FIN30210 Lecture Notes - Lecture 7: Marginal Product, Longrun

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ochrecricket616

21 Feb 2017

School

Department

Finance

Course

FIN30210

Professor

Reed

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Homework #4 Pointers (Problems and how to do them in notebook)

● REMEMBER: When your using the midpoint formula to find the price elasticity, TAKE

THE ABSOLUTE VALUE!!

● So when using the elasticity, PUT THE CORRECT SIGN BACK IN

● When you maximize revenue, it has to be when elasticity is 1.

○ So, like with #6, if you were asked previously to maximize revenue or what the

points are at maximum revenue, then you know the elasticity has to be 1 so it’s

unitary elastic.

● WHEN YOU KNOW THE PRICE ELASTICITY, USE THIS EQUATION:

○ Ep = %Change in Q / %Change in P = [(Q2-Q1)/Q1] / [(P2-P1)/P1]

■ NOTE: Midpoint formula is the same EXCEPT instead of putting it over

Q1 or P2, you put it over the average of the 2 [(Q1+Q2]/2)

Lesson 5

The Production Function

● We’re really trying to minimize costs to maximize profits.

The Cobb-Douglas Production Function

● Constant returns to scale, when we double our input, we double our output

Short vs. Long-Run

● Long-run - I can change any one of my inputs in the production process (nothing is

fixed).

● Short-run - Something in the production process is fixed.

● *Returns to scale: long-run

○ = Everything is able to change and we have to change everything

*The Law of Diminishing Marginal Productivity

● Something has to remain fixed

● Output is increasing as I add in more inputs but at a decreasing rate

Total, Average, and Marginal Products

● Hold capital (K) fixed, so looking at the changes of output given the changes of labor (L)

● AP == TP / L = Total Product / Actual Labor

● Marginal product of labor = MP = Change in Q / Change in L = TP’ with respect to labor

○ ANY TIME USE THE WORD MARGINAL, TAKE THE DERIVATIVE

● Problem 5.1: constant returns to scale

● Find the maximum of total product of labor by taking the derivative of total product to

get marginal product and set that to zero.

● Increasing: 1st and 2nd derivatives > 0...

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Document Summary

Homework #4 pointers (problems and how to do them in notebook) Remember: when your using the midpoint formula to find the price elasticity, take. So when using the elasticity, put the correct sign back in. When you maximize revenue, it has to be when elasticity is 1. So, like with #6, if you were asked previously to maximize revenue or what the points are at maximum revenue, then you know the elasticity has to be 1 so it"s unitary elastic. When you know the price elasticity, use this equation: Ep = %change in q / %change in p = [(q2-q1)/q1] / [(p2-p1)/p1] Note: midpoint formula is the same except instead of putting it over. Q1 or p2, you put it over the average of the 2 [(q1+q2]/2) We"re really trying to minimize costs to maximize profits. Constant returns to scale, when we double our input, we double our output.

Related Questions

5. (15 points) Assume that a company is expected to produce EBITDA of $90M in perpetuity. The corporate tax rate the company is subject to is 35%. To maintain the existing production capacities, capital expenditures are expected to be at $10M per year, in perpetuity. Annual depreciation, expected in perpetuity as well, is $10M. The current risk-free rate is 3%, and it is expected to remain so in perpetuity. The company has $200M in long-term debt, which is considered by the bank to be risk-free, so the interest rate the firm pays on its debt is 3%. The company expects to hold that amount of debt in perpetuity. Using stock returns on a comparable company that operates in the same industry, and has debt outstanding equal to 40% of the market value of its total capital, analysts estimated that the comparable companyâs beta is 1.8. The analysts believe the companies are comparable in all respects except for the capital structure, and do not expect that beta to change over time. You also know that the estimate of the market risk premium for the foreseeable future is 5%. Assume that the probability of financial distress for the firm is negligible, so that you can disregard it.

Calculate the total value of the firm.

__________________

Calculate the value of the firmâs equity.

__________________

Calculate the weighted average cost of capital (WACC) the firm should use when evaluating new projects in its industry.

__________________

Assume that the firm decided to issue additional debt in the amount of $150M. Also assume that the risk of the firmâs debt would not change due to the issuance of new debt.

What do you expect the value of the firmâs equity to be if the company were to issue new debt and use the proceeds from this debt issue to repurchase equity?

__________________

What price would the firm repurchase the equity at, assuming the firm has 90K common shares outstanding?

__________________

Calculate the new, post-restructuring WACC.

__________________

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FIN30210 Lecture Notes - Lecture 7: Marginal Product, Longrun

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