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Unformatted text preview: ; gee AloTéS‘
ﬁ 2. Answer each of the following by circling the correct response among the italicized choices and pro—
viding a brief explanation in each case. (2.5 marks each) (a) As n increases, the A/ P facto rises because (D Tue sew; AMOUN’T; P, I: §P72€AD 01/612 M026 ’Peempg, (b) In general, if interest rates decrease, the price of a bond will decrease ecause...
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ANo/Oe ‘L«N_ L€MGIT#_ (d) The value of the discount factor 6 = 1/(1 + can @176 negative because.” 0 6 IS «lo be between 400% MM! deci’éié. oo 3. Answer each of the following. (a) (3 marks) Suppose Tom deposits $2,000 today (i.e., in period 0) in an account which pays
compound interest. What will effective «annual interest rate have to be’in order for Tom’s money to double after 10 years? 7 7 7 I / Y ,r»k , 9.31.0 r Q (£2000) : 3000040 P 22: (“film (b) (4 marks) Suppose Jerry deposits $10,000 today (i.e., in period 0) in an account which pays
compound interest. He continues t6 deposit money in this account, increasing his deposit by
5% each year. How many years will it take to accumulate an amount whose present worth, is W
whoop? '(in period 0) if the effective annual rate is 7%? ’ ‘0 ‘ ' " "' ' r ; a, \°°i° boo(Ha n z I
’ ‘ H, LOS) ,4 _r a O
’V“; l03€>°° 6n. ﬁbwo.
oer—0.05 YL 'r—M’” , 7 r n r r “ K . newt tel l. I " SS 000, tie. ULM (5 M ‘Mml’wé 393*! ("d Aoweuef, ggows' 5—2' ’ ) 4,, O’ttohvx. ewe stated mu. (c) (3 marks) If the reinvestment rate is 10%, what is the composite rate for return of a project
with net cash ﬂows A0 = 3,000, A1 ; —2, 000, A2 = —5,000, A3 = 7,000 (where At denotes
the amount at the end of period t)? ' ' ’ ’ " ' V V ' ,7 ' :1: 3I°°°(l+‘l)— 2000 : Lgoo F2 : @3506") (Hi). Sooo : “3,510 {—35% (n+8) elem? = Q =9
e4 H; ‘2 Mt is
/ ' g: rate
or —.€,>’m+}§:o 4
H5 kid / 7 , q» mascunn‘d, , Answer each of the following: (a) (3 marks) If a loan is given out on the terms that ‘the nominal quarterly rate is 4% and interest
is compounded monthly’, what is the effective annual interest rate? (4:.04 4 7
' fur19" I.
T71: :35 = 3 ('04) 300 ‘2 (b) (4 marks) A 10—year bond with face value of $ 10,000 has a bond rate of 8% paid quarterly. If a
potential buyer wishes to earn a nominal annual rate of return of 12% on the investment, what
is the maximum price she would be willing to pay? (Use formula to calculate.) “We QMounT ‘Fma €404 cowhue: 1S 1%}: ’0)ooo=200 ’ " 6‘4: 12.612) = .03 n = 1o754s4o In, "PW :§o<>(£.) .03);4o .4 lo,oo¥€_, .0340)
O _
: 200' (hos) m } 30,000 i _40 ::
Gosﬂwgﬁo  (A03) c 300(93.u4;;m¢) + loioooloaossscsa) a: 4,622.954 + 3,065. 562 = $1628.52? '
(c) (3 marks) A collateral bond with a face value of $8000 was purchased by an investor for $5900. The bond was due in 8 years, and it had a bond interest rate of 5% per year, payable semian
nuallyplf the investor kept the bond to maturity, what is the equation that must be solved to
ﬁnd the investor’s rate of return per semiannual period? Evggv C Madras “rHeBomn Piavs 192;. 3000: 200 ~ 7 7 ’3 "a; as e it
~ :PW : 2006;? 52,16) I 8000 (“9 , “)6? ‘69 {Elbe “TH; INveyroe PAID S‘ioo. Tim serve: ‘
5900 =ﬂoo{;§;)dz,le)+gooo(‘g,c§,I6}. ' 75 5. Answer each of the following; (a) (5 marks) Army Research Laboratory scientists developed a diffusionenhanced adhesion process
that is expected to signiﬁcantly improve the performance of multifunction hybrid composites.
NASA engineers estimate that composites made using the new process will result in savings in
many space exploration projects. The cash ﬂows for one project are shown below. State the equation which must be solved to determine the rate of return per year. gem/so ﬂog—{'80 (3) , .
i ' ‘ . 3C° : A ‘ g ‘
C) ‘
(b) (5 marks) A permanent endowment at the University of Alabama is to award scholarships to
engineering students. The awards are to be made beginning next year. A lumpsum donation of X dollars is made today. The interest from the endowment is to fund 100 students each year. A decision has been made to set funding per student to 10,000 in year 1 and then to increase it each year by %2. If the applicable interest rate is 5%, what must X be to continue funding 100 students per year forever? io,ooo IO)0°C> (115°?) ’°’°°° (“‘02”): + . . .
' ____’_____.. + f
X“ '00 “by; (Hops? ((+OS)3
3
.02
: [pomooo ‘ + [.02 yi+ !.°’2)2 J???) + . . . ]
l + .os lv35 ‘ ‘35 ' J.
:‘152530‘9594f “.qHAQSSh
: 35, 3.33553 . 33 _. .ﬂ “ a; I.“ t
,5" «fl 5.; iii .5 *\ i in‘W \ “ m. J ‘ a e; l V W
S v Q f’ “300 (TE) Mg” leof'ﬁbiigyf’pE/c'ivg 4‘ $66 75:95.2 g) ﬂigg Cr?” ($1 blSC UH“ ' 6. TWO mutually exclusive projects have the estimated cash ﬂows shown below. Using ‘annual worth’
analysis, determine which project should be selected at an interest rate of 20% per year. (Factor
values for i = 20% appear below.) What implicit assumption must be made for your analysis to be valid? Project B
80,000
—7,000 year 1, increasing by 1000 per year 4,000
(P/A, i, n) I (P/G, i, n)
0.8333
1.5278 First cost,
Annual cost per year
Salvage value,
Life, years 2.2
3.64 I
5.368 0.65455
0.47473 o
0.38629 0.27473
0.18629 7.4416 0 0.334380 4.9061 ..1.6405 .9
0.10071 9.9299 0.30071
0.07742 12.9159 0.27742 4.2998 0.2326 0.06061 16.4991 0.26061
5.1598 0.1938 0.04808 20.7989 0.24808 25.2552 5.22252 4.5225
7.4301 0.1346 0.0311 32.1504 0.23110 4.3271 11.4335
12.8871 14.233
15.4667 3.4841 —
‘ gw(A):—4Q,ooo {Syﬂozyﬂ .. @000
: ,4‘91000 (0'4‘F4 $3) — £9000
= r r r A,
i o ' 90%.]; :
ﬁlm/(B): 80,000{ﬂ_}§o7§, ZFooo —looo (glﬂoA/5)+4,M0{%I ) A. g 00(533453) 1000 ﬂ1000(L6406)+4,ooo(39.1g438.)
= — 0,0 ,
( ) _ 96,1501; 1)ooo 16405 4 531.52 * ‘ 2515265223 2 (i) 4W(4)7AW(B)' =7 CHOOSE A. e SeveeAL ASS’UMF'TIOIUS  . .
IS 79041” THE Sefewces e? “We ‘P’aase
3x5 :15“ “Time m? “The MAIN 0N6 Be Neeveo Foe Mam‘l venes 963.. QT U3 H—L k V / 7 i , op msenmv'o .4543. ,. ’  ,, , 7. A ﬁrm must select among the following three mutually exclusive projects: [—— Project A I Project B I Project C A E” i...—
) Initial Cost (in year 0) 1000 1500 1900 ' loco  Koo #900
Annual Revenues (in years 1 and 2) 1,000 2,000 2,400 sub 80° 10°
‘— Annual Costs (in years 1 and 2) 500 1 1200 1,700 5°C (300 :00 (a) (5 marks) What is the rate of return of each project? 8 + (loco$00) 82 ?ﬁ63€£1 A‘ O =lOoo + (loco—Soc) ’ a ,
O : 400° + Secs“? >055 I‘ll “4(052) .. "+3 “4465+? S=~7¢~w~7ﬂ 2 ":Llro
A g . WM
2
77203633: o:\Seo 4 8008248006 _ 81. Vl€A_4(8)(_K}
oens+85+gﬁ =3 5" 9(2) _' _— 200442245§
6529914 ‘ ?ee1emC20;—\aoo+?oa5+ 330632 :3 i I
e ~ia+?F9+?6’=3 6t“ ‘gi WWy'me [iii/11M: cg: ~12» Aig,'14acs(Less) 39.7914 (b) (5 marks) Determine using incremental ROR analysis which project should be chosen by the
ﬁrm assuming the M ARR = 5% . 54c“ HA5 , 64 Mllan =7 NONG SHOW!) 39 CONMDGSZED. lo) .
gee M Tes 6m? C00 Aron (
(c) U$:A 1F EACW}? (EACH)? AND PGFLACG €3in21 WM: '5) yc—Aas’. 0 § op {5:58 cm? : 0 ...
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