# Basic concepts in economics

Wyandotte Chemical Company sells various chemicals to the automobile industry. Wyandotte currently sells 30,000 gallons of polyol per year at an average price of $15 per gallon. Fixed costs of manufacturing polyol are $90,000 per year and total variable costs equal $180,000. The operations research department has estimated that a 15 percent increase in output would not affect fixed costs but would reduce average variable costs by 60 cents per gallon. The marketing department has estimated the arc elasticity of demand for polyol to be -2.0.

a) How much would Wyandotte have to reduce the price of polyol to achieve a 15 percent increase in the quantity sold?

b) Evaluate the impact of such a price cut on (i) total revenue, (ii) total costs, and (iii) total profits.

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#### Solution Preview

a) How much would Wyandotte have to reduce the price of polyol to achieve a 15 percent increase in the quantity sold?

Percent change in quantity sold=+15%

Arc elasticity of demand=-2.0

Percent change in price=Percent change in quantity sold/arc elasticity of demand=15%/(-2)= -7.50%

Price should reduce by 7.5%

b) Evaluate the impact of such a price cut on (i) total ...

#### Solution Summary

Solution describes the steps to calculate needed reduction in price to achieve a given target of increase in quantity sold. It also studies the impact of such price change on total cost, total revenue and total profit.

Basic Concepts in Security Valuation

Problem 1

Mudvayne, Inc., is trying to determine its cost of debt. The firm has a debt issue outstanding with 20 years to maturity that is quoted at 107 percent of face value. The issue makes semiannual payments and has an embedded cost of 9 percent annually.

What is the company's pretax cost of debt?

If the tax rate is 35 percent, what is the aftertax cost of debt?

Problem 2

The Zombie Corporation's common stock has a beta of 1.6. If the risk-free rate is 5.6 percent and the expected return on the market is 10 percent, what is the company's cost of equity capital?

Problem 3

Scanlin, Inc., is considering a project that will result in initial aftertax cash savings of $1.78 million at the end of the first year, and these savings will grow at a rate of 2 percent per year indefinitely. The firm has a target debt-equity ratio of 0.80, a cost of equity of 11.8 percent, and an aftertax cost of debt of 4.6 percent. The cost-saving proposal is somewhat riskier than the usual project the firm undertakes; management uses the subjective approach and applies an adjustment factor of 3 percent to the cost of capital for such risky projects.

What is the maximum initial cost the company would be willing to pay for the project?

Problem 4

Erna Corp. has 4 million shares of common stock outstanding. The current share price is $76, and the book value per share is $5. Erna Corp. also has two bond issues outstanding. The first bond issue has a face value of $90 million, has a coupon of 5 percent, and sells for 94 percent of par. The second issue has a face value of $70 million, has a coupon of 6 percent, and sells for 104 percent of par. The first issue matures in 20 years, the second in 3 years.

a. What are Erna's capital structure weights on a book value basis?

b. What are Erna's capital structure weights on a market value basis?

c. Which are more relevant, the book or market value weights?

Problem 5

Mullineaux Corporation has a target capital structure of 45 percent common stock, 15 percent preferred stock, and 40 percent debt. Its cost of equity is 14 percent, the cost of preferred stock is 5 percent, and the pretax cost of debt is 7 percent. The relevant tax rate is 40 percent.

a. What is Mullineaux's WACC?

b. What is the aftertax cost of debt?

Problem 6

Pendergast, Inc., has no debt outstanding and a total market value of $180,000. Earnings before interest and taxes, EBIT, are projected to be $25,000 if economic conditions are normal. If there is strong expansion in the economy, then EBIT will be 10 percent higher. If there is a recession, then EBIT will be 20 percent lower. Pendergast is considering a $60,000 debt issue with an interest rate of 5 percent. The proceeds will be used to repurchase shares of stock. There are currently 6,000 shares outstanding. Ignore taxes for this problem.

a-1. Calculate earnings per share (EPS) under each of the three economic scenarios before any debt is issued.

a-2. Calculate the percentage changes in EPS when the economy expands or enters a recession.

b-1. Assume that the company goes through with recapitalization. Calculate earnings per share (EPS) under each of the three economic scenarios assuming the company goes through with recapitalization

b-2. Given the recapitalization, calculate the percentage changes in EPS when the economy expands or enters a recession.

Problem 7

Rise Against Corporation is comparing two different capital structures: an all-equity plan (Plan I) and a levered plan (Plan II). Under Plan I, the company would have 205,000 shares of stock outstanding. Under Plan II, there would be 155,000 shares of stock outstanding and $2.30 million in debt outstanding. The interest rate on the debt is 6 percent, and there are no taxes.

a. If EBIT is $250,000, what is the EPS for each plan?

b. If EBIT is $500,000, what is the EPS for each plan?

c. What is the break-even EBIT?

Problem 8

Chandeliers Corp. has no debt but can borrow at 8.1 percent. The firm's WACC is currently 9.9 percent, and the tax rate is 35 percent.

a. What is the company's cost of equity?

b. If the firm converts to 25 percent debt, what will its cost of equity be?

c. If the firm converts to 50 percent debt, what will its cost of equity be

d-1 If the firm converts to 25 percent debt, what is the company's WACC

d-2 If the firm converts to 50 percent debt, what is the company's WACC

Problem 9

ABC Co. and XYZ Co. are identical firms in all respects except for their capital structure. ABC is all equity financed with $575,000 in stock. XYZ uses both stock and perpetual debt; its stock is worth $287,500 and the interest rate on its debt is 8.5 percent. Both firms expect EBIT to be $64,000. Ignore taxes.

a. Rico owns $34,500 worth of XYZ's stock. What rate of return is he expecting

b. Suppose Rico invests in ABC Co and uses homemade leverage. Calculate his total cash flow and rate of return.

c. What is the cost of equity for ABC and XYZ?

d. What is the WACC for ABC and XYZ?

Problem 10

Pendergast, Inc., has no debt outstanding and a total market value of $240,000. Earnings before interest and taxes, EBIT, are projected to be $28,000 if economic conditions are normal. If there is strong expansion in the economy, then EBIT will be 12 percent higher. If there is a recession, then EBIT will be 25 percent lower. Pendergast is considering a $140,000 debt issue with an interest rate of 6 percent. The proceeds will be used to repurchase shares of stock. There are currently 12,000 shares outstanding. Ignore taxes for questions a and b. Assume the company has a market-to-book ratio of 1.0.

a-1 Calculate return on equity (ROE) under each of the three economic scenarios before any debt is issued.

a-2 Calculate the percentage changes in ROE when the economy expands or enters a recession.

Assume the firm goes through with the proposed recapitalization.

b-1 Calculate the return on equity (ROE) under each of the three economic scenarios.

b-2 Calculate the percentage changes in ROE when the economy expands or enters a recession

Assume the firm has a tax rate of 35 percent.

c-1 Calculate return on equity (ROE) under each of the three economic scenarios before any debt is issued.

c-2 Calculate the percentage changes in ROE when the economy expands or enters a recession.

c-3 Calculate the return on equity (ROE) under each of the three economic scenarios assuming the firm goes through with the recapitalization.

c-4 Given the recapitalization, calculate the percentage changes in ROE when the economy expands or enters a recession.

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