PS1 - ECO 362 October 5 2007 PROBLEM SET 1 FINANCIAL...

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ECO 362 October 5, 2007 PROBLEM SET 1 FINANCIAL INVESTMENTS (ECO 362) Professor: Burt Malkiel Exercise 1 (a) (USING CALCULATOR) For the f rst project we have 7 consecutive payments from year 1 to 7 of 330 and a last payment of 1 , 000 at year 8. Let i be the interest rate, so that NPV = F 0 + 8 X j =1 C i (1 + i ) j = F 0 + C 1 1+ i + C 1 (1 + i ) 2 + ··· + C 1 (1 + i ) 8 = 2 , 000 + 330 × 7 X j =1 1 (1 + i ) j + 1 (1 + i ) 8 × 1 , 000 = 2 , 000 + (1 + i ) 7 1 i (1 + i ) 7 × 330 + 1 (1 + i ) 8 × 1 , 000 since 7 X j =1 1 (1 + i ) j = 1 (1+ i ) 1 (1+ i ) 8 1 1 (1+ i ) = (1 + i ) 7 1 i (1 + i ) 7 . Hence, substituting by i = 12% ,weget NPV = 2 , 000 + 330 × (1 . 12) 7 1 0 . 12(1 . 12) 7 + 1 (1 . 12) 8 × 1 , 000 , = 90 . 077 . (USING TABLES) The best way (in terms of time) is by decomposing the cash F ows in two components —as we did above—: (a) annuity of 330 ,and(b )p a y o f of 1 , 000 at the end (of the project). Looking at Table B, for seven periods and an interest rate of 12% ,weget 4 . 5638 . Alternatively, if we look at the Table for annuities (Table C) we obtain that the factor for 7 periods at a 12% is 10 . 089 . But this is the value of the annuity at t =7; so ,wehavetod iscountthatpayment , 10 . 089 (1 . 12) 7 =4 . 5638 . Next, we have to f nd the discount rate for the last payment: (Table A) 0 . 4039 . Therefore, NPV = 2 , 000 + 330 × 4 . 5638 + 1 , 000 × 0 . 4039 = 90
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ECO 362 October 5, 2007 Project 1 Project 2 Project 3 Project 4 NPV 90 . 08 173 . 04 30 . 41 92 . 96 Hence, Project 3 has the highest rank. (b) Recall that the IRR is the discount rate that makes the sum of discounted cash f ows equal to zero, that is, the rate r such that 0= I 0 + C 1 1+ r + ··· + C n (1 + r ) n = I 0 + n X j =1 C j (1 + r ) j . We have to use either Excel (or alternatively, a F nancial calculator e.g. HP 17BII, HP 19BII, Texas Instruments BA II, etc.), or to interpolate i.e. compute the NPV for di f erent values of the discount rate until we get something close to zero. Using Excel, we get 10 . 9% , 11 . 3% , 12 . 3% and 11% for projects 1, 2, 3 and 4, respectively. So the ranking becomes 3, 2, 4 and 1. Note that in some special cases, one can obtain
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This note was uploaded on 10/15/2008 for the course ECO 362 taught by Professor Harrisonhong during the Fall '08 term at Princeton.

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PS1 - ECO 362 October 5 2007 PROBLEM SET 1 FINANCIAL...

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