# Diagnostic Examination

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1 Diagnosic Examinaion TOPIC XV: ENGINEERING ECONOMICS TIME LIMIT: 45 MINUTES 1. Approximaely how many years will i ake o double an invesmen a a 6% effecive annual rae? (A) 10 yr (B) 12 yr (C) 15 yr (D) 17 yr 2. An individual conribues \$200 per monh o a 401(k) reiremen accoun. The accoun earns ineres a a nominal annual ineres rae of 8%, wih ineres being credied monhly. Wha is he value of he accoun afer 35 years? (A) \$368,000 (B) \$414,000 (C) \$447,000 (D) \$459, A graduaing high school suden decides o ake a year off and work o save money for college. The suden plans o inves all money earned in a savings accoun earning 6% ineres, compounded quarerly. The suden hopes o have \$5000 by he ime school sars in 12 monhs. How much money will he suden have o save each monh? (A) \$396/mo (B) \$405/mo (C) \$407 /mo (D) \$411/mo 5. \$5000 is pu ino an empy savings accoun wih a nominal ineres rae of 5%. No oher conribuions are made o he accoun. Wih monhly compounding, how much ineres will have been earned afer five years? (A} \$125U (B) \$1380 (C) \$1410 (D) \$ An engineer deposis \$10,000 in a savings accoun on he day her child is born. She deposis an addiional \$1000 on every birhday afer ha. The accoun has a 5% nominal ineres rae, compounded coninuously. How much money will be in he accoun he day afer he child's 21s birhday? (A) \$36,200 (B) \$41,300 (C) \$64,800 (D) \$84, A machine coss \$10,000 and can be depreciaed over a period of four years, afer which is salvage value will be \$2000. Wha ishe sraigh-line depreciaion in year 3? (A) \$2000 (B) \$2500 (C) \$4000 (D) \$ A gold mine is projeced o produce \$20,000 during is firs year of operaion, \$19,000 he second year, \$18,000 he hird year, and so on. If he mine is expeced o produce for a oal of 10 years, and he effecive annual ineres rae is 6%, wha is is presen worh? (A) \$118,000 (B) \$125,000 (C) \$150,000 (D) \$177, A groundwaer reamen sysem is needed o remediae a solven-conaminaed aquifer. The sysem coss \$2,500,000. I is expeced o operae a oal of 130,000 hours over a period of 10 years and hen have a \$250,000 salvage value. During is firs year in service, i is operaed for 6500 hours. Wha is is depreciaion in he firs year using he MACRS mehod? (A) \$113,000 (B) \$125,000 (C) \$225,000 (D) \$250,000 PPI

2 DE XV-2 FE REvIEw MANuAL 9. A machine iniially cosing \$25,000 will have a salvage value of \$6000 afer five years. Using MACRS depreciaion, wha will is book value be afer he hird year? (A) \$5470 (B) \$7200 (C) \$10,000 (D) \$13,600 1 O. Given he following cash flow diagram and an 8% effecive annual ineres rae, wha is he equivalen --- arrnual-expense-ovetlie five-year-p-eriod? = 0 \$50 \$100 = 5 \$150 \$150 \$200 he building has had no deerioraion or decrease i uiliy. Wha should he warehouse sell for oday? n (A) \$427,000 (B) \$540,000 (C) \$678,000 (D) \$691, A delivery company is expanding is flee by five vans a a oal cos of \$75,000. Operaing and mainenance coss for he new vehicles are projeced o be \$~0,QQ_Ol :rea~_f()_r l:e_!l_e~ eiglj.~ YE:!a.f.. _._ A_f(;Jr~gl;l y_ears,- he vans will be sold for a oal of \$10,000. Annual revenues are expeced o increase by \$40,000 wih he expanded flee. Wha is he company's rae of reurn on he purchase? (A) 19.7% (B) 20.8% (C) 21.7% (D) 23.2% 14. A company is considering replacing is air condiioner. Managemen has narrowed he choices o wo alernaives ha offer comparable performance and considerable savings over heir presen sysem. The effecive annual ineres rae is 8%. Wha is he benefi-cos raio of he beer alernaive? \$500 (A) \$209 (B) \$218 (C) \$251 (D) \$ The consrucion of a volleyball cour for he employees of a highly successful mid-sized publishing company in California is expeced o cos \$1200 and have annual mainenance coss of \$300. A an effecive annual ineres rae of 5%, wha is he projec's capialized cos? (A) \$1500 (B) \$2700 (C) \$7200 (D). \$18, A warehouse building was purchased 10 years ago for \$250,000. Since hen, he effecive annual ineres rae has been 8%, inflaion has been seady a 2.5%, and I II iniial cos \$7000 \$9000 annual savings \$1500 \$1900 salvage value \$500 \$1250 life 15 yr 15 yr (A) 1.73 (B) 1.76 (C) 1.84 (D) A gourme ice cream sore has fixed expenses (ren, uiliies, ec.) of \$50,000/yr. Is wo full-ime employees each earn \$25,000 per year. There is also a par-ime employee who makes \$14,000 plus \$6000 in overime if sales reach \$120,000 in a year. The ice cream coss \$4/L o produce and sells for \$7 fl. Wha is he minimum number of liers he sore mus sell o break even? (A) L (B) L (C) L (D) L ~P~P_I~ --~w~w~w~ ~P~P~i~2~p~a~s~s~-~c~o~m~

3 D I A G N 0 5 T I c E X A M I N A T I 0 N E N G I N E E R I N G E c 0 N 0 M I c 5 DE XV -3 Use he sinking fund facor. 1. Deermine he number of years for he compound amoun facor o equal 2. F= 2P = P(F/P, i%, n) 2= (F/P,6%,n) = (1 +i = ( ln 2 = ln 1.06n = n(ln 1.06) ln2 n=-- ln 1.06 = 11.9 yr (12 yr) Alernaively, use he 6% facor able. n is approximaely 12 years. Answer is B. A= F(A/ F, i%, n) = (\$5000)(A/ F, 1.5%, 4) = (\$5000) ( ) ( ) 4-1 = \$ ;\$_ quarer monhly savings = mo 3 quarer- = \$407/mo 4. This cash flow is equivalen o a \$20,000 annual series wih a -\$1000/year gradien. Use he facor ables. 2. The effecive rae per monh is i = I... = 0 08 = m 12 Use he uniform series compound amoun facor. F = A(FjA, i%, n) Because compounding is monhly, n is he number of monhs. n= (35 yr) (12 ~n = 420 mo F=A((l+r-1) = (\$200) (( ) = \$459,227 (\$459,000) 3. The effecive rae per quarer is i =I...= 0 06 = m 4 There are four compounding periods during he year. n=4 p = (\$20,000)(P I A, 6%, 10) - (\$1000)(P /G, 6%, 10) = (\$20,000)(7.3601) - (\$1000)( ) = \$117,600 (\$118,000) 5. The effecive annual ineres rae is ie = ( 1 + :) m - 1 = (1 + oi~5)12-1 = The oal fuure value is F= P(F/P,i%,n) = P(1 +i = (\$5000)( ) 5 = \$6417 The ineres available is ineres = F - P = \$ \$5000 =\$1417 (\$1420) (This problem can also be solved by calculaing he effecive ineres rae per period and compounding for 60 monhs.)

4 DE XV -4 F E R E v I E w M A N u A L 6. The uniform series compound amoun facor does no include a conribuion a = 0. Therefore, calculae he fuure value as he sum of a single paymen and an annual series. F= P(FIP, r%, n) + A(FIA,r%, n) = P(ern) + A(ern- 1) er -1 = (\$10,000)eC0 05)( 21 (0.05}(21} 1) ) + (\$1000) e - ( e(0.05} _ 1 = \$64,808 (\$64,800) 7. Wih he sraigh-line mehod, depreciaion is he same in each year. D3= D= C- Sn n \$10,000 - \$2000 4yr =\$2000iyr (\$2000) 8. MACRS depreciaion depends only on he original cos, no on he salvage cos or hours of operaion. Di = C(facor) D1 = (\$2,500,000)(0.10) = \$250, Book value is he iniial cos less he accumulaed depreciaion. Use he MACRS facors for a five-year recovery period. BV= C- LDi j=l = C- L ( C(facorj)) j=l 10. Firs, find he presen worh of all of he cash flow s. p = \$500 + (\$50)(P I A, 8%, 5) + (\$50)(P I G, 8%, 4) + (\$100)(PIF,8%,5) = \$500 + (\$50)(3.9927) + (\$50)(4.6501) + (\$100)(0.6806) = \$1000 Nex, find he effecive uniform annual expense (cos). EUAC=.(\$IOOO)(AjP;8%,5) = (\$1000)(0.2505) = \$ Find he capialized cos of he annual mainenance and add he iniial consrucion cos o i. p = c +.:! = \$ \$ 300 i 0.05 = \$ Ideally, he curren price should be he fuure worh (from 10 years ago) adjused for inflaion. Use he inflaion-adjused ineres rae, d, ogeher wih he single paymen compound amoun facor. d= i+ f +if = (0.08)(0.025) = F=P(FIP,d%,n) = (\$250,000)( ) 10 = \$690,902 (\$691,000) = C (1 -±facorj) J=l = (\$25,000) ( 1 - ( )) = \$7200 Answer is B. ~P~P~I~ ~w~w~w~ ~p2p~i~2~p~a~s~s~.c~o~m~

5 D I A G N 0 s T I c E X A M I N A T I 0 N E N G I N E E R I N G E c 0 N 0 M I c s DE XV -5 e. e. e 13. Rae of reurn is he effecive annual ineres rae ha would make he invesmen's presen worh zero. p = 0 = -(\$75,000) + (\$40,000- \$20,000)(PI A, i%, 8) + (\$10,000) (PI F, i%, 8) \$75,000 = (\$20,000) (( i) - i(1 + i) 8 1 ) + (\$10,000)(1 + i)- 8 By-rial-and-error, i=0~217 (21. 7%}: 14. Compue he presen worh of he benefis and coss for each alernaive. Salvage value should be couned as a decrease in cos, no as a benefi. For alernaive I, B = (\$1500)(P I A, 8%, 15) = (\$1500)(8.5595) = \$12,839 c = \$7000- (\$500)(P IF, 8%, 15) = \$7000- (\$500)(0.3152) = \$6842 For alernaive II, B = \$12,839 = 1 88 c \$6842. B= (\$1900)(PIA,8%, 15) = (\$1900)(8.5595) = \$16,263 C = \$9000- (\$1250)(PI F, 8%, 15) = \$9000- (\$1250)(0.3152) = \$8606 B = \$16,263 = 1 89 c \$8606. The alernaives canno be compared o one anoher based simply on heir raios. Insead, perform an incremenal analysis. Err - B 1 \$16,263- \$12,839 Crr- C1 \$8606-\$6842 = 1.94 Because he incremenal analysis raio is greaer han one, alernaive II is superior. 15. Calculae he coss and revenues assuming sales of \$120,000 are exceeded. coss= \$50,000 + (2)(\$25,000) + \$14,000 revenues= ( 7!) Q + \$ ( 4! ) Q A he break-even poin, coss equal revenues. revenues= coss (7!) Q= \$120,000 + ( 4!) Q Q= L Check he assumpion ha sales exceed \$120,000. ( 7!)( L) = \$280,000 [ok] PPI

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