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# pvextra - Present Value and discount rates What is R Econ...

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Present Value and “discount rates” What is R? Econ 71a: Spring 2007 Lecture 3.1(extra)

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Two Cases Have funds to invest, compare with other investments Borrow funds for project
Problem Purchase condominium today for \$50,000 Receive rent in years 1-2 of \$1,000 Sell it in year 3 years for \$50,000 Is this worth it? Interest is 5% per year

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Two Methods Use current funds to invest in building Compare these with some other 3 year investment “Interest” is return from alternative investment Borrow funds to invest Pay back loan in 3 years Pay back parts of the loan with rental payments “Interest” is borrowing interest rate
Method 1: Compare Bank Account versus Condo FV ( Condo ) = (1000)(1.05)+(1000)(1.05) 2 +50000 FV ( Bank ) = 50,000(1.05) 3 FV ( Condo ) > FV ( Bank ) (1000)(1.05)+(1000)(1.05) 2 +50000 - 50000(1.05) 3 > 0 - 50000+ 1000 (1.05) + 1000 (1.05) 2 + 50000 (1.05) 3 > 0 NPV > 0

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Method 2: Borrow money Borrow 50,000 today Pay back 1000 in years 1 and 2 Repay rest of loan in year 3 Sell Condo
Time Line Year 0 - 1 Owe bank 50,000 At year 1 owe 50,000(1.05) - 1000 Year 1 -2 Owe bank 50,000(1.05)-1000 At year 2 owe (50,000(1.05)-1000)(1.05)-1000 Year 3

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