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Unformatted text preview: Question 1 (10 points) Consider the following two investment alternatives: Net Cash Flow End of Year Machine A Suppose that your ﬁrm needs either machine for only 2 years. The net proceeds from the
sale of Machine B (at the end of year 2) are estimated to be $200. What should be the
required net proceeds from the sale of Machine A so that both machines could be
considered economically indifferent at an interest rate of 10%? (Hint: Use a Present Worth analysis).
0. 10°“ 0. 32.54 W
w
PWA , 4,000 + qoo (P/F, mark, I) +— (zoo + s)£P/F, 109°, 2)
= 4,000 + SIS. H + (olel + one»! 8 x 474.31 + o. 82.1.48 ”“4 030°“ ~73
PW; = —2,000 +2500(PIF, 10%,!) + NOOHOOMPIF. '0 W : 2,ooo t— 2, 2.72.75 + 824:4
, {0614.15 .— Let rwA = Pws
474.3: +0.9u945 = IOCt‘HS' Question 2 (20 points) Two methods of carrying away surface runoff water from a new subdivision are being
evaluated. Method A involves digging a ditch at an immediate cost of $30,000.
Redigging and shaping would occur every 5 years forever at a cost of $10,000 each.
Method B requires laying of concrete pipes. Upfront investment costs for this design are
$40,000 and replacements would be required at 30year intervals at a net cost of $40,000
forever. a) Draw the cash ﬂow diagrams for both methods. b) At i— — 15% (annual rate), which method is the better one? 0) Suppose you could use an interest rate of 4/ m. Would it change your
recommendation? What does this tell you about longlife projects? 09 Method. A MW 8
O 0
saw 40,000 40,0120 40.000 """
5 '30 000 0.0433
in RNA; ’
) A —quoo(A[Fl‘S"°,5> , qssaa?’
FWAa, ‘ T ' 0J5 ' : ~$3a arse67
PWA‘ FW‘. + PWA‘ = '30,000 ' qggb.b7 ) PW“ . 4000:) 42911».
A ,qopoo AIF 15°). 303 3, _ “3.33
WI” ' T ’ 01$ ,——'—"—"""
PWB ‘ 40,000  40,000 HF 6;. 30) ,
0.011 ‘ 71m Iowa the interest rate, Hmmore ecumenical long—life. pwjem m. Question 3 (10 points) a) What inﬁnite equal annual payment series is equivalent to the cash ﬂow stream
shown below? (i = 8% annually). b) What is the capitalizedequivalent worth in year 0 of the inﬁnite payment cash
ﬂow stream shown below? 9 lO 11 12 13 14 15 16 years 1
l
I
l
I
I
l
l
I 300
325 325 325 325l325 325 325 325 “9 Sequam @6413 wow ‘6 yam so ’15ququ 5 Am.“ (.7853 33131 0.2575
Pscqucm. " 3350/14, 3%, .2) + 300(P/A, 3%, 4)(F/F, 37., 2,)
4. 501 0.8573 I 7853 0.5302. ‘ K‘M
'501P/‘4/ 3%,”)‘P/F. 3&2) 4— 325(PIA,%%,1)(P/Eg%’(p)
5 579.5725 f 851.83‘11973265 +3b5’ZJIblp = /5 97. 33 Asquwccs [magma <57» 3) .277 (1356 ”EB 273373 273‘ b) Milﬁlled Equiv WovH't . #7 ”5" lat/7,713]
79“ t 008 a; 3474 20 Question 4 (15 points) Suppose Tim has just graduated from the University of Michigan with an IOE degree. He decides to accept a job with a local office of an international consulting ﬁrm, and is
hired at a salary which pays $2275 every two weeks. He deposits this into his checking
account, which earns 3.5%, compounded daily. (Assume 365 days per year and 52 weeks per year) Tim has become interested in the work of Ronald McDonald House, and would like to
donate 10% of his endof—year account balance to this organization. Unfortunately, Tim
is afraid that if he waits to make the donation until the end of the year, he may not have
saved enough money. To make sure he can donate the whole amount, he would like to make a series of uniform donations equivalent to the amount he would have given at the end of each year. How
much should each monthly payment be? Please draw a cash ﬂow diagram. $2275 MW”.. ._ WW I ' ___________ z;
o How muck does 77m make in I ygar ?
F = 2.57» ﬂﬁﬂwm ”WW—EN.
H’ 345 {ole/85+ vyiodé/YW
C : g—é—E wheres» pamas /Qc$t\,lN‘0‘+ 170‘0d ll. 'e 2é @a'ymenk :pgﬁocjg , ' 31,5
awe/m, Lav Lb = ( H ‘LféiSS)I—1vo.tgai \HW—L 7 
“P = It? ]=s22:s[(‘*0'09’§iﬂ1t = 58,081.5‘8 :5 (W L)” aoosstl woomwﬂ W ‘070 OQ Ca’mmbg 5 O,V1£$S$I06?I;g)s w; “55.5% M = 3é5 :M—trcs+ Qaiods/Ycer C ‘ 3% hives? ?0‘"0CLS/’P<9Hm5"l’ Pm'OA' K = [2 ’PWWWL patods Mae)”
5
0+ ng°§§>%—1 = 0.261270 mom/LR, L =——> {m = A= (9 [Maxi
(H—DU—l Y = $57mi51 3 L 0.00 241200020] 23'
1.0024312 _ I 2] :ﬁ ~7
30 14513. 30
W two/WV» S g.......__..m_.__‘ Question 5 (20 points)
Please answer the following three parts worth X points each. a) A series of monthly deposits of $1250 each are made to an account which earns 7%
interest, compounded quarterly. If this series lasts for 4V2 years, how much is in the
account at the end? b) Suppose you are told that an investment earns a market interest rate of 13%. Upon
further investigation, you discover that the inﬂationfree interest rate used in determining
the market rate was 6.5%. What was the average rate of inﬂation assumed in computing
the market interest rate? c) Acme Co. will purchase a new metal stamping machine with a total cost basis of
$100,000. The service life of the machine is 5 years, after which it will have a salvage
value of $50,000. For tax purposes, the machine falls under the 7—year MACRS personal property category.
For this category, the depreciation rates as a percent of the original cost basis are: If the marginal tax rate and capital gains tax rate is 40%, how much will be paid in gains
(loss) taxes at the end of year 5?
Indicate if it is a gain or a loss. 8) Hoﬁ’hly 0‘6QOSH'5 ~——‘? LM00%\\I = (1+ 0 08)}? 1: O (9670 We have 40235 roe/300$ = Sci/world‘s F s A [Ui'D'N’l]=$lZSﬁQE(1'OOéb)5t—J% 43050 1.1? l 000.66
39) (3—057. L=U+ 3—L'ﬁ . —_:_ ' ' 033—004,5
ingn F 42 l—ui'b 34,0055 4E
G) Y I 3
W _,_§99av_awe 4.3.. Kink/36)::  soot.
’— $)O0,000 : "—' $50/OOO'$26,77
1 Maﬁa/am) : $14,260 555/1110 ; $23,125
1 mammal) : 324%; $4.1, 220 (mm. Tax = 0,4022 22
3 5300003749) = 53 37,490 M3 1 30 Ta“?
4 $3001¢to.32c4€3)= 3 ILL/go $33, 240 I ﬁg;
5’ {mm/10.843/7lz My“; .3; '33. 1a: ( Idf'iﬁ‘;
25% Question 6 (25 points) Consider the following financial data (in actual dollars) for a possible project:
0 Required capital investment at time n=0: $100,000 Project service life: 5 years Salvage value at n=5: $50,000 Annual revenue: $115,000 Annual 0&M costs (not including depreciation): $ 80,000 Marginal tax and capital gains rates: 40% Note: There are two parts to this question, parts (a) and (b).
(a) Assuming 7year MACRS, determine the project net incomes and net cash ﬂows for this project. Fill in the following two tables. You may leave the numbers in
units of thousands of dollars (K). Note: The 7—year MACRS table is given inthe— d previous problem. In addition, the capital investment, service life, and salvage
value are the same here as they are in tieprevious problem. Income Statement :5
a I m i c. C
k I. .2:
«4% i ”7
81w 9.
“‘ I o” I
ml 5* ‘ 'M
Q n ‘ 5" w
s»:
A5 I ‘4 5
“ h
w
u; must Taxable Income
Income Taxes , . . I , _————_
6;, 3675 —m' N
N
h] f ~53
Q
Q
5
a; Cash Flow Statement ————“
___——_—
—l—nl__m
m—
—___—_—
————_——
—HIIIIE_—_——
v 3  _—__——
—f_—____—
——_——_—
——————_ (b) Assuming a MARR of 15%, would you accept this project?
Justify your answer. s7 ..... (5’ ..... ~+ TIER} My?
4 19.9% + 53,494
"'5‘ MST"
:IHJS? >0 Z>Ia aceP‘é /PW>°’) ...
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 Spring '07
 Maull

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