1. PROBLEM
A man bought a government bond, which cost P1000 and will pay P50
interest each year for 20 years. The bond will mature at the end of 20
years and he will receive the original P1000. If there is a 2% annual
inflation during this period, what rate of return will the investor receive
after considering the effect of inflation?
Solution:
50
i' = (100) = 0.05
1000
i' = i + f + if
0.05 = i + 0.02 + i(0.02)
i = 0.0294
i = 2.94%
,2. PROBLEM
The maintenance of Isuzu diesel engine is expected to be $155 at the end of the first year
and it is expected to increase $35 each year for the following years. What sum of money
should be set aside now to pay the maintenance for the eight-year period? Assume MARR
to be 6%.
Present worth factor (P/A, 6%, 8) = 6.2098
Sinking fund factor (A/F, 6%, 8) = 0.1010
Compound amount factor (F/A, 6%, 8) = 9.897
Uniform gradient series factor (P/G, 6%, 8) = 19.845
Solution: 0 1 2 3 4 5 6 7 8
P1 ⎡⎣(1 + i) - 1⎤⎦
n
A
=
(1 + i)n i
(
= P / A, 6%, 8 ) A A A A A A A A=155
P1 P1
= 6.2098 (present worth factor)
A
1875
P1 = 155(6.2098)
P1 = $962.50 G=35
35
n
P (1 + i) - 1 n
= 2 - 1 2 3 4 5 6 7
G i (1 + i)n i(1 + i)n 0 1 2 3 4 5 6 7 8
P2
G
(
= P / G, 6%, 8 ) P2
P2
= 19.845 (uniform gradient series factor)
G
P2 = 35(19.845)
P2 = $694.58
P = P1 + P2
P = 962.50 + 694.58
P = $1,657
,3. PROBLEM
Manny Villar is selecting materials for a low cost housing development. The building wil be maintained for
at least 75 years, and the agency uses an i of 6%.
All costs are per square (equals 100 square feet).
Min. Quality Max. Quality
Metal Roofing
Shingles Shingles
Buy $35 $70 $120
Install $70 $70 $100
Annual Maintenance $5 $3 $1
Life (years) 15 25 50
➀ Which of the following grades of shingles and metal roofing is the most effective?
➁ How much do the EACs change if a horizon of 50 years is used? The i is still 6%. How much is the
percentage increased for minimum quality shingles?
Solution:
➀ Most effective grade of shingles and metal roofing
A = 35 + 70 = 105
105(1 + i)n
EACminQ = +5
(1 + i)n - 1
105(1 + 0.06)15 (0.06)
EACminQ = +5
(1 + 0.06)15 - 1
EACminQ = $15.81
A = 70 + 70 = 140
140(1 + 0.06)25 (0.06)
EACmaxQ = +3
(1 + 0.06)25 - 1
EACmaxQ = $13.95
A = 120 + 100 = 220
220(1 + 0.06)50 (0.06)
EACmetal = +1
(1 + 0.06)50 - 1
EACmetal = $14.96
Manny Villar should choose the higher quality shingles. Cheapest $13.95
, 3. PROBLEM cont.
➁ Since 50 is a multiple of 25 and 50, the EAC for the maximum quality shingles is still $13.95 per
square, and the EAC for the metal roofing is still $14.96 per square.
Present Worth(min.Q)
105 105 105
= 105 + 15
+ 30
+ 45
(1 + i) (1 + i) (1 + i)
105 105 105
= 105 + 15
+ 30
+ 45
(1 + 0.06) (1 + 0.06) (1 + 0.06)
Present Worth(min.Q) = 174.72
174.72(1 + i)n i
EACminQ = +5
(1 + i)n - 1
174.72(1 + 0.06)50 (0.06)
EACminQ = +5
(1 + 0.06)50 - 1
EACminQ = $16.08 per square
EAC (increase) = 16.08 – 15.81
EAC (increase) = $0.27
(16.08 - 15.81)
%increased = (100)
15.81
%increased = 1.7%
A man bought a government bond, which cost P1000 and will pay P50
interest each year for 20 years. The bond will mature at the end of 20
years and he will receive the original P1000. If there is a 2% annual
inflation during this period, what rate of return will the investor receive
after considering the effect of inflation?
Solution:
50
i' = (100) = 0.05
1000
i' = i + f + if
0.05 = i + 0.02 + i(0.02)
i = 0.0294
i = 2.94%
,2. PROBLEM
The maintenance of Isuzu diesel engine is expected to be $155 at the end of the first year
and it is expected to increase $35 each year for the following years. What sum of money
should be set aside now to pay the maintenance for the eight-year period? Assume MARR
to be 6%.
Present worth factor (P/A, 6%, 8) = 6.2098
Sinking fund factor (A/F, 6%, 8) = 0.1010
Compound amount factor (F/A, 6%, 8) = 9.897
Uniform gradient series factor (P/G, 6%, 8) = 19.845
Solution: 0 1 2 3 4 5 6 7 8
P1 ⎡⎣(1 + i) - 1⎤⎦
n
A
=
(1 + i)n i
(
= P / A, 6%, 8 ) A A A A A A A A=155
P1 P1
= 6.2098 (present worth factor)
A
1875
P1 = 155(6.2098)
P1 = $962.50 G=35
35
n
P (1 + i) - 1 n
= 2 - 1 2 3 4 5 6 7
G i (1 + i)n i(1 + i)n 0 1 2 3 4 5 6 7 8
P2
G
(
= P / G, 6%, 8 ) P2
P2
= 19.845 (uniform gradient series factor)
G
P2 = 35(19.845)
P2 = $694.58
P = P1 + P2
P = 962.50 + 694.58
P = $1,657
,3. PROBLEM
Manny Villar is selecting materials for a low cost housing development. The building wil be maintained for
at least 75 years, and the agency uses an i of 6%.
All costs are per square (equals 100 square feet).
Min. Quality Max. Quality
Metal Roofing
Shingles Shingles
Buy $35 $70 $120
Install $70 $70 $100
Annual Maintenance $5 $3 $1
Life (years) 15 25 50
➀ Which of the following grades of shingles and metal roofing is the most effective?
➁ How much do the EACs change if a horizon of 50 years is used? The i is still 6%. How much is the
percentage increased for minimum quality shingles?
Solution:
➀ Most effective grade of shingles and metal roofing
A = 35 + 70 = 105
105(1 + i)n
EACminQ = +5
(1 + i)n - 1
105(1 + 0.06)15 (0.06)
EACminQ = +5
(1 + 0.06)15 - 1
EACminQ = $15.81
A = 70 + 70 = 140
140(1 + 0.06)25 (0.06)
EACmaxQ = +3
(1 + 0.06)25 - 1
EACmaxQ = $13.95
A = 120 + 100 = 220
220(1 + 0.06)50 (0.06)
EACmetal = +1
(1 + 0.06)50 - 1
EACmetal = $14.96
Manny Villar should choose the higher quality shingles. Cheapest $13.95
, 3. PROBLEM cont.
➁ Since 50 is a multiple of 25 and 50, the EAC for the maximum quality shingles is still $13.95 per
square, and the EAC for the metal roofing is still $14.96 per square.
Present Worth(min.Q)
105 105 105
= 105 + 15
+ 30
+ 45
(1 + i) (1 + i) (1 + i)
105 105 105
= 105 + 15
+ 30
+ 45
(1 + 0.06) (1 + 0.06) (1 + 0.06)
Present Worth(min.Q) = 174.72
174.72(1 + i)n i
EACminQ = +5
(1 + i)n - 1
174.72(1 + 0.06)50 (0.06)
EACminQ = +5
(1 + 0.06)50 - 1
EACminQ = $16.08 per square
EAC (increase) = 16.08 – 15.81
EAC (increase) = $0.27
(16.08 - 15.81)
%increased = (100)
15.81
%increased = 1.7%
