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Problem Set 1 Solution Corporate Finance: Theory and Practice (The Chinese University of Hong Kong)

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Remarks: 1. Write or type your answers legibly on an A4-sized paper. 2. Please submit your assignment to the course drop box at CYT 2/F. 3. No late submission is accepted.

Amarasuriya Lever, Inc., a prominent consumer products firm, is debating whether or not to convert its all-equity capital structure to one that is 40 percent debt. Currently there are 2,000 shares outstanding and the price per share is $70. EBIT is expected to remain at $16,000 per year forever. The interest rate on new debt is 8 percent, and there are no taxes. Current D/E: 100% Equity  D/E = 0; V = 2,000 × $70 = $140,000 Proposed D/E: 40% Debt; 60% Equity  D/E = 0.4/0.6 = 0.67 EBIT = 16,000 forever; Rd = 8%; Tc = 0% a)

Ms. Tirichati, a shareholder of the firm, owns 100 shares of stock. What is her cash flow under the current capital structure, assuming the firm has a dividend payout rate of 100 percent?

$16, 000  $8 / Share 2, 000 Payout = 100%  $8 100 Shares $800 NI / #Shares 

b)

What will Ms. Tirichati’s cash flow be under the proposed capital structure of the firm? Assume that she keeps all 100 of her shares. Under the proposed D/E, the firm has to: 1) Borrow 40% of V = $140,000 × 40% = $56,000 2) Buyback E at $70

New #Shares Outstanding = 2,000 

$56, 000  1, 200 $70

After recapitalizing D/E by (1) & (2), the new D/E becomes:

56, 000  0.67 70 1, 200 EBIT - Interest New #Shares $16,000  $56,000  8%  1, 200  $9.6 / Share

NI / #Shares 

$9.6 100 Shares $960 c)

Suppose Amarasuriya Lever does convert, but Ms. Tirichati prefers the current all-equity capital structure. Show how she could unlever her shares of stock to recreate the original capital structure. To unlever: 1) Firm borrows  She lends 40% of her wealth 2) Firm buybacks  She sells 40% of her shares & lends at 8% 40% × 100 Shares at $70 = 40 × $70 = $2,800 Interest income = $2,800 × 8% = $224

$9.6 60 Shares Interest  576  224 (Same as part (a))  800 d)

Using your answer to part (c), explain why Amarasuriya Lever’s choice of capital structure is irrelevant. The question shows no matter how a firm alters its capital structure, shareholders can homemade / re-create the capital structure that they desire. Since they can create any capital structure they like, they won’t pay for a premium for a particular structure. Therefore, capital structure is irrelevant.

Alpha Corporation and Beta Corporation are identical in every way except their capital structures. Alpha Corporation, an all-equity firm, has 5,000 shares of stock outstanding, currently worth $20 per share. Beta Corporation uses leverage in its capital structure. The market value of Beta’s debt is $25,000, and its cost of debt is 12 percent. Each firm is expected to have earnings before interest of $35,000 in perpetuity. Neither firm pays taxes. Assume that every investor can borrow at 12 percent per year. Alpha: 100% Equity; V = 5,000 × $20 = $100,000 Beta: D = 25,000; Rd = 12% EBIT = 35,000 forever; Tc = 0%; Ri = 12% a)

What is the value of Alpha Corporation? V(Alpha) = E(Alpha) = $100,000

b)

What is the value of Beta Corporation? By MMI, V(Beta) = V(Alpha) = $100,000

c)

What is the market value of Beta Corporation’s equity? V(Beta) = D(Beta) + E(Beta) E(Beta) = V(Beta) – D(Beta) = 100,000 – 25,000 = $75,000

d)

How much will it cost to purchase 20 percent of each firm’s equity? Alpha: 20% × 100,000 = $20,000 Beta: 20% × 75,000 = $15,000

e)

Assuming each firm meets its earnings estimates, what will be the dollar return to each position in part (d) over the next year? Alpha: 35,000 × 20% = $7,000 Beta: {35,000 – (25,000 × 12%)} × 20% = $6,400

f)

Construct an investment strategy in which an investor purchases 20 percent of Alpha’s equity and replicates both the cost and dollar return of purchasing 20 percent of Beta’s equity. How an investor in Alpha replicates Beta’s investor cost & return? Following Beta’s investor structure, he invests 20% in Beta’s debt & equity. Investor in Alpha can: 1) Borrow $5,000 (20% × $25,000) 2) Invest $20,000 in Alpha Dollar return = 7,000 – 5,000 × 12% = $6,400  same as part (e) Cost = 20,000 – 5,000 = $15,000  same as part (d)

g)

Is Alpha’s equity more or less risky than Beta’s equity? Explain. Alpha’s equity is less risky than Beta’s as Beta uses leverage.

Locomotive Corporation is planning to repurchase part of its common stock by issuing corporate debt. As a result, the firm’s debt-equity ratio is expected to rise from 40 percent to 50 percent. The firm currently has $7.5 million worth of debt outstanding. The cost of this debt is 10 percent per year. Locomotive expects to have an EBIT of $3.75 million per year in perpetuity. Locomotive pays no taxes. Before: D/E = 0.4; D = 7.5; Rd = 10% After: D/E = 0.5 EBIT = 3.75 forever; Tc = 0% a)

What is the market value of Locomotive Corporation before and after the repurchase announcement? Before: D/E = 0.4  7.5/E = 0.4  E = 18.75 V = D + E = 7.5 + 18.75 = 26.25 After: V = 26.25  MMI

b)

What is the expected return on the firm’s equity before the announcement of the stock repurchase plan? Re = NI/E = (EBIT – Int)/E = [3.75 – (7.5 × 10%)]/18.75 = 16%

c)

What is the expected return on the equity of an otherwise identical all-equity firm? All-equity firm: D/E = 0 MMII: Re = Ra + D/E(Ra – Rd) 0.16 = Ra + 0.4(Ra – 0.1) Ra = 14.29% For all-equity firm, Re = Ra = 14.29% Another way to show is: V = EBIT/r 26.25 = 3.75/r  r = 14.29%

d)

What is the expected return on the firm’s equity after the announcement of the stock repurchase plan? After: Re = Ra + 0.5(Ra – Rd) = 0.1429 + 0.5(0.1429 – 0.1) = 16.44%

Lauria Manufacturing, Inc., plans to announce that it will issue $2 million of perpetual debt and use the proceeds to repurchase common stock. The bonds will sell at par with a 6 percent annual coupon rate. Lauria is currently an all-equity firm worth $10 million with 500,000 shares of common stock outstanding. After the sale of the bonds, Lauria will maintain the new capital structure indefinitely. Lauria currently generates annual pretax earnings of $1.5 million. This level of earnings is expected to remain constant in perpetuity. Lauria is subject to a corporate tax rate of 40 percent. Proposed: D = 2; coupon = 6%; at par  Rd = 6% Current: 100% Equity; V = 10; #Shares = 500,000 EBIT = 1.5 forever; Tc = 40% a) What is the expected return on Lauria’s equity before the announcement of the debt issue? ROE before the announcement: Re = NI/E = (EBIT – Tax)/E = (1.5 – 1.5 × 0.4)/10 = 9% b) Construct Lauria’s market value balance sheet before the announcement of the debt issue. What is the price per share of the firm’s equity? Asset Total

10 10

100% E Total

10 10

Price per share = E/#Shares = 10/0.5 = $20/share c) Construct Lauria’s market value balance sheet immediately after the announcement of the debt issue. Immediate after the announcement but MMI with tax: VL = VU + D × Tc = 10 + 2 × 40% = 10.8

the debt issue:

Asset PV(tax shield) Total

10 0.8 10.8

D E Total

0 10.8 10.8

Note: The announcement of debt issue will increase its value by 0.8 because of the PV(tax shield). Tax affects V when D/E changes. d) What is Lauria’s stock price per share immediately after the repurchase announcement? Price per share = E/#Shares = 10.8/0.5 = $21.6/share e) How many shares will Lauria repurchase as a result of the debt issue? How many shares of common stock will remain after the repurchase? #Shares repurchases = D/New share price = 2m/21.6 = 92,592.59shares #Shares remain = 500,000 – 92,592.59 = 407,407.41shares f) Construct the market value balance sheet after the restructuring. After restructuring, Asset PV(tax shield) Total

10 0.8 10.8

D E 407,407.41@$21.6 Total

g) What is the required return on Lauria’s equity after the restructuring? ROE after restructuring, MMII with tax: Re = Ra + D/E(Ra – Rd)(1-Tc) = 9% + 2/8.8(9% - 6%)(1-40%) = 9.41% > 9% in part (a)

2 8.8 10.8

Steinberg Corporation and Dietrich Corporation are identical firms except that Dietrich is more levered. Both companies will remain in business for one more year. The companies’ economists agree that the probability of the continuation of the current expansion is 80 percent for the next year, and the probability of a recession is 20 percent. If the expansion continues, each firm will generate earnings before interest and taxes (EBIT) of $2 million. If a recession occurs, each firm will generate earnings before interest and taxes (EBIT) of $800,000. Steinberg’s debt obligation requires the firm to pay $750,000 at the end of the year. Dietrich’s debt obligation requires the firm to pay $1 million at the end of the year. Neither firm pays taxes. Assume a discount rate of 13 percent. Steinberg EBIT Payoff to bondholders Payoff to stockholders

Expansion (80%) 2,000,000 750,000 1,250,000

Recession (20%) 800,000 750,000 50,000

Dietrich EBIT Payoff to bondholders Payoff to stockholders

Expansion (80%) 2,000,000 1,000,000 1,000,000

Recession (20%) 800,000 800,000 0

a) What are the potential payoffs in one year to Steinberg’s stockholders and bondholders? What about those for Dietrich’s? Steinberg potential payoffs: E = (0.8 × 1,250,000 + 0.2 × 50,000)/1.13 = 893,805 D = (0.8 × 750,000 + 0.2 × 750,000)/1.13 = 663,717 Dietrich potential payoffs: E = (0.8 × 1,000,000 + 0.2 × 0)/1.13 = 707,965 D = (0.8 × 1,000,000 + 0.2 × 800,000)/1.13 = 849,557

b) Steinberg’s CEO recently stated that Steinberg’s value should be higher than Dietrich’s because the firm has less debt and therefore less bankruptcy risk. Do you agree or disagree with this statement? V(Steinberg) = D + E = 663,717 + 893,805 = 1,557,522 V(Dietrich) = D + E = 849,557 + 707,965 = 1,557,222 The values of the two firms are identical  MMI Note: The EBITs of the two firms are identical; it’s an example of re-distributing of wealth between bond- and stockholders....