A123

Chapter 6

Investment Decision Rules

6-1. Your brother wants to borrow $10,000 from you. He has offered to pay you back $12,000 in a year. If the cost of capital of this investment opportunity is 10%, what is its NPV? Should you undertake the investment opportunity? Calculate the IRR and use it to determine the maximum deviation allowable in the cost of capital estimate to leave the decision unchanged. NPV = 12000/1.1 – 10000=909.09. Take it! IRR = 12000/10000 – 1 = 20% The cost of capital can increase by up to 10% without changing the decision 6-2. You are considering investing in a start-up company. The founder asked you for $200,000 today and you expect to get $1,000,000 in nine years. Given the riskiness of the investment opportunity, your cost of capital is 20%. What is the NPV of the investment opportunity? Should you undertake the investment opportunity? Calculate the IRR and use it to determine the maximum deviation allowable in the cost of capital estimate to leave the decision unchanged.

⎛ 1000000 ⎞ NPV = ⎜ ⎟ − 200000 = −6193 9 ⎝ 1.2 ⎠ ⎛ 1000000 ⎞ IRR = ⎜ ⎟ ⎝ 200000 ⎠

1/9

− 1 = 19.58%

Do not take the project. A drop in the cost of capital of just 20 – 19.58 – 0.42% would change the decision. 6-3. You are considering opening a new plant. The plant will cost $100 million upfront. After that, it is expected to produce profits of $30 million at the end of every year. The cash flows are expected to last forever. Calculate the NPV of this investment opportunity if your cost of capital is 8%. Should you make the investment? Calculate the IRR and use it to determine the maximum deviation allowable in the cost of capital estimate to leave the decision unchanged. Timeline: NPV = –100 + 30/8% = $275 million. Yes, make the investment. IRR: 0 = –100 + 30/IRR. IRR = 30/100 = 30%. Okay as long as cost of capital does not go above 30%.

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Berk/DeMarzo • Corporate Finance, Second Edition...