03-PS1-PV_sol

03-PS1-PV_sol - MIT Sloan School of Management J. Wang...

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MIT Sloan School of Management J. Wang 15.407 E52-456 Fall 2003 Problem Set 1: Present Value Solution 1. (a) The NPV of the project is 10 t =1 170 , 000 / (1 + 14%) t - 800 , 000 = $86 , 739 . 66 (b) At the end of 5 years, there will be 5 more years of income from the project, therefore it will be worth 5 t =1 170 , 000 / (1 + 14%) t = $583 , 623 . 76 2. An annuity of $1 over the next 12 years is worth 1 8% [1 - 1 (1+8%) 12 ] = $7 . 536 Therefore, Basset can buy 2653.90 units of $1 annuity and receive $2563.90 every year. 3. Value of this year’s production = $1,400,000 The growth rate of profit = 1 . 02 * 0 . 96 - 1 = - 2 . 080% Using the annuity with growth formula, the PV of the oil well is 14 * 100 , 000 * 1 8%+2 . 080% [1 - ( 1 - 2 . 080% 1+8% ) 18 ] Therefore, PV of the well’s production is $11,508,076. 4. Sam wants to accumulate $300 , 000 * 1 . 02 20 = $445 , 784 . 22 in nominal term at the end of 20 years. PV of this amount is 168,011.38. (a) An annuity of $1 over the next 20 years is worth PV of
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This note was uploaded on 01/19/2011 for the course 15 15.407 taught by Professor Wang during the Fall '03 term at MIT.

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03-PS1-PV_sol - MIT Sloan School of Management J. Wang...

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