3S03_2015_Assignment01_Solution - ECONOMICS 3S03 Industrial...

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ECONOMICS 3S03: Industrial Organization Department of Economics McMaster University Fall 2015 Assignment 1: Solution Due: October 9, 2015 The assignment will be due at the start of class and can be done in groups (maximum of 5 per group). 1 Investment 1.1 Using the model from class about debt and equity investments. What interest rate would the firm have to promise debt holders to make an investor indifferent between holding debt or shares in the company? SOLUTION : Debt holders: E ( r d ) = παI (1 + r ) + (1 - π ) γI - αI αI Equity owners always receive whatever is not paid out to debt holders which gives their expected return as Equity owners: E ( r e ) == π ( σI - αI (1 + r )) + (1 - π )0 - (1 - α ) I (1 - α ) I Now if the firm want to provide an interest rate on the debt such that a potential investor is indifferent between how they invest their money, in terms of expected returns, then we set E ( r d ) = E ( r e ) which gives us r * = σ - 1 - π π 1 - α α γ - 1 1.2 How does the return to equity owners change with the proportion of the investment that is provided by debt? That is, how does the return change with α . Also provide an explanation as to why the expected return increases or decreases. SOLUTION: r E = πI ( σ - α (1 + r )) + (1 - π ) · 0 - (1 - α ) I (1 - α ) I ∂r E ∂α = π ( σ - (1 + r )) (1 - α ) 2 So to determine the sign of this we really need to look at whether σ - (1 + r ) R 0. We know that for the firm to undertake this project that σ α (1 + r ) in order for the firm to at least cover
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the promise to debt holders if the project is successful. Usually we would think that an increase in α will increase the expected return to equity holders because in the even of bankruptcy the assets remains the same (ie zero) while if the project is successful their return increases.
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