Kuai,
I need help in this part:
Debt:
227,000 7.4 percent coupon bonds outstanding, 25 years to maturity, selling for 109 percent of par; the bonds have a $1,000 par value each and make semiannual payments.
Common stock:
8,500,000 shares outstanding, selling for $70.70 per share; the beta is 1.2.
Preferred stock:
447,000 shares of 6 percent preferred stock outstanding, selling for $80.70 per share.
Market:
8 percent expected market risk premium; 6 percent risk-free rate.
The new RDS project is somewhat riskier than a typical project for DEI, primarily because the plant is being located overseas. Management has told you to use an adjustment factor of 3 percent to account for this increased riskiness. Calculate the appropriate discount rate to use when evaluating DEI’s project.
PLEASE HELP ME STEP-BY-STEP!
To calculate the appropriate discount rate for DEI's project, you need to consider the risk factors involved. In this case, the project is riskier due to its location overseas.
Step 1: Find the risk-free rate
The risk-free rate refers to the return on a risk-free investment, such as government bonds. In this case, the risk-free rate is given as 6%.
Step 2: Find the market risk premium
The market risk premium is the additional return investors expect to earn for taking on additional risk compared to a risk-free investment. In this case, the market risk premium is given as 8%.
Step 3: Calculate the adjusted discount rate
Since the project is riskier due to its location overseas, an adjustment factor of 3% is provided. To calculate the adjusted discount rate, you need to add this adjustment factor to the risk-free rate.
Adjusted Discount Rate = Risk-Free Rate + Adjustment Factor
Adjusted Discount Rate = 6% + 3%
Adjusted Discount Rate = 9%
Therefore, the appropriate discount rate to use when evaluating DEI's project is 9%.
To calculate the appropriate discount rate, you need to consider the components of the company's capital structure and the riskiness of the project compared to the company's typical projects.
Step 1: Determine the cost of debt.
The cost of debt is the yield or return required by bondholders. In this case, the company has 227,000 bonds outstanding with a 7.4 percent coupon rate. Since the bonds are selling for 109 percent of par, it means they are selling for $1,090 each. The coupon payments are semiannual, so you need to divide the coupon rate by 2. The formula to calculate the cost of debt is:
Cost of debt = (Coupon payment / Bond price) + (Par value - Bond price) / Number of years to maturity
Coupon payment = (Coupon rate / 2) * Par value
Bond price = Selling price per bond
Calculate the coupon payment:
Coupon payment = (7.4 / 2) * $1,000 = $37
Next, calculate the cost of debt:
Cost of debt = ($37 / $1,090) + ($1,000 - $1,090) / 25 = 0.0339 + (-0.036) = -0.0021
Step 2: Determine the cost of common equity.
The cost of common equity is the return required by shareholders. One way to estimate it is by using the capital asset pricing model (CAPM), which takes into account the risk-free rate, the expected market risk premium, and the company's beta. The formula is:
Cost of equity = Risk-free rate + (Beta * Market risk premium)
Given that the risk-free rate is 6 percent and the expected market risk premium is 8 percent, you can substitute these values into the equation. The beta is given as 1.2.
Cost of equity = 0.06 + (1.2 * 0.08) = 0.06 + 0.096 = 0.156
Step 3: Determine the cost of preferred stock.
The cost of preferred stock is the return required by preferred shareholders. In this case, the company has 447,000 shares of 6 percent preferred stock selling for $80.70 per share. The formula to calculate the cost of preferred stock is:
Cost of preferred stock = Preferred dividend / Preferred stock price
Calculate the preferred dividend:
Preferred dividend = Preferred stock price * Preferred dividend rate
Preferred dividend rate = 6% = 0.06
Preferred dividend = $80.70 * 0.06 = $4.842
Next, calculate the cost of preferred stock:
Cost of preferred stock = $4.842 / $80.70 = 0.06
Step 4: Determine the weights of each component.
The weights represent the proportion of each component in the company's capital structure. To calculate the weights, add up the market values of the debt, common stock, and preferred stock and divide them by the total market value of the capital structure.
Total market value = (Number of bonds * Selling price per bond) + (Number of common shares * Selling price per share) + (Number of preferred shares * Selling price per share)
Total market value = (227,000 * $1,090) + (8,500,000 * $70.70) + (447,000 * $80.70) = $247,330,300
The weight of debt = (Number of bonds * Selling price per bond) / Total market value
Weight of debt = (227,000 * $1,090) / $247,330,300
The weight of equity = (Number of common shares * Selling price per share) / Total market value
Weight of equity = (8,500,000 * $70.70) / $247,330,300
The weight of preferred stock = (Number of preferred shares * Selling price per share) / Total market value
Weight of preferred stock = (447,000 * $80.70) / $247,330,300
Step 5: Calculate the weighted average cost of capital (WACC).
The WACC is the weighted average of the costs of each component, taking into account the weights calculated in step 4. The formula to calculate WACC is:
WACC = (Weight of debt * Cost of debt) + (Weight of equity * Cost of equity) + (Weight of preferred stock * Cost of preferred stock)
WACC = (Weight of debt * -0.0021) + (Weight of equity * 0.156) + (Weight of preferred stock * 0.06)
Substitute the values calculated in step 4:
WACC = (Weight of debt * -0.0021) + (Weight of equity * 0.156) + (Weight of preferred stock * 0.06)
Finally, adjust the WACC for the higher riskiness of the project by adding the adjustment factor of 3 percent:
Adjusted WACC = WACC + Adjustment factor
Now, you can calculate the appropriate discount rate to use when evaluating DEI's project.