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Unformatted text preview: ever. • Question: What is the present value of the annuity? • We know that NPV = $1000/r. Suppose r = 0.1 then the present value of your annuity is $1000/0.1 = $10,000. • That is a lot of money, but far less than an infinite amount. • Notice that if r decreases, then the present value of the annuity increases. • Similarly, if r increases, then the present value of the annuity decreases. • For example, you can show that a 50% decline in the interest rate will double the value of an annuity. Transition from flow to stock Transition from flow to stock • If a resource is generating $20.000/year for the forth seeable future future and the discount rate is 4% the price of the resource should be $500.000 • If a resource generates $24K annually and is sold for $720K, the implied discount rate is 24/720=1/30=3.333% • If the real price of the resource (oil) is • • • • • The impact of price expectation The impact of price expectation expected to go up by 2% The real discount rate is 4%­ What is the value of an oil well which provides for the for seeable 5000 barrel annually, and each barrel earns 30$ (assume zero extraction costs)? 1. Is It (A) $3.750K (B) $7.500K ? 2.If the discount rate is 7% will you Pay $2 millions for the well? 3.What is your answer to 1. If inflation is 1%? Answers Answers • 1.B 5000*30/(.04­.02)=150.000/.02 =$7.500.000 • 2. 150.000/(.07­.02)=150.000/.05= 3000000>2000000 ­yes • 3. If inflation is 1% real price growth is only 1% and 150.000/(.04­.03)=150.000/.03= $5000000 • One percentage interest reduce value by 1/3. The Social Discount Rate The Social Discount Rate • The social discount rate is the interest rate used to make decisions regarding public projects. It may be different from the prevailing interest rate in the private market. Some reasons are: • Differences between private and public risk preferences —the public overall may be less risk averse than a particular individual due to pooling of individual risk. • Externalities—In private choices we consider only benefits to the individuals; in public choices we consider benefits to everyone in society. private discount rate. In evaluating public projects, the lower social discount rate should be used when it is appropriate. • It is argued that the social discount rate is lower than the Uncertainty and Interest Rates Uncertainty and Interest Rates • Lenders face the risk that borrowers may go bankrupt and not be able to repay the loan. To manage this risk, lenders may take several types of actions: • Limit the size of loans. • Demand collateral or co­signers. • Charge high­risk borrowers higher interest rates. (Alternatively, different institutions are used to provide loans of varying degrees of risk.) Risk­Yield...
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