Appearance
question:Scanlin, Inc. is evaluating a project with initial aftertax cash savings of 1.81 million at the end of the first year. These savings are expected to grow at a 1% annual rate indefinitely. The company targets a debt-equity ratio of 0.75, with a cost of equity of 12.1% and an aftertax cost of debt of 4.9%. Since this project is riskier than the firm's typical ventures, an adjustment factor of 2% is applied to the cost of capital. What is the maximum amount Scanlin, Inc. would be willing to pay for the project, ensuring the net present value (NPV) remains zero?
answer:To determine the maximum initial cost, we must calculate the net present value (NPV) at which it becomes zero. First, we find the adjusted weighted average cost of capital (WACC). Given the debt-equity ratio of 0.75, the equity weight is 1 - 0.75 = 0.25. With a 2% risk adjustment, the WACC is calculated as follows: WACC = (Debt Weight * After-Tax Cost of Debt) + (Equity Weight * Cost of Equity) WACC = (0.75/1.75) * 4.9% + (0.25/1.75) * (12.1% + 2%) WACC = 0.4286 * 4.9% + 0.1429 * 14.1% WACC ≈ 9.01% Next, we discount the aftertax cash savings to their present value: Present Value of Savings = Initial Savings / (WACC - Growth Rate) Present Value of Savings = 1.81 million / (9.01% - 1%) Present Value of Savings ≈ 22.60 million Thus, the maximum initial cost that Scanlin, Inc. would be willing to pay for the project is 22.60 million, ensuring a zero NPV.
question:Cook Company's condensed income statement for the year ending December 31, 2011, includes the following: - Income before extraordinary gain: 30,000 - Extraordinary gain, net of tax expense of 2,000: 5,000 - Net income: 35,000 - Preferred stock dividends declared: 3,000 - Common stock dividends declared: 5,000 - Common stock outstanding at the beginning of 2011: 20,000 shares - Additional common shares issued on July 1, 2011: 1,000 shares - Preferred stock is non-convertible. Calculate the earnings per share (EPS) and determine the recurring EPS.
answer:a. To calculate the earnings per share (EPS), we use the following formula: EPS = (Net income - Preferred dividends) / Weighted average of common shares outstanding The weighted average of common shares for the year, including the additional shares issued on July 1, is: 20,000 shares (beginning of year) + (1,000 shares × 6/12) = 20,000 shares + 500 shares = 20,500 shares Now, let's calculate the EPS: EPS = (35,000 - 3,000) / 20,500 shares EPS = 32,000 / 20,500 shares EPS = 1.56 per share b. To determine the recurring EPS, we exclude the extraordinary gain: Recurring EPS = (Net income - Preferred dividends - Extraordinary gain) / Weighted average of common shares outstanding Recurring EPS = (35,000 - 3,000 - 5,000) / 20,500 shares Recurring EPS = 27,000 / 20,500 shares Recurring EPS = 1.32 per share Thus, the recurring EPS is 1.32 per share.
question:Find the value of x if f(x) = 22, given that f(x) = 2(x + 6).
answer:To find the value of x, we can substitute f(x) with 22 in the given equation and solve for x. f(x) = 2(x + 6) 22 = 2(x + 6) 11 = x + 6 x = 11 - 6 x = 5 Therefore, the value of x is 5.
question:Evaluate the function f(x) = e^{2x+5} + cos(9-9x) at the point x = -17.
answer:To evaluate the function f(x) at x = -17, we substitute -17 for x in the expression: f(-17) = e^{2(-17) + 5} + cos(9 - 9(-17)) f(-17) = e^{-34 + 5} + cos(9 + 153) f(-17) = e^{-29} + cos(162) Now, calculate the exponential and cosine terms: f(-17) = frac{1}{e^{29}} + cos(162) f(-17) approx 0.000000000000000000000000000000000067 + 0.206 Rounded to a more manageable precision for educational purposes: f(-17) approx 0.206 Therefore, the value of the function at x = -17 is approximately 0.206.