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IE343_HW6_Solutions - HomeworkAssignment#6Solutions PU R D...

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Homework Assignment #6 Solutions IE 343 ʹ Homework Assignment #6 Solutions ʹ Page 1 PURDUE UNIV ERSIT Y Hom e work A ss ignm e nt #6 IE 343: Engin ee ring E c onomi c s A ss ign e d: 01 O c t 2010 Fall 2010 Du e : 08 O c t 2010 In s tru c tor: A . Capponi Missing name on the top of each page submitted ± 2 Not stapled together ± 2 Not completed on the correct template ± 10 Probl e m 1 (15 poin ts ) Find th e int e rnal rat e of r e turn of a two-y e ar inv e s tm e nt that , for an initial paym e nt of $1 , 000 , g e n e rat e s a r e v e nu e of $500 at th e e nd of th e fir s t y e ar , and a r e v e nu e of $300 at th e e nd of th e s ec ond y e ar . The present worth of this investment as a function of the interest rate i is given by ܹܲሺ݅ሻ ൌ െͳͲͲͲ ൅ ହ଴଴ ଵା୧ ଷ଴଴ ሺଵା୧ሻ Let ݔ ൌ ଵା୧ . In order to find the internal rate of return i, we need to find to solve the second order equation ͵ͲͲݔ ൅ ͷͲͲݔ െ ͳͲͲͲ ൌ Ͳ which may be rewritten as ͵ݔ ൅ ͷݔ െ ͳͲ ൌ Ͳ thus yielding ݔ ൌ ͳǤͳ͹ and ݔ ൌ െʹǤͺͶ Since i > -1, then x > 0. Therefore, the solution is ݔ ൌ ͳǤͳ͹ . ͳǤͳ͹ ൌ ଵା୧ ݅ െͳͶ Ǥ͹Ψ 1000 500 300 0 1 2
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Homework Assignment #6 Solutions IE 343 ʹ Homework Assignment #6 Solutions ʹ Page 2 Probl e m 5-46 (15 poin ts ) A s mall c ompany pur c ha s e d now for $23 , 000 will lo s e $1 , 200 e a c h y e ar th e fir s t four y e ar s . An additional inv e s t e d $8 , 000 in th e c ompany during th e fourth y e ar will r e s ult in a profit of $5 , 500 e a c h y e ar from th e fifth y e ar through th e fift ee nth y e ar . At th e e nd of 15 y e ar s , th e c ompany c an b e s old for $33 , 000 . a . D e t e rmin e th e IRR . ܹܲሺ݅ ሻ ൌ െʹ͵ǡͲͲͲ െ ͳǡʹͲͲሺܲȁܣǡ ݅ ǡ Ͷሻ െ ͺǡͲͲͲሺܲȁܨǡ ݅ ǡ Ͷሻ ൅ ͷǡͷͲͲሺܲȁܣǡ ݅ ǡ ͳͳሻሺܲȁܨǡ ݅ ǡ Ͷሻ ൅ ͵͵ǡͲͲͲሺܲȁܨǡ ݅ ǡ ͳͷሻ To find the solution to the equation ܹܲሺ݅ ሻ ൌ Ͳ , we can either do linear interpolation or use Excel. We will use both methods.
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