### Calculate the variance on a portfolio

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QUESTION 1

ExxonMobil (NYSE: XOM) is currently trading at \$20.75 on the NYSE. ExxonMobil is also listed on NASDAQ and assume it is currently trading on NASDAQ at \$20.50.

QUESTION: Does an arbitrage opportunity exist and if so how would you exploit it and how much would you make on a block trade of 1,000 shares?

QUESTION 2

SmithBuilt Corp. (SMI) is expected to have a 25 percent growth rate for the next four years (affecting D1, D2, D3, and D4). Beginning in year five, the growth rate is expected to drop to 7 percent per year and last indefinitely.

QUESTION: If SMI just paid a \$2.00 dividend and the appropriate discount rate is 15 percent, then what is the value of a share of SMI?

QUESTION 3

Consider two mutually exclusive projects with the following cash flows:

 Project C/F0 C/F1 C/F2 C/F3 C/F4 C/F5 C/F6 TRO \$(41,215) \$12,500 \$14,000 \$16,500 \$18,000 20,000 N/A XYZ \$(46,775) \$15,000 \$15,000 \$15,000 \$15,000 \$15,000 \$15,000

QUESTION: If the discount rate for project XYZ is 15%, then what is the NPV for project XYZ?

QUESTION 4

Consider the following realized annual returns:

 Year End Market Realized Return Microsoft Realized Return 1996 21.2% 88.3% 1997 30.3% 56.4% 1998 22.3% 114.6% 1999 25.3% 68.4% 2000 -11.0% -62.8% 2001 -11.3% 52.7% 2002 -20.8% -22.0% 2003 33.1% 6.9% 2004 13.0% 9.2% 2005 7.3% -0.9%

QUESTION: Using the data provided in the table, calculate the average annual return, the variance of the annual returns, and the standard deviation of the average returns for the market from 1996 to 2005.

QUESTION 5

Consider the following returns:

 Year End Asus Realized Return Dell  Realized Return Oracle  Realized Return 2000 20.1% -14.6% 0.2% 2001 72.7% 4.3% -3.2% 2002 -25.7% -58.1% -27.0% 2003 56.9% 71.1% 27.9% 2004 6.7% 17.3% -5.1% 2005 17.9% 0.9% -11.3%

QUESTION: Calculate the variance on a portfolio that is made up of equal investments in Dell's and Oracle's stock.

QUESTION 6

The Momentus Corporation is considering launching a new product and is trying to determine an appropriate discount rate for evaluating this new product. Momentus has identified the following information for three single division firms that offer products similar to the one Momentus is interested in launching:

 Comparable Firm Equity Cost of Capital Debt Cost of Capital Debt-to-Value Ratio Techtron Corp. 12.50% 6.50% 50% Xenon Inc. 13% 6.10% 40% Flatiron Ltd. 14% 7.10% 60%

QUESTION: Based upon the three comparable firms, calculate the most appropriate unlevered cost of capital for Momentus to use on this new product.

QUESTION 7

Consider a project with free cash flows in one year of \$90,000 in a weak economy or \$117,000 in a strong economy, with each outcome being equally likely. The initial investment required for the project is \$80,000, and the project's cost of capital is 15%. The risk-free interest rate is 5%.

Bancorp Inc. has no debt, a total equity capitalization of \$50 billion, and a beta of 2.0. Included in Bancorp's assets are \$12 billion in cash and risk-free securities.

QUESTION: Calculate Bancorp Inc.'s value and unlevered beta considering the fact that Bancorp's cash is risk-free.

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