• In a perfect world, the stock price will drop by the amount of the dividend on the ex-dividend date.

Homemade Dividends

Example: ABC Inc. is an all-equity firm that expects to generate EBIT=$100,000 this year (t=0) and EBIT of $200,000 next year (t=1) at which time it will cease to exist. It plans to pay $50,000 in dividends to its shareholders at t=0 and invest the remaining $50,000 for one year at 10%. Assume everyone is risk-neutral, the risk-free interest rate is 10%, and the firm has 10,000 shares outstanding.

Yuri does not like these high dividends and would rather have only D=$2/share paid. If Yuri has 600 shares, what should he do? ABC will pay D=$5/share, and its ex-dividend price will be {($50K*1.1+$200K)/1.1}/10,000=$23.18.

Yuri would like to receive only $2*600=$1200 instead of 5*600=$3000 that he will receive. Hence, he should use $1,800 to buy 1800/$23.18=77.65 shares right after the dividends are paid.

The net income of ABC Inc. is $45,000. The company has 20,000 outstanding shares and a 100% payout policy. The expected value of the firm one year from now is $1,635,000. The appropriate discount rate for ABC is 12%, and the dividend tax rate is zero.

1. What is the current value of the firm assuming the current dividend is not paid?
2. What is the ex-dividend price of Rookie’s stock if the board follows its current policy?
3. They proposed that Rookie sell enough shares to finance a $4.60 dividend. Comment on the claim that the low dividend is depressing the stock price. Support your argument with calculations.
4. At what price will the new shares sell? How many will be sold?

Solution:

1. Value = $45,000 + $1,635,000/1.12 = $1,504,821
2. Cum-dividend stock price = $1,504,821/20,000 = $75.24
   Current dividend = $45,000/20,000= $2.25
   Ex-dividend stock price = $75.24 – 2.25 = $72.99
3. According to MM, dividend policy is irrelevant. If the dividend increases to $4.60, then:
   Total dividends = $4.60*20,000=$92,000
   Dollars raised = $92,000 – 45,000 = $47,000
   New shareholder value in one year = $47,000*1.12 = $52,640. Old shareholder value in one year = $1,635,000 – 52,640 = $1,582,360
   Current value of the firm: $92,000 + $1,582,360/1.12= $1,504,821

Chapter 16: Capital Structure

R.O.A = (earnings/Assets), R.O.E = (Earnings/Equity)

E.P.S = (earnings/shares)

E.B.T = (Earnings Before Taxes – Interest)

No Taxes

• Modigliani-Miller Proposition I: V_L = V_u: The value of the levered firm is the same as the value of the unlevered firm.
• MM Proposition II:
• Leverage increases risk and return to stockholders (cost of equity).

r_s: Expected return on equity or stock, cost of equity, r_B= Cost of Debt, interest rate, R₀ = ROE_unlevered

Quiz Example

If the firm with D=E=$1M would like to increase its D/E ratio from D/E=1 to D/E=3, how much additional debt is needed? Answer: V=2M, Vu=Vl=, hence, new D=$1.5M; hence, the firm needs to issue $500,000 of new debt. (D/E = 3 means D/V= 3/4 à V = D* 4/3 à new D = (2×3)/4) = 1.5

With Taxes

• MM Proposition I: V_L = V_U + T_C B Shareholders can achieve any pattern of payouts through homemade leverage. They increase the firm’s value. There is NO CHANGE in THE STOCK PRICE in the MM Theorem.
• Vu = [EBIT*(1-Tc)]/Ro, Ro: cost of capital on all equity firms.
• V_L =

T_C B: Present value of the tax shield.

• MM Proposition II with Taxes:
• Leverage increases the risk and return to stockholders.

Quiz Example

If the firm with D=E=$1M increases its D/E ratio to D/E=3, how much additional debt is needed if the corporate tax rate is 20%? Answer: 2M=V_L=V_U+0.2*D= V_U+0.2*1. Hence, V_U=$1.8M. Under the new D/E ratio, D/V=3/4 or V=D*4/3. Hence, D*4/3=V= V_U+0.2D=1.8+0.2D. Therefore, new debt D=1.8/(4/3-0.2)=1.58824 (accept it as the correct answer). Hence, the firm needs to issue an extra $0.58824M.

Homemade Leverage

Shortcut: The expected return on your strategy (borrow and buy an unlevered firm) should be the same as the expected return on levered equity. If you want to invest $K of your own money, you want to borrow $B to achieve “homemade” B/K=D/E of the levered firm.

If for each $1 of your own investment you borrow $x, your expected return will be (1+x)*RU-x*RD.

Hence, solve ($1+x)*R_U-x*R_B=R_L to find x.

Homemade Unleveraged

Shortcut: Invest in the equity of a levered firm (XYZ) and at the risk-free rate in the same proportion as the D/E ratio in the levered firm. Think of it as buying debt and equity of XYZ in the proportion that will guarantee yourself a fixed share of the firm’s profit in any state of the world. The expected return on your strategy should be the same as the expected return on levered equity.

If for each $1 of your own investment you invest $x (D/E) at the risk-free rate, your expected return will be (1-x)*RL+x*Rb. Hence, solve ($1-x)*RL + x*Rb=RU to find x, where RB= interest rate.

If you spend $1000, you need to borrow (1,000*X) from the levered firm and (1000*1-X) at the risk-free rate.

Quiz Example

If the firm with D=E=$1M increases its D/E ratio to D/E=3, how much additional debt is needed if the corporate tax rate is 20%? Answer: 2M=V_L=V_U+0.2*D= V_U+0.2*1. Hence, V_U=$1.8M. Under the new D/E ratio, D/V=3/4 or V=D*4/3. Hence, D*4/3=V= V_U+0.2D=1.8+0.2D. Therefore, new debt D=1.8/(4/3-0.2)=1.58824 (accept it as the correct answer). Hence, the firm needs to issue an extra $0.58824M.

Homemade Leverage

Shortcut: The expected return on your strategy (borrow and buy an unlevered firm) should be the same as the expected return on levered equity. If you want to invest $K of your own money, you want to borrow $B to achieve “homemade” B/K=D/E of the levered firm.

If for each $1 of your own investment you borrow $x, your expected return will be (1+x)*RU-x*RD.

Hence, solve ($1+x)*R_U-x*R_B=R_L to find x.

Homemade Unleveraged

Shortcut: Invest in the equity of a levered firm (XYZ) and at the risk-free rate in the same proportion as the D/E ratio in the levered firm. Think of it as buying debt and equity of XYZ in the proportion that will guarantee yourself a fixed share of the firm’s profit in any state of the world. The expected return on your strategy should be the same as the expected return on levered equity.

If for each $1 of your own investment you invest $x (D/E) at the risk-free rate, your expected return will be (1-x)*RL+x*Rb. Hence, solve ($1-x)*RL + x*Rb=RU to find x, where RB= interest rate.

If you spend $1000, you need to borrow (1,000*X) from the levered firm and (1000*1-X) at the risk-free rate.

Examples of Bankruptcy Costs

• A reduction in sales due to customers’ hesitation to buy from a company that has a high chance of declaring bankruptcy and not honoring its warranty.
• Legal fees that the company needs to pay during the bankruptcy procedure.
• Shareholders’ desire to invest in risky projects even when such projects have a negative NPV.

Example 1

ABC Inc. expects to generate a risk-free EBIT of $15,000 by the end of this year, and it expects it to grow at a steady rate of 4% per year forever. The cost of debt is 6%. The corporate tax rate is 20%. Find the optimal D/E ratio (assume no or infinitesimal bankruptcy costs). Answer: D/E=0.5. Because taxes are positive, interest payments must be equal to EBIT. Hence, current debt must be equal to D=15000/0.06=$250K (so that I=$250K*0.06=$15,000), and it should grow at 4% forever. Hence, V=15000/(0.06-0.04)=$750K. Since D=$250K, we must have E=$750K-$250K=$500K and D/E=$250K/$500K=0.5.

Example 2

Consider a 2-period model (T=0 and T=1) in which a firm has $200K in debt payable at T=1 (note: this is the total debt payable at T=1 and includes both the principal and the interest). Next year (at T=1), the firm can generate either $150K with a probability of 20% or $300K with a probability of 80%. Find the administrative cost of bankruptcy (in the event that the firm becomes bankrupt) if everyone is risk-neutral, the annual interest rate is 7%, and today’s (at T=0) value of debt is $175K. Answer: $13.75K. Solution: ((150-x)*0.2+200*0.8)/1.07=$175. Hence, x=(200*0.8+150*0.2-175*1.07)/0.2=$13.75K.