Sample Test 2 Solutions

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Sample Test 2 Solutions
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Problem 1

• The following material costs are anticipated over
  a 5-year period9000, 11,000, 14,000, 18,000
  and 23,000. It is estimated that a 4 inflation
  rate will apply over the time period in question.
  The material costs given above are expressed in
  then-current dollars. The time value of money,
  excluding inflation, is estimated to be 7.
  Determine the present worth equivalent for
  material cost.
• What do we know?
• T1 A1 9,000
• T2 A2 11,000
• T3 A3 14,000
• T4 A4 18,000
• T5 A5 23,000
• j .04
• d .07
• i d j dj .07 .04 (.07)(.04) .1128

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Problem 1
PW(i) 9000(1 .1128) -1 11,000(1.1128) -2
14,000(1.1128) -3 18,000(1.1128) -4
23,000(1.1128) -5 PW(i) 8088 8883 10,160
11738 13,479 PW(i) 52,348
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Problem 2
ABC Company bonds sell for 96. The bonds have a
face value of 1,000 and a dividend rate of 7
per year payable annually. Assume the bond
matures in 25 years and the fifth annual dividend
was paid yesterday. If you buy the bond today
a) What is the current yield? b) What is the
yield to maturity? What do we know? Face value
F 1000 Dividend rate .07 n 25 years a)
Dividend Div rate face value (.07)(1000)
70/year Current yield 70/960 .0729
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Problem 2
b) PW(i) 0 -960 70(PA, i, 25) 1000(PF,
i, 25) Try i 7.0 -960 70(11.6536)
1000(.1842) 0 -960 815.752 184.2
39.952 Try i 8.0 -960 70(10.6748)
1000(.1460) 0 -960 747.236 146 -66.764
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Problem 3
A firm purchases a new computer for 15,000 the
computer will be used for 4 years and is then
sold for 5,000. Annual disbursement for
operating , maintenance , and software costs
equals 5,000/year over the 4-year period. The
computer replaced an older manual system that
cost 12,000/year. What is the internal rate of
return for the new computer. What do we know? P
-15,000 N 4 F 5,000 (salvage) A
-5,000/year A old 12,000 P new old (i) 0
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Problem 3
Try i 20 P(20) -15,000 7000(PA, i, 4)
5000(PF, i, 4) 0 P(20) -15,000
7000(2.5887) 5000(.4823) 0 P(20) -15,000
18120.9 2411.5 5532.4 Try i 30 P(30)
-15,000 7000(2.1662) 5000(.3501) 0 P(30)
-15,000 15163.4 1750.5 1913.9 Try i
40 P(30) -15,000 7000(1.8492) 5000(.2603)
0 P(30) -15,000 12944.4 1301.5
-754.1 Now interpolate
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Problem 3
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Problem 4
Maintenance on a reservoir is cyclical with the
following costs occurring over a 5-year period
5,000, 2,000, 7,000, 0, and 2,000, It is
anticipated that the sequence will repeat itself
every 5 years forever. Determine the capitalized
cost of the maintenance costs based on a time
value of money of 10.
0
1
2
3
4
5
2,000
2,000
5,000
7,000
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Problem 4
P(10) 5000(1.10) 1 2000(1.10) 2
7000(1.10) 3 2000(1.1) 5 P(10) 4545 1653
5259 1242 P(10) 12,699 A P(A/P, i, n)
12,699(AP, 10, 5) A 12,699(.2638) A
3349.99 CW A/I 3350/.10 33,500
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Problem 5
Assume a deposit is made at t-2 of 300 and at
t4 of 200. Also, assume the interest rate is
10 in years 1 and 2 and 12 in years 3 and 4.
What uniform annual series over years 1-4 is
equivalent to the two deposits mentioned above?
Pa 300(1.10) 2 200(1.12) 2 (1.10) 2 Pa
248 200(.797)(.826) Pa 248 132 Pa 380 Pb
A(1.10) 1 A(1.10) 2 A(1.12) -1 (1.10) 2
A(1.12) 2 (1.10) 2 Pb .909A .826A .738A
.658A Pb 3.13A Pa Pb 380 3.13A A 121
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Problem 5
A
300
200
10
10
12
12
0
1
2
3
4
B
0
1
2
3
4