Need Help on Cost of Equity

R

RG9er

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Dec 15, 2007
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I have been struggling with the following problem for a week. I can't seem to figure it out, despite having the information and the correct formula. I compute it but don't get any of the 4 multiple choices. Here it is:

The Common stock of Detroit Engines has a beta of 1.34. The market rate of return is 11.5 percent and the risk-free rate is 4 percent. What is the firm's cost of equity?

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I am to use the Security Market Line formula (SML) which is Re = Rf + Be (Rm - Rf)

where:

Rf = Risk Free Rate
Rm - Rf = Market Risk Premium (Market Risk Prem. is the difference between rate of return & risk free rate)
Be = Beta

Using the given numbers, I put it: Re = .4 + 1.34 (11.5 - .4)

Here is where I have trouble. I calculate the formula and come up with: 15.27 percent, but this answer is not listed as any of the answers in the multiple choice selections. Am I doing something wrong with my calculations? Did I set up the formula incorrectly? Any help would be appreciated. I have been going nuts over this and am ready to give up. I feel like my math is correct but I MUST be doing something wrong. PLEASE HELP!
 
My calculator produces the same. However, the problem indicates 11.5% and 4%. It seems to me when plugged into the formula you should convert the percents to decimals and use .115 and .04. You gave no indication as to what the choices are, so I don't know if you were only off by the location of the decimal point.
 
Here are the choices:

(a) 10.05 percent
(b) 12.98 percent
(c) 14.05 percent
(d) 15.50 percent
(e) 15.67 percent
 
To do the calculation you must convert the given percents to decimals. Your answer will be in decimal form. If you want your answer expressed as a percent, you must convert from decimal form back to percents.

The Common stock of Detroit Engines has a beta of 1.34. The market rate of return is 11.5 percent and the risk-free rate is 4 percent. What is the firm's cost of equity?

Re = Rf + Be (Rm - Rf)
Re = .04 + 1.34 (.115 - .04) = .04 + 1.34(.075) = .04 + .1005 = .1405 = 14.05%
 
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