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HW3Notes

# HW3Notes - 1 g 1 r and simplify Ch 6#3 In the second...

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Homework 3 Notes Ch. 6 #1 My recommendation is to do part c in excel. Calculate a column of PV Bene°ts and a column of PV Costs in small increments of r (e.g. r = 0 : 03 ; r = 0 : 031 ; r = 0 : 032 ; etc.). When PV Bene°ts is very close to PV Costs, then you have your cuto/ discount rate, c . Ch. 6 #2 In the second line, change the number 10,000,000 to 2,000,000 . Here±s a big hint for part c: Since the bene°ts are increasing by 3% per year, we have to somehow get that number into our present value formula. Here±s how we got the present value formula in the °rst place: For a number x ° 1 , we have P T t =1 x t = x ° x T +1 1 ° x (you can take my word for it). If we plug in the discount factor 1 1+ r , then we get P T t =1 ( 1 1+ r ) t = ( 1 1+ r ) ° ( 1 1+ r ) T +1 1 ° ( 1 1+ r ) = 1 r [1 ± ( 1 1+ r ) t ] after simplifying. This is the formula that you have from lecture. Now assume that bene°ts are growing by g % each year. Then bene°ts in year 1 get multiplied by (1 + g ) , bene°ts in year 2 get multiplied by (1 + g ) 2 , and bene°ts in year t get multiplied by (1 + g ) t . So now, the PV bene°ts are P T t =1 ( 1+ g 1+ r ) t . Using the formula above, you can now derive a new formula for °nding the PV bene°ts.
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Unformatted text preview: ( 1+ g 1+ r ) and simplify. Ch. 6 #3 In the second paragraph of the problem, it says that the cost is \$100 to install. Change this number to \$130 . Now, how to use hyperbolic discounting: The problem gives us a discount rate in the form & (1+ t ) where & = 0 : 05 . The point of this is that if & = 0 : 05 is the market discount rate, then with hyperbolic discounting the discount rate is decreasing each period - i.e. it±s no longer constant. However, we don±t need the discount rates to solve the problem. In part a, we want to calculate the discount factors for each period. The hyperbolic discount factor in period t is 1 (1+ t ) & and again & = 0 : 05 . For example, in part b the discounted bene&ts in year 3 are 1 (1+3) & (30) . Now, just add up all the discounted bene&ts to get the PV Bene&ts. 1...
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