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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