Exam 6: Differential Calculus Techniques in Management and Long-Term Investment Analysis

RCB Corporation is considering the purchase of a machine for which the initial cash outlay will be $100,000. Predicted net cash inflows before depreciation and taxes are $25,000 per year for the next five years. The machine will be depreciated (using the straight-line method) over the 5-year period with a zero estimated salvage value at the end of the period. The corporation's marginal tax rate is 40 percent and its cost of capital is 12 percent. (a)Determine the annual net cash flow after depreciation and taxes for years 1-5. (b)Determine the internal rate of return. (c)Determine the net present value. (d)Should RCB purchase the machine? Why or why not? NOTE: This problem requires the use of present value tables or a financial calculator.

The production superintendent of the Holloway Company has proposed that the firm purchase a new $40,000 grinding machine for use in the plant. The machine is expected to generate $10,000 per year in pre-tax cash savings (labor and spoilage) for the next 10 years. At the end of 10 years the salvage value of the machine is estimated to be $5,000. Holloway uses straight-line depreciation and its marginal income tax rate is 40 percent. The firm's cost of capital is 12 percent. (a)What are the net cash inflows after depreciation and taxes for the machine in years 1-10? (b)What is the net present value for the machine? (c)What is the internal rate of return for the machine? (d)Would you recommend purchasing the machine? Why or why not? NOTE: This problem requires the use of present value tables or a financial calculator.

The capital structure of Wildcat Wells, an independent petroleum exploration and drilling company, consists of 40 percent debt and 60 percent equity capital. Debt capital consists of a bond (which matures in 10 years) issued five years ago at an interest rate of 10 percent. Since then market interest rates have risen substantially. The firm has been advised by its investment banker that additional debt financing (bonds) could be obtained at a rate of 12 percent. In the last six years of operations, Wildcat Wells has averaged a 12 percent compound rate of growth in earnings and dividends. This rate is expected to continue for the foreseeable future. Next year's dividend is projected to be $.75 per share. The firm's stock is currently selling for $25 per share. Wildcat Wells has a 40 percent marginal income tax rate. (a)What is the firm's after-tax cost of debt financing? (b)What is the firm's after-tax cost of internal equity capital? (c)Assuming that Wildcat Wells plans to maintain its present capital structure, what is the firm's weighted cost of capital?

Project post-audit reviews are rarely of practical value because capital investments are sunk, irreversible costs.

Aspen Industries currently pays an annual common stock dividend of $5.00 per share. The company's dividend has grown steadily over the past 10 years at a 7 percent rate and this rate is expected to continue for the foreseeable future. The company's stock currently sells for $70 per share. The company can issue new common stock at a net price of $65 per share. (a)Determine the firm's cost of internal equity capital using the dividend capitalization (constant-growth) model. (b)Determine the firm's cost of external equity capital using the dividend capitalization (constant-growth) model.

Piedmont Power Company's common stock has a beta, $\beta$ , estimated to be .85. The risk-free rate is 8 percent and the expected market return is 14 percent. Compute Peidmont's cost of equity capital.

If the first derivative of Y with respect to X is: dY/dX = -4.X², then the second derivative is: