Titan Mining Corporation has 7.6 million shares of common stock outstanding, 280,000 shares of 4.5% preferred stock outstanding, and 165,000 bonds with a semi-annual coupon rate of 5.9% outstanding, par value $2,000 each. The common stock currently sells for $61 per share and has a beta of 1.15, the preferred stock has a par value of $100 and currently sells for $95 per share, and the bonds have 19 years to maturity and sell for 109% of par. The market risk premium is 7.1%, T-bills are yielding 3.5%, and the company’s tax rate is 25%. A. What is the firm’s market value capital structure?
B. If the company is evaluating a new investment project that has the same risk as the firm’s typical project, what rate should the firm use to discount the project’s cash flows?

A. The Capital structure is : 4.23 % - Equity, 6.59 % - Preferred Shares and 89.17 % - Debt

B. The  firm should discount the project’s cash flows at 4.45 %.

Explanation:

Total Market Value = Market Value of Equity + Market Value of Debt + Market Value of Preferred Shares

Market Value of Equity =  280,000 shares × $61

                                      =   $17,080,000

Market Value of Preferred Shares = 280,000 shares × $95

                                                        = $26,600,000

Market Value of Debt = 165,000 bonds × $2,000 × 109%

                                    = $359,700,000

Total Market Value = $403,380,000

Capital Structure :

Weight of Equity = $17,080,000 / $403,380,000 × 100

                            = 4.23 %

Weight of Preferred Shares = $26,600,000 / $403,380,000 × 100

                                              = 6.59 %

Weight of Debt = $359,700,000 / $403,380,000 × 100

                          = 89.17 %

Thus, the market value capital structure is : 4.23 % - Equity, 6.59 % - Preferred Shares and 89.17 % - Debt

Firms use the Weighted Average Cost of Capital (WACC) to discount the project’s cash flows.

Cost of Debt, r

PV = $2000 × 109 % = - $2,100

PMT = ($2,000 × 5.9%) ÷ 2 = $59

n = 19 × 2 = 38

P/YR = 2

FV = $2,000

r = ?

Using a Financial Calculator, Pretax cost of debt, r is 5,47 %

After tax cost of debt = Interest × ( 1 - tax rate)

                                   = 5,47 % × ( 1 - 0.25)

                                   = 4.10 %

Cost of Equity

Cost of Equity = Return on Risk Free Security + Beta × Return on Risk Premium Portfolio

                       = 3.5 % + 1.15 × 7.1%

                       = 11.67 %            

Cost of Preference Stock            

Cost of Preference Stocks = 4.5%

WACC = ke(W/V) + kd(D/V) + kp(P/V)

           =  11.67 % × 4.23 % + 4.10 % × 89.17 % + 4.5% × 6.59 %

           =  4.45 %

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