Question

Roger has a levered cost of equity of 0.12. He is thinking of investing in a project with upfront costs of $8 million, which pays $2 million per year for the next 8 years. He is going to borrow $4 million to offset the startup costs at a rate of 0.05. His tax rate is 0.3. He will repay this loan at the end of the project. What is the NPV of this project, using the FTE method?

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Correct Answer

643,693 margin of error +/- 10,000

Answer 1

The NPV is computed as shown below:

Net Initial investment is computed as follows:

= - upfront cost + loan amount

= - $ 8,000,000 + $ 4,000,000

= - $ 4,000,000

cash flow of each year from year 1 till year 7 is computed as follows:

= ($ 2,000,000 - Amount of loan x cost of loan) x (1 - tax rate)

= ($ 2,000,000 - $ 4,000,000 x 0.05) x (1 - 0.30)

= $ 1,800,000 x 0.70

= $ 1,260,000

Cash flow of year 8 is computed as follows:

= ($ 2,000,000 - Amount of loan x cost of loan) x (1 - tax rate) - loan repaid

= ($ 2,000,000 - $ 4,000,000 x 0.05) x (1 - 0.30) - $ 4,000,000

= $ 1,800,000 x 0.70 - $ 4,000,000

= $ 1,260,000 - $ 4,000,000

= - $ 2,740,000

So, the NPV will be as follows:

= Net initial investment + cash flow of year 1 / (1 + 0.12)¹ + cash flow of year 2 / (1 + 0.12)² + cash flow of year 3 / (1 + 0.12)³ + cash flow of year 4 / (1 + 0.12)⁴ + cash flow of year 5 / (1 + 0.12)⁵ + cash flow of year 6 / (1 + 0.12)⁶ + cash flow of year 7 / (1 + 0.12)⁷ + cash flow of year 8 / (1 + 0.12)⁸

= - $ 4,000,000 + $ 1,260,000 / 1.12¹ + $ 1,260,000 / 1.12² + $ 1,260,000 / 1.12³ + $ 1,260,000 / 1.12⁴ + $ 1,260,000 / 1.12⁵ + $ 1,260,000 / 1.12⁶ + $ 1,260,000 / 1.12⁷ - $ 2,740,000 / 1.12⁸

= $ 643,693.1943

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