# A corporation has 11,000,000 shares of stock outstanding at a price of $40 per share. They just... ## Question: A corporation has 11,000,000 shares of stock outstanding at a price of$40 per share. They just paid a dividend of $2 and the dividend is expected to grow by 4% per year forever. The stock has a beta of .8, the current risk-free rate is 3%, and the market risk premium is 6%. The corporation also has 200,000 bonds outstanding with a price of$1,100 per bond. The bond has a coupon rate of 7% with semiannual interest payments, a face value of $1,000, and 13 years to go until maturity. The company plans on issuing debt until they reach their target debt ratio of 60%. They expect their cost of debt to be 8% and their cost of equity to be 11% under this new capital structure. The tax rate is 40% a. What is the required return on the corporation's stock? b. What is the expected return on the corporation's stock? c. What is the yield to maturity on the company's debt? d. What percent of their current market value capital structure is made up of debt? e. What is their WACC using their target capital structure and expected costs of debt and equity under the target capital structure? f. Given the new cost of debt, what should be the new price of the bond? g. Given the new cost of equity, what should be the new price of the stock? ## Cost of capital: Cost of Capital is the rate of return that is the firm expects to earn from its cash flows to satisfy the incremental value of the firm. We know for any business the primary target is to create value or generate the net cash flows which should compensate for the investments. However, the cost of capital depends on the source of capital (generally an equity cost of capital is higher than the debt capital cost). The composite cost of capital (WACC) is calculated as the weighted cost of capital from all applicable sources. ## Answer and Explanation: • Price P =$40
• D0 = $2 • g = 4% • beta = 0.8 • Rf = 3% • MRP = 6% a. What is the required return on the corporation's stock? From CAPM model, required rate of return Kr= Rf+ beta*MRP =3%+ 0.8*6% =7.80% b. What is the expected return on the corporation's stock? From the stock valuation model we get P0 = D1/(Ke-g) where Ke = required rate of return So {eq}$40 = $2*(1+4\%)/(Ke-4\%) ...............(1) {/eq} Solving the equation (1) for Ke we get {eq}Ke = 9.20\% {/eq} c. What is the yield to maturity on the company's debt? We assume semiannual YTM = r We know, value of the bond will be: We know, value of the bond: {eq}P = c * F * [1 - 1/(1 + r)^t]/r + [F* /(1 + r)^t] ...............2) {/eq} Where, • r is the YTM • c is the periodic coupon rate on the bond (i.e. annual coupon rate divided by number of coupon payments per year), • t is the total number of coupon payments outstanding till maturity and • F is the face value of the bond Putting the values in (2) we get {eq}$1100 = $1000*3.5%*[ 1-1/(1+r)^{26} )] /r +$1000/(1+r)^{26} .............(3) {/eq}

Solving for r in (3) we get

r = 2.94%

So, annual yield = 2.94%*2 = 5.88%

d. What percent of their current market value capital structure is made up of debt?

Value of debt = 200,000*$1100 =$ 220,000,000

Value of stock = 11,000,000*$40 =$ 440,000,000

So proportion of debt = $220,000,000/ ($ 220,000,000+ $440,000,000) =33.33% e. What is their WACC using their target capital structure and expected costs of debt and equity under the target capital structure? Target capital structure = D/(D+E) = 60% They expect their cost of debt to be 8% and their cost of equity to be 11% at target capital structure. WACC = Ke*We+ Kd*Wd*(1-Tax) =11%*40% + 8%*60%*(1-40%) =7.28% f. Given the new cost of debt, what should be the new price of the bond? We assume the new price of the bond = P1 From (2) we get: {eq}P 1=$1000*3.5\%*[ 1-1/(1+4\%)^{26} )] /r + $1000/(1+4\%)^{26} {/eq} =$ 920.09

g. Given the new cost of equity, what should be the new price of the stock?

We assume the new price = P2

Considering the dividend discount model, we get

P2 = D1/(Ke-g) = $2*(1+4%)/(11%-4%) =$ 29.71

Required Return vs. Cost of Capital

from

Chapter 14 / Lesson 1
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Let's take a look at how required return and cost of capital each offer different perspectives in figuring out the opportunity cost of different investment decisions.