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ECOS2201-prelect12 - D E R E M E N S EAD E M MUTA T...

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S I D E R M E N S · E A D E M · M U T A T O University of Sydney ECOS2201 - Lecture 12 1
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Project Selection Which projects should a firm undertake? Calculate Net Present Value of projects revenues and costs and undertake if positive 2
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Net Present Value $100 today at annual interest rate of 10% becomes $110 in one year So present value of $110 in one year is NPV = FV 1 + r = 110 1 . 1 = 100 (1) 3
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More generally, if get stream of payments in the future, F 1 in one year, F n in n years, then NPV = F 1 1 + r + F 2 (1 + r ) 2 + ... + F n (1 + r ) n (2) Question: Consider a silver mine that requires an investment of 2 mill. immediately and 1 mill. after 1 year, two years, three years, and four years. The mine then starts producing silver and yields net revenue of 750,000 in years 5 to 44 (40 years). Write down formula for NPV? 4
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Answer: See board. At r = . 05, NPV=5,042,000 At r = . 1, NPV=-160,000 So undertake project if r = . 05 but not if r = . 1 5
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Often stream of payments is uncertain - price of silver varies as do costs How do we take risk into account when selecting projects? The basic problem - which projects increase a firm’s value and which projects decrease a firm’s value? 6
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Every project has a cost and produces a random risky stream of net payments Therefore, it is like a share (asset) - it has a cost and a risky stream of payments (dividends) Undertake project (buy a share) if value of risky stream of payments is greater than cost. BUT what interest rate use to discount future values ? How do we do NPV calculation? 7
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Expected Return and Variance for a Single Asset Rate of return given by R = p 1 - p 0 p 0 , (3) where p 1 is value of asset in period 1 and a random variable and p 0 is value of asset in period 0.
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