Question

# A project requires an initial investment of \$500,000 depreciated straight-line to \$0 in 12 years. The...

A project requires an initial investment of \$500,000 depreciated straight-line to \$0 in 12 years. The investment is expected to generate annual sales of \$850,000 with annual costs of \$700,000 for 12 years. Assume tax rate of 30% and the market risk premium of 6.0%, and the risk free rate of 10%. If the NPV of the project is \$341,385.22 what is the beta of the project?

Depreciation = Initial Investment / No. of years = \$500,000 / 12 = \$41,666.67

OCF = [(Sales - Costs) x (1 - t)] + [Depreciation x t]

= [(\$850,000 - \$700,000) x (1 - 0.30)] + [\$41,666.67 x 0.30]

= \$105,000 + \$12,500 = \$117,500

To find the cost of capital, we need to put the following values in the financial calculator:

 INPUT 12 -500,000 117,500 0 TVM N I/Y PV PMT FV OUTPUT 21.15

So, Cost of Capital = 21.15%

According to CAPM,

kE = rF + beta[MRP]

21.15% = 10% + beta[6%]

beta = [21.15% - 10%] / 6% = 1.86

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