09 cost of capital - lecture problems solutions

# Npv c c 1 1r 1 c 2 1r 2 c 3 1r 3 c 2000000 c 1 c 2 c

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NPV = C 0 + [C 1 / (1+r) 1 ] + [C 2 / (1+r) 2 ] + [C 3 / (1+r) 3 ] + … C 0 = -\$2,000,000 C 1 , C 2 , C 3 , … make up a growing perpetuity where C 1 = \$200,000 and g = .006 The present value of C 1 , C 2 , C 3 , … = C 1 / (r – g) Because the project is considered by all to be more risky than the average-risk project at Wawanakwa, the project’s cost of capital is greater than Wawanakwa’s WACC. Since the difference between the cost of capital for this project and the cost of capital for an average-risk project at Wawanakwa is 3 percentage points, r = WACC for Wawanakwa + .030 = .086 + .030 = .116 NPV = -2,000,000 + 200,000/(1.116) 1 + (200,000×1.006)/(1.116) 2 + (200,000×1.006 2 )/(1.116) 3 + ... = -2,000,000 + present value of a growing perpetuity where C 1 =200,000, g=.006, and r=.116 = -2,000,000 + [200,000 / (.116 – .006)] = -2,000,000 + [200,000 / .110] = -2,000,000 + 1,818,182 = -181,818 NPV < 0, so Wawanakwa should not pursue the project 5

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Lecture problems – cost of capital Part E: Should Wawanakwa Corporation, which has a WACC of 8.6% and makes frozen food for grocery stores, undertake a project to open a restaurant if the restaurant project would involve an investment of \$2 million today, an expected cash flow of \$200,000 in one year, and subsequent cash flows that would continue forever and increase by 0.6 percent every year? Some key WACCs include those of Wawanakwa (8.6%), the average WACC for frozen food industry (13.6%), Darden which owns Olive Garden, Red Lobster, & others (14.6%), and Safeway (9.6%). NPV = C 0 + [C 1 / (1+r) 1 ] + [C 2 / (1+r) 2 ] + [C 3 / (1+r) 3 ] + … C 0 = -\$2,000,000 C 1 , C 2 , C 3 , … make up a growing perpetuity where C 1 = \$200,000 and g = .006 The present value of C 1 , C 2 , C 3 , … = C 1 / (r – g) r = the WACC for Darden = .146, because the appropriate cost of capital for any project is based on the risk of the project, and the most appropriate cost of capital in this case would be the cost of capital associated with the risk of opening and running restaurants, which is what Darden does, not necessarily the risk of making frozen food for grocery stores, which is what Wawanakwa does, the risk of opening and running grocery stores, which what Safeway does, or the risk associated with the frozen food industry.
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