SOLVED PROBLEMS IN
ENGINEERING ECONOMICS
CLSU-AE Board Exam Review
Materials
1
Determine the ordinary simple interest on P35,000 for 7
months and 15 days if the rate of interest is 8%?
Given:
P = 35,000
i = 8%
n = 7mos & 15 days = 15days/30days = 0.5mo
= 7.5mos/12 = 0.625 year
Solution:
I = P x ix n
= P35,000 x 0.08 x 0.625
= P1,750
CLSU-AE Board Exam Review
Materials
2
Compare the interest earned by $10,000 for 7 years at 6%
simple interest per year with the interest earned by the same
amount for five years at 6% compounded annually.
Simple interest:
I=Pxixn
= 10,000 x 0.06 x 7
= $4,200
Compound interest:
F = P (F/P,6%, 7)
= 10,000 (1+0.06)7
= 10,000 (1.5036)
= $15,036.30
I=F–P
= $15,036.30 - $10,000
= $5,036.30
CLSU-AE Board Exam Review
Materials
3
At a certain interest rate compounded quarterly, P1,000 will
amount to P4,500 in 15 years. What is the amount at the end
of 10 years?
Given: For 15 years
P = P1,000
;
n = 15 (4) = 60 periods
F = P4,500
For 10 years:
F
Solution:
F
= P (1+i)n
4,500 = 1,000 (1+i)60
4.5
= (1+i)60
4.5 1/60 =1+i
i
= 1.02538 – 1
i
= 2.538%
CLSU-AE Board Exam Review
Materials
=
=
=
=
P (1+i)n
1,000 (1+0.02538)40
1,000 (2.725)
P2,725.17
4
A man possesses a promissory note, due 3 years, hence
whose maturity value is P6,700.48. If the rate of interest is
10% compounded semi-annually, what is the value of this
note now?
Given:
F = P6,700.48
i = 10% / 2 = 5%
n = 3 years x 2 = 6 periods
Solution:
P = F (1+i)-n
= 6,700.48 (1+0.05)-6
= 6,700.48 (0.746)
= P5,000
CLSU-AE Board Exam Review
Materials
5
A bond with a par value of P1,000 and a bond rate of 9%
payable annually is to be redeemed at P1,050 at the end of 6
years from now. If it sold now, what should be the selling
price to yield 8%?
Given:
C = P1,050
Z = P1,000
i = 8%
r = 9%
n = 6 years
Solution:
Vn = C (P/F, i%, n) + rZ (P/A, i%, n)
= 1,050 (P/F, 8%, 6) + 0.09(1,000) (P/A, 8%, 6)
= 1,050 (0.6302) + 90 (4.6229)
= 661.71 + 416.06
= 1,077.77
CLSU-AE Board Exam Review
Materials
6
On land worth P800,000, an investor constructs a building worth P3,000,000
containing a theater, a bank, stores and offices. The owner estimates that
the annual receipts from rentals will be P720,000, and annual expenses to
cover taxes, insurance and maintenance of the building will be P80,000. He
also estimates that the land can be sold for P1,200,000, the building for
P2,000,000 at the end of 20 years. If his money is now earning 15% before
taxes, will this property earn enough for the investment to be justified? Use
AW method.
Solution:
AW(15%) = R – E – CR(i%)
= 720,000 – 80,000 –
[ (3,800,000) (A/P, 15%, 20) – 3,200,000 (A/F, 15%, 20)]
= 640,000 – [ (3,800,000) (0.1598) – 3,200,000 (0.0098)]
= 640,000 – (607,240 – 31,360)
= 640,000 – 575,880
= 64,120
SINCE AW(15%) > O, the investment is justified.
CLSU-AE Board Exam Review
Materials
7
A machine is purchased on the basis of guaranteed
performance. However, initial tests indicate that the operating
cost will be P500 more per year than guaranteed. If the
expected life is 25 years and money is worth 10%, what
deduction from the purchase price would compensate the
buyer for the additional operating cost?
Given:
A = P500
N = 25 years
i = 10%
Solution:
P = A (P/A, 10%, 25)
= P500 (9.0770)
= P4,538.50
CLSU-AE Board Exam Review
Materials
8
How much money would you have to deposit for five
consecutive years starting one year from now if you want to be
able to withdraw P100,000 fifteen (15) years from now?
Assume the interest is 15% compounded annually.
Solution:
P5 = F (P/F, 15%, 10)
= P100,000 (0.2472)
= P24,720
P5 = F5 ; Solve for A ; N = 5 years
A = F (A/F, 15%, 5)
= 24, 720 (0.1483)
= P3,665.98
CLSU-AE Board Exam Review
Materials
9
A farmer wants to buy a new combine rather than hire a
custom harvester. The total fixed costs for the desired combine
are $21,270 per year. The variable costs (not counting the
operator's labor) are $8.75 per hour. The farmer can harvest 5
acres per hour. The custom harvester charges $16.00 per acre.
How many acres must be harvested per year to break-even?
Solution:
Fixed costs = $21,270
Charge of custom harvester= $16/A
Variable costs = $8.75/hr / 5 A/hr = $1.75/A
BEP = CF / (p-cv)
= $21,270 / ($16/A - $1.75/A)
= $21,270 / $14.25/A
= 1,493 Acres
CLSU-AE Board Exam Review
Materials
10
What is the principal amount if the principal plus interest at the
end of 3 years is P 15,000 for a simple interest of 20% per
annum?
Solution:
F = P (1 + ni)
P = F / (1 + ni)
= 15,000 [ 1+ 3(0.20)]
= 15,000 (1.6)
= 24,000
CLSU-AE Board Exam Review
Materials
11
How long will it take the money to triple itself if invested at 8%
compounded annually?
Solution:
Let P = 1.00 and F = 3.00
F = P (1 + i)n
3 = 1 (1+0.08)N
3 = 1.08N
ln3/ ln1.08 = N
N = 14.27 years or 15 years
CLSU-AE Board Exam Review
Materials
12
What if it is compounded quarterly?
Solution:
i = 8/4 = 2%
F = P (1+i)N
3 = 1 (1+0.02)N
3 = 1.02N
ln3/ ln1.02 = N
N = 55.48 periods or quarters = 13.87 years or 14 years
CLSU-AE Board Exam Review
Materials
13
How much can be paid for a $5,000, 10% bond, with interest
paid semi-annually, if the bond matures 12 years hence?
Assume that the purchaser will be satisfied with 8% nominal
interest compounded semi-annually.
Solution:
N = 12 x 2 = 24 periods
r = 10% / 2 = 5% per period
i% = 8% / 2 = 4% per period or semi-annually
C = Z = $5,000
Vn = C (P/F, i%, n) + rZ (P/A, i%, n)
= $5,000 (0.05) (P/A, 4%, 24) + $5,000 (P/F, 4%, 24)
= $250 (15.2470) + $5,000 (0.3901)
= $3,811.75 + $1,950.5
= $5,762.25
CLSU-AE Board Exam Review
Materials
14
A one-bagger concrete mixer can be purchased with a down
payment of P8,000 and equal installments of P600 each paid at
the end of every month for the next 12 months. If money is
worth 12% compounded monthly, determine the equivalent
cash price of the mixer.
Solution:
N = 12 months ; i = 12% compounded monthly or 1% per month
PW = 8,000 + 600 (P/A, 1%, 12)
= 8,000 + 600 (11.2551)
= 8,000 + 6,753.06
= 14, 753.06
CLSU-AE Board Exam Review
Materials
15
An electrical appliance manufacturer has fixed costs of P80M
per year and its output capacity is 100,000 appliances per
year. The variable cost is P1,600 per unit, and the product sells
for P3,600 per unit. What is the manufacturer’s breakeven
point?
Solution:
BEP = CF / p – cv
= 80,000,000 / 3,600 – 1,600
= 40,000 units
in % capacity:
= 40,000 units/100,000 units per year
= 0.40 or 40%
CLSU-AE Board Exam Review
Materials
16
What annual rate of simple interest is earned by an investment
of P28,000 if it accumulates P3,552.50 in interest after twentyone months?
Solution:
I = P x i x n ; n = 21 months (1 year/12 months) = 1.75 years
i = I / Pn
= 3,552.50 / 28,000 x 1.75
= 3,552.50 / 49,000
= 0.0725 or 7.25%
CLSU-AE Board Exam Review
Materials
17
A company produces circuit boards that are used to update
computer equipment. The fixed cost is P3.15M per month and
the variable cost is P3,975 per circuit board. The selling price
per unit is p=11,250 – 1.5D. Maximum output of the plant is
6,000 units per month. What demand will maximize the profit
for this product?
Solution:
D* = a - cv / 2b
p = a – bD ; a = 11,250 ; b = 1.5
D* = (11,250 – 3,975) / 2(1.5)
= 7,275 / 3
= 2,425 units
CLSU-AE Board Exam Review
Materials
18
A proposed project will require an initial investment of P50,000
and is estimated to have year-end revenues and costs as
follows:
End-of-Year
Revenue
Cost
1
75,000
60,000
2
90,000
77,500
3
100,000
80,000
4
95,000
75,000
5
60,000
40,000
An additional investment of 25,000 will be required at the end
of the second year. The project would terminate at the end of
the 5th year, and the assets are estimated to have salvage
value of 30,000 at that time. What is the IRR for this project?
CLSU-AE Board Exam Review
Materials
19
Solution:
End-of-Year
Profit
1
15,000
2
-12,500
3
20,000
4
20,000
5
50,000
N
N
PW = Σ Rk (P/F,i’%,k) - Σ Ek (P/F,i’%,k) = 0
k=0
k=0
At i = 15%
PW = - 50,000 + 15,000 (P/F,15%,1) – 12,500 (P/F,15%,2)
+ 20,000 (P/F,15%,3) + 20,000 (P/F, 15%, 4) + 50,000 (P/F, 15%, 5)
= 3,038.75
At i = 18%
PW = - 50,000 + 15,000 (P/F,18%,1) – 12,500 (P/F,18%,2)
+ 20,000 (P/F,18%,3) + 20,000 (P/F, 18%, 4) + 50,000 (P/F, 18%, 5)
= -1,922
BY INTERPOLATION:
i = 16.83%
CLSU-AE Board Exam Review
Materials
20
An agricultural engineer estimated that the purchase of an
automated tiller can save a farmer P150,000 a year in a labor
cost. The tiller has an expected life of 5 years and no salvage
value. If the farmer must earn a 20% annual return on such
investment, at what amount he should spend to justify the
purchase of the tiller?
Solution:
P = A (P/A, 20%, 5)
= 150,000 (2.9906)
= 448,590
The farmer should spend no more than P448,590 in order to justify
the purchase of the tiller
CLSU-AE Board Exam Review
Materials
21
If the tiller was purchased at 448,590 and depreciated by
double-declining balance method, what is the depreciation
charge at the end of the 3rd year?
Solution:
D3 = B (1-R)k-1 (R)
= 448,590 (1 – 2/5)2 (2/5)
= 64, 596.96
CLSU-AE Board Exam Review
Materials
22
The barangay council of remote village was given some
amount of money by the national government to build a
structure that will last 30 years. Estimates of the annual costs
and revenues of various structures are as follows:
Initial Cost
Recreation Hall
Revenues less costs
P300,000
69,000 a year
Cooperative Store
400,000
76,000 a year
Clinic
200,000
40,000 a year
Nursery School
250,000
55,000 a year
A salvage value equal to 20% of the first cost is expected for each
structure. If the interest rate is 12% which structure should the
barangay council choose?
CLSU-AE Board Exam Review
Materials
23
Solution:
For Recreation Hall:
PW = -300,000 + 69,000 (P/A,12%,30)
+ (0.20)(300,000)(P/F, 12%,30)
= -300,000 + 69,000 (8.0552) + (0.20)(300,000)(0.0334)
= 257,812.8
CLSU-AE Board Exam Review
Materials
24
What is the value of the interest factor needed to find the
equivalent at time 0 of P155,000 occurring 7 years from now
when interest rate is 9% per year compounded yearly?
Solution:
F = P (1+i)n solve for the interest factor (1+ 0.09)7 = 1.8280
CLSU-AE Board Exam Review
Materials
25
In a given month, a versatile machine called “Alien” is used to make
400 units of R 60% of the time. For the remaining hours that “Alien”
is in use, 400 units of another product S are made. An overhead
charge of P80,000 per month applies to be allocated using machine
hours. What is the total cost of making R in a month if labor and
materials cost for R and S are given in the table below:
R
Material cost / unit
Labor Cost / unit
S
P150
P170
P80
P90
Solution:
Overhead charge of R/month = P80,000 (0.60) = P48,000
Material cost = 400 units (P150/unit) = P60,000
Labor cost = 400 units (P80/unit) = P32,000
TOTAL COST FOR MAKING PRODUCT R IN A MONTH
= P48,000 + P60,000 + P32,000 = P140,000
CLSU-AE Board Exam Review
Materials
26
What is the value of the interest factor needed to find a series
of equal revenues that must be received every year for 12
years to realize a return of 25% from an initial investment?
Solution:
A = P [(i 1+i)n ] / [(1+i)n -1]
solve for the interest factor [ 0.25 (1+ 0.25)12] / [(1+0.25) – 1]
= 3.6379 / 13.55
= 0.2685
CLSU-AE Board Exam Review
Materials
27
A small manufacturer of a car accessory has fixed costs of P5M
per year and its maximum output capacity is 100,000 units per
year. The variable cost is P1,000 per unit and the product sells
for P1,800 per unit. What is the economic breakeven point for
the company?
Solution:
BEP = CF/ (p-cv)
= 5,000,000 (1,800 – 1,000)
= 6,250 units
CLSU-AE Board Exam Review
Materials
28
If you invest P1,500,000 now in a house and lot, how much
must you rent your property per month for 20 years if you
want an annual return of 20% on your investment?
Solution:
A=
=
=
=
P (A/P, 20%, 20)
1,500,000 (0.2054)
P308,100 per year
P25,675 / month
CLSU-AE Board Exam Review
Materials
29
How much money will be accumulated in 3 years if a person
made a monthly deposit of P2,000 every month up to the 3rd
year when the account pays interest of 1% per month?
Solution:
F = A (F/A, 1%, 36)
= 2,000 (43.0769)
= P86,153.8
CLSU-AE Board Exam Review
Materials
30
Ferdinand Shipping Company bought a tugboat for P750,000. The
boat is expected to last for 5 years, after which it could be sold for
120,000. The following revenues and expenses are expected fot the
first operating year. Revenue = P2,000,000; Expenses = P840,000,
Depreciation = 40,000. If the company is taxed at a rate of 30%,
what is the net income at the end of the first year?
Solution:
Taxes = Taxable income x tax rate
= NIBT (t) ; where NIBT = net income before taxes
t = tax rate
NIBT = Revenues – Expenses – depreciation
= 2,000,000 – 840,000 – 40,000
= 1,120,000
Tax
= 1,120,000 (0.30) =336,000
Net income = 1,120,000 – 336,000
= 784,000
CLSU-AE Board Exam Review
Materials
31
A machine which costs P100,000 when new has a lifetime of
15 years and a salvage value equal to 20% of its original cost.
If interest rate is 10% compounded annually, what is the
capital recovery of the machine?
Solution:
CR =
=
=
=
I (A/P,i%,n) – SV (A/F, i%, n)
100,000 (A/P, 10%, 15) – 100,000 (0.20) (A/F, 10%, 15)
100,000 (0.1315) – 20,000 (0.0315)
12,520
CLSU-AE Board Exam Review
Materials
32
Your father applied for a loan in a bank and the amount of
P80,000 was approved at an interest rate of 14% of which
P11,200 was deducted and your father was given a check for
P68,000. Since you have to pay P80,000 one year after, what
then will be the effective interest rate?
CLSU-AE Board Exam Review
Materials
33
An individual approaches a banker for P500,000. The banker
advertises an interest rate of 12% per year for a five-year
loan. Your interest payments are due at the end of each year
and the principal will be repaid in a lump-sum amount at the
end of year five. Determine the yearly interests an individual is
paying and the effective annual interest being charged.
CLSU-AE Board Exam Review
Materials
34
The Alpha Machinery Corp. had to put up for sale a certain machinery.
Two bidders have the following proposals:
a. Bidder “A” offers 5M payable 20% downpayment, the balance payable
500,000 annually for 8 years.
b. Bidder “B” offers 4.5M 1M downpayment, the balance payable 250,000
semi-annually for 7 years.
Which bid is more beneficial to AMC, if money is worth 10% effective?
Solution:
For Bidder A:
PW = 5,000,000 (0.20) + 500,000 (P/A, 10%, 8)
= 1,000,000 + 500,000 (5.3349)
= 3,667,450
For Bidder B:
Solving for the interest rate per semi-annual:
i = (1 + r/M)M – 1
0.10 = (1 + r/2)2 – 1
r/2 = 0.0488 or 4.88% per semi-annual
PW = 1,000,000 + 250,000 (P/A, 4.88%,14)
= 1,000,000 + 250,000 (9.9756)
= 3,493,918
Exam Review
35
Therefore, the bid which isCLSU-AE
moreBoard
beneficial
to
AMC
is
that
from
Bidder
A.
Materials
A company imports a 30Hp sandmill costing 520,000. Bank
charges, brokerage, etc, costs 10,000. Installation costs were
40,000. Other incidental expenses amounted to 25,000.
Salvage value of the mill is estimated to be 75,000 after 20
years. Find the book value of the mill using SLM, at the end of:
a) 10 years b) 15 years
Solution:
B
= 520,000 + 10,000 + 40,000 + 25,000
= 595,000
d = (B – SV) / N
= (595,000 – 75,000) / 20
= 26,000
d10 = 26,000 (10)
= 260,000
BV10= 595,000 – 260,000
= 335,000
d15 = 26,000 (15)
= 390,000
BV15= 595,000 – 390,000
= 205,000
CLSU-AE Board Exam Review
Materials
36
A man wishes to purchase a car with a total cost of 450,000.
He made a down payment of 50,000 and the balance payable
in 24 monthly installments. If the effective interest rate is 12%
for each year computed on the total balance to be paid by
installment. How much would each installment payment be?
Solution:
Monthly installment:
Interest rate per month = i = (1 + r/M)M – 1
0.12 = (1 + r/12)12 – 1
r/2 = 0.00949 or 0.949% per month
A
= (450,000 – 50,000) (A/P, 0.949%,24)
= 400,000 (0.0467)
= 18, 717.92
CLSU-AE Board Exam Review
Materials
37
Suppose you are earning 12,000 a month and you can only afford to buy a
car which will require a downpayment of 10,000 and monthly amortization
of not more than 30% of your monthly salary.
What would be the maximum cash value of a car you can purchase if the
seller will agree to a downpayment of 10,000 and the balance payable in 4
years at 12% compounded monthly. The first payment will be due at the
end of the first month.
Solution:
Monthly amortization
= 0.30 (12,000)
= 3,600
P = A (P/A,1%,48)
= 3,600 (37.9740)
= 136,706.40
Maximum cash value
= 136,706.40 + 10,000
= 146,706.40
CLSU-AE Board Exam Review
Materials
38
Compute for the number of blocks an ice plant must be able to
sell per month to break even based on the following data:
Cost of electricity per block
Tax to be paid per block
Real State Tax
20.00
2.00
3,500/ month
Salaries and wages
25,000/ month
Others
12,000/ month
Selling price of ice
55.00/ block
Solution:
D’ =
=
=
=
CF / (p – cv)
40,500 / (55 – 22)
1,227.27
1,228 blocks
CLSU-AE Board Exam Review
Materials
39
A manufacturing firm purchased a machine worth 500,000 which
is estimated to have a salvage value of 50,000 at the end of its
10 year economic life. How much yearly deposit must the
company deposit in a sinking fund that will pay 18% interest,
compounded yearly, to accumulate the needed fund to purchase
a new machine at the end of the 10th year if a new machine will
cost 75% more by that time?
Solution:
Cost of a new machine at the end of 10th year:
= 500,000 (1.75) – 50,000
= 825,000
A
= F (A/F,18%,10)
= 825,000 (0.0425)
= 35,062.50
CLSU-AE Board Exam Review
Materials
40
Your father purchased a townhouse with a cash price of 1.5M. He
was able to negotiate with the seller to allow him to pay only a
downpayment of 20% and the balance payable in equal 60 end
of the monthly installment at 1% interest per month. On the day
he paid the 30th installment, he decided to pay the remaining
balance. How much is the monthly payment and what is the
remaining balance that he paid?
Solution:
Balance = 1,500,000 - 1,500,000 (0.20) = 1,200,000
Monthly payment:
A = 1,200,000 (A/P, 1%, 60)
= 1,200,000 (0.0222)
= 34,560
Remaining Balance:
P = 34,560 (P/A, 1%, 30)
= 34,560 (48.1734)
= 1,664,872.70
CLSU-AE Board Exam Review
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41
A company has offered a supervisor a yearly gratuity pay of 20,000
for 10 years for having been loyal, trustworthy and efficient. The
first payment is to be made one year after the retirement. The
supervisor, instead, requested that he be paid a lump sum on the
date of his retirement less interest that the company would have
earned if the gratuity is to be paid on the yearly basis. If interest is
15%, what is the equivalent lump sum that he could get?
Solution:
P = A (P/A,15%,10)
= 20,000 (5.0188)
= 100,376
CLSU-AE Board Exam Review
Materials
42
The initial cost of a processing equipment including its installation is
500,000. The BIR approved life of this equipment is 10 years for
depreciation. The estimated salvage value is 40,000, and the cost of
dismantling is estimated to be 15,000.
a) Using straight-line method, what is the annual depreciation charge?
b) What is the book value of the equipment at the end of 6 years?
Solution:
d = (B – SV) / N
= (500,000 – 40,000) / 10
= 46,000
d6 = 46,000 (6)
= 276,000
BV6= 500,000 – 276,000
= 224,000
CLSU-AE Board Exam Review
Materials
43
You were granted a loan of 25,000 by your employee with an
interest of 6% for 6 months on the principal collected in
advance. Your employee would accept a promissory note for
25,000 non-interest for 180 days. If discounted at once, find
the proceeds on the note.
Solution:
Interest = 25,000 (0.06)
= 1,500
Proceeds = 25,000 – 1,500
= 23,500
CLSU-AE Board Exam Review
Materials
44
In order to build a house, you obtain a loan of 1M from GSIS
at the rate of 12% compounded annually. How much must you
pay monthly to amortize the loan within a period of ten years?
Interest = 25,000 (0.06)
= 1,500
Proceeds = 25,000 – 1,500
= 23,500
CLSU-AE Board Exam Review
Materials
45
An asset for drilling was purchased and placed in service by a
petroleum production company. Its cost basis is 90,000 and it
has an estimated economic life of 10 years after which it will
be sold for 10,000. Find the depreciation in the first three
years using the Sum of the Years Digit method.
Interest = 25,000 (0.06)
= 1,500
Proceeds = 25,000 – 1,500
= 23,500
CLSU-AE Board Exam Review
Materials
46
Land Bank of the Philippines is advertising 9.5% accounts that
yields 9.84% annually. How often is the interest compounded?
Interest = 25,000 (0.06)
= 1,500
Proceeds = 25,000 – 1,500
= 23,500
CLSU-AE Board Exam Review
Materials
47
You borrow 5,000 for one year from a friend at an interest rate
of 1.5% per month instead of taking a loan from a bank at a
rate of 18% per year. Compare how much money you will save
or lose in the transaction.
Interest = 25,000 (0.06)
= 1,500
Proceeds = 25,000 – 1,500
= 23,500
CLSU-AE Board Exam Review
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48
You borrow 500,000 at 12% effective annual interest. You
must pay back the loan over 25 years with uniform monthly
payment due on the first day of each month. What is your
monthly payment?
Interest = 25,000 (0.06)
= 1,500
Proceeds = 25,000 – 1,500
= 23,500
CLSU-AE Board Exam Review
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49