IE343_HW6_Solutions - HomeworkAssignment#6Solutions  PU R D U E U N I V E RSI T Y I E 343 E n gi n e e r i n g E con om i cs F a l l 2010

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: HomeworkAssignment#6Solutions  PU R D U E U N I V E RSI T Y I E 343 : E n gi n e e r i n g E con om i cs F a l l 2010 I nst r u c to r : A . C a p pon i H om e w o r k A ssign m e n t #6 A ssign e d : 01 O c t 2010 D u e : 08 O c t 2010 Missing name on the top of each page submitted Not stapled together 2 Not completed on the correct template 10 2 P r ob l e m 1 (15 points) F i n d t h e i n t e r n a l r a t e o f r e t u r n o f a t w o- y e a r i n v e s t m e n t t h a t , f o r a n i n i t i a l p a y m e n t o f $1,000, ge n e r a t es a r e v e n u e of $500 a t t h e e n d of t h e f i r st y e a r , a n d a r e v e n u e of $300 a t t h e e n d o f t h e se co n d y e a r . 500 300 0 1 2 1000 The present worth of this investment as a function of the interest rate i is given by Let equation . In order to find the internal rate of return i, we need to find to solve the second order which may be rewritten as thus yielding and Since i > -1, then x > 0. Therefore, the solution is . IE343 HomeworkAssignment#6Solutions Page1 HomeworkAssignment#6Solutions  P r ob l e m 5-46 (15 points) A sm a l l co m p a n y p u r c h ase d n ow f o r $23,000 w i l l lose $1,200 e a c h y e a r t h e f i r st f ou r y e a r s. A n a d d i t ion a l i n v est e d $8,000 i n t h e com p a n y d u r i n g t h e f ou r t h y e a r w i l l r esu l t i n a p r of i t of $5,500 e a c h y e a r f r om t h e f i f t h y e a r t h r ou gh t h e f i f t e e n t h y e a r . A t t h e e n d of 15 y e a r s, t h e co m p a n y c a n b e sol d f o r $33,000. 33000 5500 5500 5500 5500 5500 5500 5500 5500 5500 5500 5500 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1200 1200 1200 1200 8000 23000 a. D ete r mi ne the I R R . To find the solution to the equation Excel. We will use both methods. , we can either do linear interpolation or use If we linearly interpolate, we obtain Using linear interpolation, we obtain that the internal rate of return i is given by IE343 HomeworkAssignment#6Solutions Page2 HomeworkAssignment#6Solutions  A more accurate answer can be obtained using Excel, which yields i = 10.01%. b . C a l c u l a t e t h e F W i f M A R R = 12 % .   c. C a lcu l a te t he E R R w hen . All net cash outflows discounted to the present: All net cash inflows compounded to period N: Solve for ERR: IE343 HomeworkAssignment#6Solutions Page3 HomeworkAssignment#6Solutions  P r ob l e m 5-49 (10 points) A n h osp i t a l p l a n s to i n v est $14,000 i n a p o r t a b l e m e d i c a l f l u o r oscop e . T h e est i m a t e d c ash o u t f l ow s a n d i n f l ow s a r e s h o w n b e l o w . W h a t i s t h e s i m p l e p a y b a c k p e r i o d f o r t h i s p r op ose d i n v est m e n t? EOY 0 1 2 ­7 8 ­12 12a a Expected CastFlow  ­10,000  ­4,000 3,000 6,000 4,000 Recoverofworkingcapital For simple payback, simp value is achieved. 0 1 2 3 4 Cumulative NetCashFlow  ­10,000  ­14,000  ­11,000  ­8,000  ­5,000 5 6  ­2,000 1,000 Year The payback period, to the nearest year, is six years. Notice that the cash flows occurring after the payback period are ignored. Thus, payback period is 6 years. IE343 HomeworkAssignment#6Solutions Page4 HomeworkAssignment#6Solutions  P r ob l e m 5-55 (15 points) T h e I n t e r n a t ion a l P a r c e l Se r v i c e h as i nst a l l e d a n e w r a d io f r e q u e n c y i d e n t i f i c a t ion syst e m t o h e l p r e d u c e t h e n u m b e r o f p a c k a ges t h a t a r e i n co r r e c t l y d e l i v e r e d . T h e c a p i t a l i n v est m e n t i n t h e syst e m is $65,000, a n d t h e p r o j e c t e d a n n u a l sa v i n gs a r e t a b l e d b e low . igi b l e , a n d t h e M A R R i s 18 % p e r y e a r . 46000 EOY 1 2 3 4 5 40000 Savings 25,000 30,000 30,000 40,000 46,000 30000 30000 25000 0 a . W h a t i s t h e F W o f t h i s i n v es t m e n t ? 65000   , so this investment is acceptable. b . W h a t i s t h e I R R o f t h e s y s t e m?  Using Excel, we find acceptable. > MARR=18%. Thus the investment is IE343 HomeworkAssignment#6Solutions Page5 1 2 3 4 5 HomeworkAssignment#6Solutions  c . W h a t i s t h e d i sco u n t e d p a y b a c k p e r i o d f o r t h i s i n v es t m e n t ? Discounted Payback Period Method Period Net Cash Flow PW of Cash Flow Cumulative PW through year k 0 -65,000 -65,000.00 1 25,000 21,187.50 -43,812.50 2 30,000 21,546.00 -22,266.50 3 30,000 18,258.00 -4,008.50 4 40,000 20,632.00 16,623.50 5 46,000 20,106.60 36,730.10 The discounted payback period, to the nearest year, is 4 years. Notice that the cash flows occurring after the payback period are ignored. Thus, payback period is 4 years. IE343 HomeworkAssignment#6Solutions Page6 HomeworkAssignment#6Solutions  P r ob l e m 5-66 (15 points) A p i e c e of n e w e q u i p m e n t h as b e e n p r op ose d b y e n gi n e e r s to i n c r e as e t h e p r od u c t i v i t y of a c e r t a i n m a n u a l w e l d i n g op e r a t ion . T h e i n v est m e n t cost is $25,000, a n d t h e e q u i p m e n t w i l l h a v e a m a r k e t (sa l v age) v a l u e of $5,000 a t t h e e n d of i ts e x p e c t e d l i f e of f i v e y e a r s. I n c r e as e d p r od u c t i v i t y a t t r i b u t a b l e to t h e e q u i p m e n t w i l l a mou n t to $8,000 p e r y e a r a f t e r e x t r a op e r a t i n g costs h a v e b e e n su b t r a c t e d f r om t h e v a l u e of t h e a d d i t ion a l p r od u c t ion . C r e a t e a si n gl e sp r e a d sh e e t t h a t c a l c u l a t e d P W , F W , A W , I R R , a n d E R R f o r t h e p r op ose d i n v est m e n t . A ssu m e t h a t p e r y e a r . D oes y o u r r e co m m e n d a t i o n c h a n ge i f t h e M A R R d e c r e as es to 18 % ? I n c r e ases to 22 % ? 5000 8000 0 8000 8000 8000 8000 1 2 3 4 5 25000      IE343 HomeworkAssignment#6Solutions Page7 HomeworkAssignment#6Solutions  The original recommendation is unchanged for a MARR =18%. However, the recommendation does change for MAR = 22% (which Note that ERR is unaffected by changes in the MARR. This is because 1) the reinvestment rate was assumed to remain at 20%, and 2) there was only a single net cash outflow occurring at t=0. IE343 HomeworkAssignment#6Solutions Page8 ...
View Full Document

This note was uploaded on 01/20/2012 for the course INDUSTRIAL 343 taught by Professor Capponi during the Spring '11 term at Purdue University-West Lafayette.

Ask a homework question - tutors are online