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

2. Two Cases Have funds to invest, compare with other investments Borrow funds for project

3. 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

4. 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

5. Method 1: Compare Bank Account versus Condo

6. 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

7. 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 Owe bank ((50,000(1.05)-1000)(1.05)-1000)1.05 50,000(1.05)^3 - 1000(1.05)^2 - 1000(1.05)

8. Case 2: Borrow money for condo

9. Compare Same calculation for each In real life the 1.05 = 1+R –Definitions of R Discount rate Required return Cost of capital Opportunity cost Two common values –Comparison rate of return (stock market) –Borrowing rate More later

10. One More Question: What R just sets NPV = 0?

11. Internal Rate of Return R that solves this is the Internal Rate of Return on the project –Borrow for less than this: NPV>0 –Borrow for more than this: NPV<0 There is no formula for this Requires computer or financial calculator –Fancy “plug and guess”