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# lect3 - Today's L ectur e Revi ew of NPV Ri sk Ti me Val ue...

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Today's Lecture Review of NPV Risk Time Value of Money

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2 Lets summarize I have convinced you (I hope) that any  investment that has positive NPV is a "no  brainer"   preferences do not affect this statement  it’s like you just get the NPV  Next we need a standard formulae to calculate  the NPV  ....
3 Present Value Formula:

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4 NET Present Value Formula:
5 Example 1 I have an offer to sell my bike for \$500.  My  brother also wants to buy the bike.  He will  pay me \$545, but he can only make the  payment in a year.  If current interest rates are  10%, which is the better deal?

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6 Example 2 Your buddy would like to start a business.  He  needs \$10,000.  If you lend him the money  and the business is successful, he will give  you \$12,000 in a year.    If interest rates are 10% what should you do? What is the present value of \$12,000?  What is the net present value of this investment?  Is 10% the correct rate to use?  What would your answer be if rates were  25%?
7 Valuing a Security Consider a security that promises a one-time  payment to its owner of \$1000 in one year.  If  the one year interest rate is 5%, what price  will this security have in a market without  arbitrage opportunities? We will call a market without arbitrage  opportunities a NORMAL market.

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8 Law of One Price Two investment opportunities that are  simultaneously available in competitive  markets must have the same price What would happen if the bond traded for \$940?   What about \$960?
9 Short Sale Selling a financial security you do not own.

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