UNIT 7 SEM PROBLEMS

What impacts the cost of capital? RISKINESS OF EARNING S THE DEBT TO EQUITY MIX OF THE FIRM FINANCIAL SOUNDNESS OF THE FIRM INTEREST RATE LEVELS IN THE US/GLOBAL MARKETPLACE

Cost of equity capital-CAPM Various approaches for computing the cost of equity capital 1.CAPM model Re = Rrf + ß (Rrm - Rrf) Where: Re = Cost of equity Rrf = Risk-free rate Rm = Equity market required return (expected return on the market portfolio) ß = beta

Cost of equity capital-CAPM Example: Let us calculate the cost of equity capital for a company whose Risk-free rate =10%, equity market required return =18% with a beta of 0.5. Re = ( ) = 0.14 or 14%.

Cost of equity capital Bond Yield Plus Risk Premium Approach In this approach, a judgmental risk premium to the observed yield on the long-term bonds of the firm is added to get the cost of equity. Cost of equity = Yield on long-term bonds + Risk Premium. Given, the yield on debt is 10% and the risk premium as 5%, calculate the cost of equity. Cost of equity = = 0.15 or 15%.

Cost of equity capital Bond Yield Plus Risk Premium Approach Challenge to this approach is the determination of the risk premium. There is no objective way to determine it and hence many financial analysts look at the operating and financial risks of the business and arrive at a subjectively determined risk premium that ranges between 2 percent and 6 percent.

Dividend Growth Model Approach -DCF The price of an equity stock depends ultimately on the dividends expected from it. It can be represented as follows Simplifying this equation, we get: and solving for r, we get

Dividend Growth Model Approach A company has issued 5000 equity shares of $100 each. Its current market price is $95 and the current dividend is $4.5 per share. The dividends are expected to grow at the rate of 6%. Compute the cost of equity capital. Here, D1 = $4.5 + growth rate 6% = $4.77 per share P0 = $95 Ke = $ % = 0.11 or 11% $95

Hurdle rates: Hurdle rates are the required rate of return used in capital budgeting. Simply put, hurdle rates are based on the firm’s WACC Large companies, with divisions that have different levels of risk, may choose to have divisional hurdle rates.

WEIGHTED AVERAGE COST OF CAPITAL (WACC) Cost of Capital WACC = wd (cost of debt) + ws (cost of stock/RE) + wp (cost of pf. stock) w d w s w p Think of the firm’s capital structure as a pie, that you can slice into different shaped pieces. The firm strives to pick the weights of debt and equity (i.e. slice the pie) to minimize the cost of capital. THE FIRM’S CAPITAL STRUCTURE IS THE MIX OF DEBT AND EQUITY USED TO FINANCE THE BUSINESS. The firm’s WACC is the cost of Capital for the firm’s mixture of debt and stock in their capital structure.

PROBLEM #1 1. Acme Company, and you were provided with the following data with the following data: Target capital structure: 40% debt, 10% preferred, and 50% common equity. The after-tax cost of debt is 5.00%, the cost of preferred is 8% the cost of retained earnings is 10%. The firm will not be issuing any new stock. What is the firm’s WACC?

PROBLEM #1 WACC=.4(.05)+.10(.08)+.5(.10)=.078

PROBLEM #2 BEST CO sold a $1,000 par value bond that now has 10 years to maturity and an 8.00% annual coupon that is paid SEMI- ANNUALLY. The bond currently sells for $700 and the company’s tax rate is 40%. What is the component cost of debt for use in the WACC calculation?

PROBLEM #2 Step 1- Find the rate Nper=10X2=20 periods Pmt=$80 divided by 2=$40 per period PV= current price negative $700 FV=1000 Type =0 You will get the rate per period=.0678 Multiply with 2 to get annual rate=.1356 or 13.56% Step 2 –Calculate cost of debt Rd=.1356(1-.4 tax rate )= 8.4%after tax cost of debt.

PROBLEM #3 Tapley Inc. recently hired you as a consultant to estimate the company’s WACC. You have obtained the following information. (1) Tapley's bonds mature in 25 years, have a 7.5% annual coupon, a par value of $1,000 and a market price of $ (2) The company’s tax rate is 40%. (3) The risk-free rate is 6.0%, the market risk premium is 5.0 and the stock’s beta is 1.5. (4) The target capital structure consists of 30% debt and 70% equity. Tapley uses the CAPM to estimate the cost of equity, and it does not expect to have to issue any new common stock What is its WACC?

PROBLEM #3- interest rate on debt Step 1- Find the rate Nper=25 periods Pmt=$75 per period PV= current price negative $ FV=1000 Type =0 You will get the rate per period=.081

PROBLEM #3 Step 2 –Calculate cost of debt Rd=.081(1-.4 tax rate )= 4.86%after tax cost of debt. Next- Cost of Capital calculation CAPM= Risk free rate+ Beta times ( risk premium) =6%+ 1.5 times( 5% risk premium) = 6%+7.5% =13.5%

PROBLEM #3 Last step WACC Calculation WACC= % of debt times Cost of Debt + % of Stock times Cost of stock =30% ( 4.86%after tax cost of debt) +70% equity times(13.5%)

PROBLEM #4 You were hired as a consultant to Locke Company, and you were provided with the following data Target capital structure: 40% debt, 10% preferred 50% common equity. The interest rate on new debt is 8% yield on the preferred is 5% the cost of retained earnings is 6%, The tax rate is 50% The firm will not be issuing any new stock. What is the firm’s WACC?.

PROBLEM #4 Cost of debt after tax=. 08 (1-.5 tax rate ) or.04 WACC Calculation=.04 (40% debt or.40 ) +.05 times (10% preferred or.10 ) +.06 times (50% common equity or.5) = WACC=.051

PROBLEM #5 quiz To help finance a major expansion, Dimkoff Development Company sold a bond several years ago that now has 20 years to maturity. This bond has a 7% annual coupon, paid quarterly, and it now sells at a price of $1, The bond cannot be called and has a par value of $1,000. If Dimkoff’s tax rate is 40%, what component cost of debt should be used in the WACC calculation?

PROBLEM #5 Step 1- Find the rate Nper=20 periods times 4=80 Pmt=$70 per period divide by 4= $17.50 PV= current price negative $ FV=1000 Type =0 You will get the rate per period as = 1.52 % Multiply with 4 to get annual rate=1.52% times 4 =6.1% Cost of debt after tax= Annual rate(1-tax Rate).061%(1-.40)=.0366

PROBLEM #6 6. A company’s perpetual preferred stock currently trades at $50 per share and pays a $4.50 annual dividend per share. If the company were to sell a new preferred issue, it would incur a flotation cost of 10%. What would the cost of that capital be?

PROBLEM #6 Step 1- Find the net price of stock after floatation cost $50( or 90% of $50) = $45 Dividend paid is $4.50 Cost of that capital = D1 divided by price of stock after floatation Cost =$4.50/45= 10%

PROBLEM #7 Assume that you are a consultant to Acme Inc. and you have been provided with the following data D1 = $1.00; P0 = $25.00; g = 6% (constant). What is the cost of equity from retained earnings based on the DCF

PROBLEM #7 We know Po= D1 r-g $25 = 1.00 r- 6% Cross multiply to get $25(r-6%) = 1.00 Divide both sides by $25 to get (r-6%) = 1.00 $25 (r-6%)=.04 Add 6% to both sides to solve R= 10%

PROBLEM #8 8. Heinz Inc. hired you as a consultant to help them estimate their cost of capital. You have been provided with the following data: rRF = 4.0%; MRP = 6.0%; b = 1.2 Based on the CAPM approach, what is the cost of equity from retained earnings?

PROBLEM #8 CAPM= Risk free rate+ Beta times ( risk premium) = 4%+ 1.2(6%) =4%+7.2% =11.2%

Payback Example Examine the three projects and note the mistake we would make if we insisted on only taking projects with a payback period of 2 years or less.