Homework 8.1 Question


Homework 8.1 Question

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NEAS
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Michael DiNicola writes:

I have a question regarding my method of solving the Module 8 Homework, problem 8.1.

Part A. I found the security market line using the given risk free rate of 8%, market risk premium of 7%, and opportunity cost of capital of 15%. This expresses the security market line by the equation: Return on Project = .08 + .07 × Beta

I plugged in the Betas for each project (these are given in the homework) and saw where the "Return on Project" fell relative to the Expected Return (Expected Return was also given in the homework). If the "Expected Return" was higher than the "Return on Project" (above the security market line), I said that the project should be accepted (I accepted projects 1 and 3). Is this the correct method?

NEAS Answer: You have answered Part B here. Part A says that if the firm expects a 15% return on each project (based on the firm’s cost of capital), it takes Projects #3 and #4 and rejects Projects #1 and #2. Part B says: if we use the required return for each project based on its beta, then the required return for Project #1 is 8% + 50% × 7% = 11.5%. The expected return is 12%, so the project should be accepted.

Part B. I used each projects Beta (given in the homework) and calculated its return using the equation above for the security market line. This always lands the project on the security market line; so according to this method, any project should be accepted (which is why it is not the relevant criterion). Is this answering the question appropriately?

NEAS Answer: (See above)


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Bjabb
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Can someone help me out and breakout the detailed approach to 8.2 A.


MConrad
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If you have taken/studied for Course FM, this will be easier to understand.  The equation written by jen11 on 6/20/2005 (see her post previously) is gotten in the same manner you would get the PV of a bond for Course FM.  The payments of 480,000 come from "Fr" in the bond equation, or (6,000,000*.08), and the 6,000,000 is equal to "c" in the bond equation, or the face value.  The PV of a bond = Fr a angle n + cv^n with n = 7 and interest rate 10%.  Hope this helps some!
Newbie34
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I am not sure how to do 8.2 C.  There was answer given of 1.16, but I'm not sure how to get that answer?
Rick Sutherland
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Getting the correct answer for homework exercise 8.2(C) depends on having calculated 8.2(A) and 8.2(B) correctly.

For 8.2(A), you should have an answer of $5,415,790 (see the 6/20/05 posting from jen11 above for how to calculate that).

For 8.2(B), you should have an answer of $24,000,000 (calculated as 500,000 shares times $48 per share).

For 8.2(C), we take a weighted average of the two projects' betas, using the market values from parts (A) and (B) as the weights. So, the answer to part (C) is 5,415,790 / (5,415,790 + 24,000,000) * 0.10 + 24,000,000 / (5,415,790 + 24,000,000) * 1.40 = 1.16.


Jordan
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Question 8.1 makes no sense to me.  Aren't we suppose to treat each project as mini-firms and evaluate them based on their own OCC (Section 10.1 3rd paragraph 9th ed)?  Betas of projects 1-4 suggest that they have a different risk from the company's existing business (company beta is 1), so the company's hurdle rate of 15% should not be used to evaluate each project.  I think ultimately the criterion should be on which project gives the highest NPV based on its own OCC and cash flow.

Or is there something that I'm missing from the question?


ypollack
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I would appreciate some clarification. The value of the firm is $48 * 500,000 = $24,000,000. The value of the debt is $5,415,789.74. The value of the firm equals the debt plus the equity (in Brealey-Myers-Allen tenth edition page 216, the asset value equals the debt plus the equity). Shouldn't the equity equal $24,000,000 minus $5,415,789.74 which equals $18,584,210.26?
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