Question

In: Finance

Your firm is considering extending its operations by building a new plant, which will require an...

Your firm is considering extending its operations by building a new plant, which will require an initial investment of $500M. You have determined that the new division will have a 50% chance of generating an annual free cash flow of $120M in perpetuity, a 40% chance of an annual cash flow of $75M in perpetuity and a 10% chance that the division will generate zero (0) cash. Your firm uses 30% debt and 70% equity to finance its operations. Its current equity beta is 2.2. The market risk premium (rm-rf) is 7% and the Treasury bill rate is 3%. The cost of debt is 8%.

The tax rate is 25%. What is the discount rate for the project? Should your firm build the new plant?

Expert Solution

Discount rate for the project

Weight of Debt = Wd = 30%

Weight of Equity = We = 70%

Market risk premium =(Rm-Rf) 7%

Equity beta = 2.2

Risk free rate = Rf = Treasury bill rate = 3%

Cost of Equity = re= Rf + Beta* Market Risk Premium

= 3% + 2.2*7%

= 3% + 15.4%

= 18.4%

Cost of Debt = rd =8%

Tax rate = t = 25%

Weighted Average Cost of Capital = [Wd*rd*(1-t)] + [We*re]

= [30% * 8% * (1-25%)] + [70%*18.4%]

= 1.8% + 12.88%

= 14.68%

Therefore, Discount rate for the project is 14.68%

Calculation of NPV of the Project

Initial Investment = $500M

Present value of Perpetuity Cash Flow at 50% = $120 M / 14.68% = $817.438692 M

Present value of Perpetuity Cash Flow at 40% = $75 M / 14.68% = $510.899183 M

Present value of Perpetuity Cash Flow at 0% = $0 M

Expected Present value of Perpetuity Cash Flows = [50% * $817.438692 M] + [40% * $510.899183 M] + [`10% * $0 M ]

= $408.719346 M + $204.359677 M+ $0 M

= $613.079023 M

NPV of the Project = Expected Present value of Perpetuity cash flow - Initial Investment

= $613.079023 M - $500 M

= $113.079023

Therefore, NPV of the Project is $113.08

NPV of the Project is greater than Zero hence the project should build the plant

jeff jeffy answered 1 year ago

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