Engr.

Mel Kenneth Mabute

FIRST Semester, A.Y. 2018-2019
1. Simple Interest
2. Compound Interest
3. Annuity
4. Factors
5. Gradients
6. Capitalized Cost
6. Simple Discount rate
7. Inflation
8. Depreciation and related Methods
9. Break-even analysis
10. Cost-Benefit Ratio
11. Rate of Return
12. MARR
13. Bonds and Stocks
14. MACRS
Example 5.1
If a man borrowed money from his
girlfriend with simple interest rate of 12%,
determine the present worth of P75,000
which is due at the end of seven months.
Example 5.2
If the sum of P12,000 is deposited in an
account earning interest rate of 9%
compounded quarterly , what will it become
after 1 year? What is the effective rate?
Example 5.3
If P500 is invested at the end of each
year for 6 years at an annual interest rate
of 7%, what is the total peso amount upon
the deposit of the sixth payment?
Example 5.4
A fund is to provide an annual
scholarship at P4,000 for the first 5 years;
P6,000 for the next 5 years and P9,000
thereafter. The fund will be established 1
year before the first scholarship is awarded.
If the fund earns 12% interest, what sum
must be deposited?
Example 5.5
A manufacturing plant installed a new
boiler at a total cost of P150,000. It is estimated
to have a useful life of ten years with the scrap
value of P5,000. Annual maintenance cost is
P10,000. If the interest is 12% compounded
annually, determine the equivalent present
worth of the annual maintenance cost.
 This is an interest transaction where
the price of the corresponding loan is set
down by subtracting the so-called discount
from the amount due. Corresponding
interest is credited at the beginning of the
discount period (interest in advance), while
in the simple interest model the interest is
credited in arrears at the end of the interest
period.
 𝐹−𝑃 𝐹−𝑃 𝑖
i= id = id =
𝑃 1 𝑦𝑒𝑎𝑟 𝐹 1 𝑦𝑒𝑎𝑟 1+𝑖

Where: P = principal
F = future value
id = simple discount rate
i = simple interest rate
Example 5.6
A C.E. borrowed P50,000 from a bank
and promises to pay the loan after 1 year.
The C.E. received P45,000 in cash.
Determine the rate of discount and the rate
of interest.
 Increase in the amount of money
needed to purchase same amount of goods
or services. Results in decrease in
purchasing power.
 if = i + f + if

Where: f = inflation rate

if = market or inflation-adjusted rate
i = real interest rate
Example 5.7
A P2,000 in 2years has an average
inflation rate of % and the real interest rate
of money is 10%. Determine the inflation-
adjusted interest rate.
 BVm = FC - Dm
Let: FC = first cost
SV = salvage value
d = depreciation charge (per year)
n = economic life
m = anytime before n
BVm = book value at m years
Dm = total depreciation for m years
Straight Line Depreciation Method
𝐹𝐶−𝑆𝑉
d= Dm = d(m)
𝑛

Sinking Fund Method

𝐹𝐶−𝑆𝑉 𝑖 1+𝑖 𝑚 −1
d= Dm = d[ ]
1+𝑖 𝑛 −1 𝑖
Sum of Years Digit Method
𝑛−𝑚+1
d = (FC − SV) 𝑛
1𝑥
𝑛
(𝑛−𝑚+1) 𝑥
Dm = (FC - SV) 𝑛𝑥
1
Declining Balance Method
𝑛
BVm = FC(1 – K)m K = 1- 𝑆𝑉/𝐹𝐶
dm = BVm-1 - BVm Dm = FC – BVm
Double Declining Balance Method
K =2/n BVm ≥ SV
Service Output Method
𝐹𝐶−𝑆𝑉
d= Dm = d(Qm)
𝑄𝑛

where:
Qm = quantity produced up to year m
Qn = quantity produced during economic life n
Example 5.8
A 30hp sand mill cost P410,000.
Salvage value of mill is estimated to be
P60,000 after 20 years. Find the appraisal
or book value of the sand mill using
straight line depreciation method after 10
years
Example 5.9
A dump truck was bought for
P300,000 six years ago. It will have a
salvage value of P30,000 four years from
now. Determine the present value of the
dump truck if the depreciation method
used is sinking fund at 6%?
Example 5.10
An asset is purchased for P9,000. Its
estimated life is 10 years, after which it will
be sold for P1,000. Find the book value at
the end of third year if sum-of-the-year’s
digit method depreciation is used.
Example 5.11
UMak purchased new 3D projectors
with a total worth of P618,000. If the
equipment is depreciated over an eight-year
period with salvage value of 5%, determine
the depreciation charge during the fifth
year using declining balance method
Example 5.12
In the previous problem, determine the
depreciation charge during the fifth year
using double-declining balance method.
Example 5.13
A property is purchased at P100,000 with a
salvage value of 10% of the original cost after 8
years of service. If during the first 4 years of
service it produces 100 units per year and 80
units each year for the remaining years. What
will be the book value after 5 years of service
using service output method?
 A method of determining when costs
exactly equal to revenue.

Cost = Revenue
Example 5.14
Steel drum manufacturers incur a
yearly fixed operating cost of P200,000.
Each drum manufactured costs P160 to
produce and sells P200. What is the
manufacturers break-even sales volume in
drums per year.
 BCR > 1 have greater benefits than
costs and if the value is significantly greater
than 1, the project should be considered.

bcr = (present value of benefit)/cost

where: benefit = net profit or income
Example 5.15
A small entrepreneur invested a capital
of P80,000 for a buy and sell business. He
estimated to have a gross income of
P25,000 annually and an operating cost of
P6,000 annually. It is assumed the
business to have a life of 10 years. If the
rate of interest is 12%, compute the BCR.
 measures the yield as a passenger of
investment over the life of a project.
𝑎𝑛𝑛𝑢𝑎𝑙 𝑛𝑒𝑡 𝑝𝑟𝑜𝑓𝑖𝑡
ROR =
𝑎𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 𝑖𝑛𝑣𝑒𝑠𝑡𝑒𝑑

where: net profit = (income or savings) - expenses

Example 5.16
It is estimated that insulation of steam
pipes in a factory will reduce the fuel bill by as
much as 20%. The cost of the insulation is
P90,000 installed and the annual cost of taxes
and insurance is 5% of the initial cost. Without
insulation, the annual fuel bill is P180,000. If
the insulation is worthless after 6 year-use,
what would be the rate of return? i=12%
 minimum return the company will
accept on the money it invests (usually
calculated by financial analysts).
Same as the interest rate used for
Present Worth, Annual Worth, and Future
Worth analysis.
Period required to recover the total.
𝑡𝑜𝑡𝑎𝑙 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 𝑖𝑛𝑣𝑒𝑠𝑡𝑒𝑑 1
Recovery Period = 𝑎𝑛𝑛𝑢𝑎𝑙 𝑛𝑒𝑡 𝑝𝑟𝑜𝑓𝑖𝑡
= 𝑅𝑂𝑅
Length of time required to recover fixed
capital.
𝑑𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑒𝑑 𝑓𝑖𝑥𝑒𝑑 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡
Payout Period = 𝑎𝑛𝑛𝑢𝑎𝑙 𝑝𝑟𝑜𝑓𝑖𝑡+𝑎𝑛𝑛𝑢𝑎𝑙 𝑑𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛
Example 5.17
It is estimated that insulation of steam
pipes in a factory will reduce the fuel bill by as
much as 20%. The cost of the insulation is
P90,000 installed and the annual cost of taxes
and insurance is 5% of the initial cost. Without
insulation, the annual fuel bill is P180,000. If
the insulation is worthless after 6 year-use,
determine the recovery period? i=12%
Example 5.18
What is the maximum amount an
investor should pay for a 25-year bond with
a P20,000 face value and 8% coupon rate
(interest only paid semi-annually)? The
bond will be kept to maturity. The
investor’s effective annual interest rate for
economic decision is 10%.
Example 5.19
ABC Corporation has preferred stock
outstanding. This stock pays an annual
dividend of P2.5. If the next dividend is paid
1 year from now and the annual required
return is 10%, what should be the value of
the preferred stock?
Example 5.20
A machinery worth P10,000 has an
anticipated salvage value of P3,000 at the
end of 7 years’ depreciable life. Compute
the depreciation of the machinery on
the 4th year only using MACRS method.
Review Innovations. May 2018 CE Review
Handout: Review Innovations. 2018