CAPM Discounted Cash Flow and Valuation

A Case Study of Modigliani- Miller Capital Structure TheoryPart 1- Static TheoryAn enduring controversy within financial theory concerns the effect of financial leverage on the value and stock price of a company. Can a company affect its overall value by selecting an optimal financing mix (debt and equity)? The firm’s mix of debt and equity financing is called its capital structure. The essentials of the capital structure and the effect of financial policies on the value of the firm were pioneering work of Noble recipients Modigliani and Miller in 1958 and 1963.1

The essential question is: Does debt financing create value? If so, how? If not, then why do so many financial mangers try to find the combination of securities that has greatest overall effect on the market value of the firm?

This short case presents a simple model of Modigliani-Miller theorem to highlight the advantage of debt financing and whether there is an optimal capital structure that maximizes the value of the firm. However, it ignores other market imperfections such as bankruptcy and agency problems among security holders that would affect the value of the firm.

Radstone, Inc., a prominent stone fabrication firm was formed 5 years ago to exploit a new continuous fabrication process. Radstone's founders, Jim Rad and Mick Rad, had been employed in the research department of a major integrated-stone fabrication company, but when that company decided against using the new process, they decided to strike out on their own. One advantage of the new process was that it required relatively little capital in comparison with the typical fabrication company, so they have been able to avoid issuing debt financing, and thus they own all of the shares. However, the company has now reached the stage where outside capital is necessary if the firm is to achieve its growth targets. Therefore, they have decided to leverage the company with swapping some of their shares with new debt.

Currently the company has value of $5 million with outstanding shares of 100,000. The company generates $1,538,461.5 in earnings before interest and taxes (EBIT) in perpetuity. The corporate tax rate is 35 percent and all earnings are paid as dividends. The company is considering the effect of $2 million and $2.5 million debt –equity swap on its cost of capital and its value. The cost of debt is 10 percent and the cost of capital is currently 20 percent. Any investment in net working capital and capital expenditure is equal to its depreciation allowances. The corporate tax rate is 35 percent.

Table 1 Current Debt Debt

Capital

Structure $2,000,000 $2,500,000 Pure Business Cash Flows: EBIT Taxes (@ 35%) Net Income +Depreciation -Capital Exp. -Change in net working capital Free Cash Flow Unlevered WACC

1. The original paper is Franco Modigliani and Merton Miller, “The Cost of Capital, Corporation Finance and the Theory of Investment,” American Economic Review (June 1958). Modigliani, F.; Miller, M. (1963). "Corporate Income Taxes and the Cost of Capital: A Correction," American Economic Review, June 1963.

Value of Pure Business Flows:(FCF/Unlevered WACC) Financing Cash Flows Interest at 10% Tax Reduction Pretax Cost of Debt Value of Financing Effect: (Tax Reduction/Pretax Cost of Debt Total Value (Sum of Values of Pure Business Flows and Financing effects


Capital

Structure

Book Value of Debt $ - $2,000,000 $2,500,000

Book Value of Equity $5,000,000 $3,000,000 $2,500,000 V=D+E $5,000,000 $5,000,000 $5,000,000 Market Value of Debt $2,000,000 $2,500,000 Market Value of Equity V=D+E Pretax Cost of Debt 10.00% 10.00% 10.00%After-Tax Cost of Debt 35% 6.50% 6.50% 6.50%Market Value Weights of Debt Equity Cost of Equity 20.00% Weighted-Average Cost of Capital 20.00%

EBIT

$ 1,538,461.50

$ 1,538,461.50

$ 1,538,461.50

Taxes (@ 35%) Net Income + Depreciation -change in NWC -Capital exp. Free Cash Flow Value of Firm (FCF/WACC)


Capital

Structure Cash Flow to Debtholders (interest) Pretax Cost of Debt Value of Debt:(Interest/Rd) Cash Flow to Shareholders: EBIT Interest


Pretax Profit Taxes (@ 35%) Net Income + Depreciation - change in NWC - Capital exp. Cash Flow to Shareholders: Cost of Equity Value of Equity (FCFEquity/RE) Value of Equity plus Value of Debt

Questions:

a. What is the value of the firm under each capital structure?b. What is the cost of equity and weighted average cost of capital for each capital structure?c. What is the value of tax shield under each level of debt financing?d. Why does the value of firm change and specifically where do the changes occur?e. As the firm levers up, how does the increase in value get apportioned between

debtholders and stockholders?f. What is the price per share under each capital structure?g. Are the shareholders better or worse off? Explain

Part 2- Dynamic Capital Structure of Modigliani-Miller- Adjusted Present Value (APV)

The Company generated $1,465,201.43 in earnings before interest and taxes (EBIT) last year and is expected to increase by 5 percent for the next 3 years and after which at a constant rate of 3 percent in perpetuity. The expected interest expense is also expected to grow over next 3 years before the capital structure becomes constant. The cost of debt is 10 percent and the Company’s cost of capital currently is 20 percent. Any investment in net working capital and capital expenditure is equal to its depreciation allowances. The corporate tax rate is 35 percent. Using information from part one, answer the following questions for both levels of financing:

a. What is the estimated terminal unlevered value of operations (i.e., the value at Year 3 immediately after the FCF at Year 3)?

b. What is the current unlevered value of operations? c. What is the terminal value of the tax shield at Year 3? d. What is the current value of the tax shield? e. What is the current total value?


Income Statement

Years 12/31/20 12/31/20 12/31/201 12/31/201 12/31/201 $ 12/31/2011. The original paper is Franco Modigliani and Merton Miller, “The Cost of Capital,

Corporation Finance and the Theory of Investment,” American Economic Review (June 1958). Modigliani, F.; Miller, M. (1963). "Corporate Income Taxes and the Cost of Capital: A Correction," American Economic Review, June 1963.

11 12 3 4 5 42,735.00

7

Sales $80,000,

000 $100,000,000

$125,000,000.00

$150,000,000.00

$172,500,000.00

$ 189,750,000.00

$199,237,500.00

Cost of sales

($69,600,000.00)

($87,000,000.00)

($108,750,000.00)

($130,500,000.00)

($150,075,000.00)

$ (165,082,500.00)

($173,336,625.00)

EBITDA

$10,400,000.00

$13,000,000.00

$16,250,000.00

$19,500,000.00

$22,425,000.00

$ 24,667,500.00

$25,900,875.00

Depreciation

($1,750,000)

($2,000,000)

$ (2,500,000)

$ (3,000,000)

$ (3,450,000)

$ (3,795,000.00)

$ (3,984,750)

EBIT $8,650,000

$11,000,000

$ 13,750,000

$ 16,500,000

$ 18,975,000

$ 20,872,500.00

$ 21,916,125

Interest Expense

($900,000)

($1,000,000)

($1,066,000)

($1,113,400)

($1,128,160)

($1,096,696)

($1,008,804)

Taxabele Income

$7,750,000

$10,000,000

$ 12,684,000

$ 15,386,600

$ 17,846,840

$ 19,775,804.00

$ 20,907,321

Tax (40%)

($3,100,000)

($4,000,000)

$ (5,073,600)

$ (6,154,640)

$ (7,138,736)

$ (7,910,321.60)

$ (8,362,928)

Net Income

$4,650,000

$6,000,000

$ 7,610,400

$ 9,231,960

$ 10,708,104

$ 11,865,482.40

$ 12,544,393

Outstanding Shares

10,000,000

10,000,000

10,000,000

10,000,000

10,000,000

$ 10,000,000.00

10,000,000

EPS $0.47 $0.60 $ 0.76

$ 0.92

$ 1.07

$ 1.19

$ 1.25

Dividend

$0.14 $0.18 $ 0.23

$ 0.28

$ 0.32

$ 0.36

$ 0.38

Part 1Part 2Time 1 2 3 4 5

FCF $7,600,0

$7,000,0

$7,000,0

$11,400,00

$11,400,00

$16,360,00

$16,360,

$21,496,00

$21,496,00

$30,255,

$26,270,80


00 00 00 0 0 0 000 0 0 550 0 Change - NWC

$8,000,000

$11,250,000

$11,250,000

$14,500,000

$14,500,000

$17,425,000

$17,425,000

$19,667,500

$19,667,500

$20,900,875

$20,900,875

CapEx

$5,000,000

$10,000,000

$10,000,000

$10,000,000

$10,000,000

$9,000,000

$9,000,000

$6,900,000

$6,900,000

($189,750)

$3,795,000

DCF $ 6,354,393.61

$ 9,394,139.32

$ 12,238,030.12

$ 14,596,944.09

$ 16,193,982.36

Part 3: DCF Balance Sheet Bala

nce Sheet

1.25

1.2 1.15 1.15 1.1 1.1 1.05

1.05 0.1

Year 12/31/2011

12/31/2012

12/31/2013

Adjusted 2013

12/31/2014

Adjusted 2014

12/31/2015

Adjusted 2015

12/31/2016

Adjusted /2016

12/31/2017

Adjusted 2017

Cash $3,0

00,000

$4,000,000

$ 5,000,000.00

$ 5,000,000.00

$ 6,000,000.00

$ 6,000,000.00

$ 6,900,000

$ 6,900,000

$ 7,590,000

$ 7,590,000

$ 7,969,500

$ 7,969,500

Acounts Receivable

$5,000,000

$6,000,000

$ 7,500,000.00

$ 7,500,000.00

$ 9,000,000.00

$ 9,000,000.00

$ 10,350,000

$ 10,350,000

$ 11,385,000

$ 11,385,000

$ 11,954,250

$ 11,954,250

Inventory

$7,000,000

$8,000,000

$ 10,000,000.00

$ 10,000,000.00

$ 12,000,000.00

$ 12,000,000.00

$ 13,800,000

$ 13,800,000

$ 15,180,000

$ 15,180,000

$ 15,939,000

$ 15,939,000

Current Assets

$150,000,000

$18,000,000

$22,500,000.00

$22,500,000.00

$27,000,000.00

$27,000,000.00

$31,050,000.00

$31,050,000.00

$34,155,000.00

$34,155,000.00

$35,862,750.00

$35,862,750.00

Gross Fixed

$35,000,

$40,00

$50,000,

$50,000,

$60,000,00

$60,000,

$69,000,

$69,000,

$75,900,00

$75,90

$79,695,

$79,69


Assets 000 0,000

000.00

000.00

0.00 000.00

000.00

000.00

0.00 0,000.00

000.00

5,000.00

Less: acumulated Depreciation

($6,000,000)

($8,000,000)

($10,500,000)

($10,500,000)

($13,500,000)

($13,500,000)

($16,950,000)

($16,950,000)

($20,745,000)

($20,745,000)

($24,729,750)

($24,729,750)

Net Fixed Assets

29000000

$32,000,000

$39,500,000.00

$39,500,000.00

$46,500,000.00

$46,500,000.00

$52,050,000.00

$52,050,000.00

$55,155,000.00

$55,155,000.00

$54,965,250.00

$54,965,250.00

Total Assets

44000000

$50,000,000.00

$62,000,000.00

$62,000,000.00

$73,500,000.00

$73,500,000.00

$83,100,000.00

$83,100,000.00

$89,310,000.00

$89,310,000.00

$90,828,000.00

$90,828,000.00

Accounts Payable

$4,200,000

$5,000,000

$6,250,000

$6,250,000

$7,500,000

$7,500,000

$8,625,000

$8,625,000

$9,487,500

$9,487,500

$9,961,875

$9,961,875

Notes Payable Interest Rate 5%

$5,000,000

$5,000,000

$5,000,000

$5,000,000

$5,000,000

$5,000,000

$5,000,000

$5,000,000

$5,000,000

$5,000,000

$5,000,000

$5,000,000

Current Liabilities

$9,200,000

$10,000,000

$11,250,000

$11,250,000

$12,500,000

$12,500,000

$13,625,000

$13,625,000

$14,487,500

$14,487,500

$14,961,875

$14,961,875

Long-term Debt (couon rate 7.5%)

$9,000,000

$10,000,000

$10,000,000

$10,000,000

$10,000,000

$10,000,000

$10,000,000

$10,000,000

$10,000,000

$10,000,000

$10,000,000

$10,000,000

New debt

$1,100,000

$790,000

$246,000

($524,400)

($1,464,870)

Total debt

$9,000,000

$11,100,000

$11,100,000

$11,890,000

$11,890,000

$12,136,000

$12,136,000

$11,611,600

$11,611,600

$10,146,730

Commo $10, $10 $10, $10, $10,0 $10, $10, $10, $10,0 $10 $10, $10


n Stock (10m shares par value $1)

000,000

,000,000

000,000

000,000

00,000

000,000

000,000

000,000

00,000

,000,000

000,000

,000,000

New stock

$1,100,000

$790,000

$246,000

($524,400)

($1,464,870)

Total Stock

$11,100,000

$11,100,000

$11,890,000

$11,890,000

$12,136,000

$12,136,000

$11,611,600

$11,611,600

$10,146,730

Paid-in-capital

$10,000,000

$10,000,000

$10,000,000

$13,300,000

$13,300,000

$15,670,000

$15,670,000

$16,408,000

$16,408,000

$14,834,800

$14,834,800

$10,440,190

retained earnings

$5,800,000

$10,000,000

$15,250,000

$15,250,000

$21,550,000

$21,550,000

$28,795,000

$28,795,000

$36,764,500

$36,764,500

$45,132,475

$45,132,475

Equity $20,000,000

$20,000,000

$35,250,000

$39,650,000

$45,950,000

$49,110,000

$56,355,000

$57,339,000

$65,308,500

$63,210,900

$71,578,875

$65,719,395

total Liability & Equity

44000000

$50,000,000

$56,500,000

$62,000,000

$69,550,000

$73,500,000

$81,870,000

$83,100,000

$91,932,000

$89,310,000

$98,152,350

$90,828,000

Additional Funds

$5,500,000

$3,950,000

$1,230,000

($2,622,000)

($7,324,350)

Assumptions and Capital Structure

Capital structure = d/v or d/(d+e)

EXHIBIT 3-Financial Data (Millions)

d/v 20%

Company Elite BIC e/v 80%Debt (Market Value)

$10 $50 0.8

Equity $30 $125 Tax 40%1. The original paper is Franco Modigliani and Merton Miller, “The Cost of Capital,

Corporation Finance and the Theory of Investment,” American Economic Review (June 1958). Modigliani, F.; Miller, M. (1963). "Corporate Income Taxes and the Cost of Capital: A Correction," American Economic Review, June 1963.

Beta 1.5 1.25 Cost of Debt

6.00%

Per Share Data: Cost of Equity

11.80%

Earnings per share

$0.60 $3.25 WACC 10.160000%

Dividend per share

$0.18 $0.65

Stock price (12/31/2012)

$4.00 $36.50

EXHIBIT 4- Total Annual Return , 1926-2012

Geometric Mean

Arithmetic Mean

Small company stocks

12.20%

16.70%

Large company stocks

10.10%

12.10%

Treasury Bonds 5.70% 6.10%Treasury Bills 3.50% 3.50%Inflation 2.90% 3% EXHIBIT 5 Equity Risk Premium Arithmetic Average Geomet

ric Average

MRP T. bills

MRP T. bonds MRP T. bills

MRP T. bonds

1928-2013-Large Cap

8.60% 6.00% 6.60% 4.40%

1928-2013-Small Cap

13.20%

10.60% 13.20% 6.50%

Treasury Bills

Treasury Bonds

Corporate Rate

Yields in 2012 1% 2.80% 6%


CAPM Discounted Cash Flow and Valuation

Documents

Transcript of CAPM Discounted Cash Flow and Valuation