# Business, Financial, and Economics math questions

August 13, 2019
###### How much do we sacrifice to protect the environment?
August 13, 2019

Business, Financial, and Economics math questions
Passing along Costs

In 2010, the costs of powdered milk, cocoa, coffee, and wheat rose at double-digit rates. Wildfires in Russia has caused wheat and other crop prices to shoot up. Cocoa prices reached a 33-year high in July, helped along by speculative activities, including the London-based commodity trading house Armajaro Holdings Ltd.’s move to store 240,000 metric tons of cocoa, worth roughly \$1 billion. Tea prices went up significantly on account of higher fuel costs and poor harvests in India.

Big consumer goods companies often find ways to offset the commodity price increases, sometimes through cost0cutting and sometimes by passing along higher prices to retailers and consumers. J.M. Smucker Co. riased prices about 9 percent on products in its coffee lineup, which includes Folgers, Dunkin’ Donuts and Millstone brands. In response to rising milk prices, Danone, which makes yogurt products, increased prices in markets including Mexico and Poland. Unilever’s chief financial officer noted that tea costs have gone up, and Unilever has already sent that higher cost down the chain on its consumer tea products.

1. Suppose the price of coffee beans increases by \$0.20 per pound. What is the effect of this raw material price increase on the demand for roasted coffee? If one pound produces 50 cups of coffee, would the price of a cup of coffee rise by \$0.01? Explain.

2. The article reports that J.M. Smucker Co. plans to increase its coffee prices by 9 percent. If Smucker has a lot of rivals but has a brand name that has value, will this 9 percent increase in retail prices imply that profit will rise by 9 percent?

3. Is it optimal for a firm to slash prices to retain market share? Is cutting prices during a recession and then raising them in a recovery a good strategy?

Profit Maximization

6. The demand function is Q = 100 – 0.5P. The cost function is TC = C = 100 + 60Q + Q^2.

a. Find MR and MC
b. Demonstrate that profit is maximized at the quantity where MR = MC
c. Derive the relationship between marginal revenue and the price elasticity of demand, and show that the profit-maximizing price and quantity will never be in the inelastic portion o the demand curve.

7. Explain the competitive process when a firm earns a positive economic profit.

8. Explain what is different between firms in monopolistic competition and firms in oligopoly. What does this difference mean for prices and quantities and for economic profit.

9. A firm has estimated the following demand function for its product:

Q = 8 – 2P + 0.10I + A

where Q is quantity demanded per month in thousands, P is product price, I is an index of consumer income, and A is advertising expenditures per month in thousands. Assume that P = 10, I = 100, A = 20.
Based on this information, calculate values for: quantity demanded, price elasticity of demand; income elasticity of demand, and advertising elasticity.

12. The market supply and demand functions for a product traded on a perfectly competitive market are given below:

QD = 40-P
QS = -5+4P
Based on this information, calculate the equilibrium price and quantity in the market.

13. Now, suppose the competitive market in 12 is monopolized. Calculate the price and quantity for the market.

Capital Structures

1. The Benly Company needs to raise funds for a major expansion. The company is debating whether to issue stock or to issue bonds. If the company issues bonds, then its debts will increase and it will be under additional stress to ensure that its revenues can cover the costs of its debt. If it issues stock, the current owners will lose power and influence. What should the company do? Explain your answer.

5. The marketing director of National Midland Mortgage has been arguing with senior management about building a \$50 million publishing facility. Other managers worried about the assumptions in the analysis that support the investment – an increase in the number of mortgages processed and a reduction in processing costs. What if the mortgage market did not grow as expected?

a. Should the National Midland invest in the publishing facility?
b. What assumptions might the marketing director have made to make the investment look worthwhile?

6. Bob Davies must decide whether to invest \$100,000 in his own business or in another local business. Both investment projects have an expected life of five years. The cash flow of each is as follows:

Year Davies Other
1 20,000 10,000
2 30,000 10,000
3 40,000 30,000
4 10,000 40,000
5 5,000 50,000

Suppose the risk of the projects is the same and is accounted for by a risk premium of 6 percent per year. Would either investment make sense? Which would be better?

11. Explain what the incentives of bondholders and stockholders are. Are they the same? How do they differ? Will a firm with no debt act differently than a firm with a significant amount of debt?

16. In 2010 few firms were investing in new projects or expanding. Yet, interest rates were extremely low. Why, with this very low cost of capital would firms not be investing in new projects?

Financial Statements

1. Calculate the value added for each of the following firms.

Microsoft:

Value of output 2,750
Wages and Salaries 400
Cost of capital 40
Cost of materials 1650

Barclays Bank:
Value of output 5,730
Wages and Salaries 3,953
Cost of capital 918
Cost of material 556

General Motors:
Value of output 50,091
Wages and Salaries 29,052
Cost of capital 15,528
Cost of material 7,507

5. Explain why economic profit provides a better measure of profit than accounting profit

8. Explain what occurs when a new technology makes another one obsolete in terms of economic profit. Consider firm A to be an existing firm using old technology. Firm B is the new firm with the new technology. Firm A earned positive profits for years, but with the entrance of Firm B, Firm A’s goods and services are no longer desired.

9. In measuring economic profit:

a. How do you deal with a one-time event?
b. How do you deal with money provided by relatives to get the business started?
c. How do you handle off-balance-sheet expenses – that is, expenses that are incurred by the firm but are not measured as part of the firm’s balance sheet?

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