Study guide
4.3 Engineering Economics & Financial Analysis
PRC Electronics Engineering Licensure Examination Study Guide Exam
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1 Chapter 1: Introduction & Board Exam Strategy
1.1 PRC ECE Licensure Exam Overview & Regulation 1.2 Table of Specifications & Exam Strategy
2 Chapter 2: Mathematics Foundations
2.1 College & Advanced Algebra 2.2 Trigonometry & Solid Mensuration 2.3 Analytic Geometry & Differential Calculus 2.4 Integral Calculus & Applications
3 Chapter 3: Advanced Mathematics for ECE
3.1 Differential Equations & Circuit Transients 3.2 Complex Numbers & Laplace Transforms 3.3 Fourier Series, Fourier Transforms & Z-Transforms 3.4 Vector Analysis, Matrices & Probability
4 Chapter 4: GEAS - Engineering Sciences & Economics
4.1 Engineering Physics & Materials Chemistry 4.2 Engineering Mechanics & Strength of Materials 4.3 Engineering Economics & Financial Analysis 4.4 Computer Fundamentals & C/C++ Programming
5 Chapter 5: GEAS - Management, Materials, Environment & CAD
5.1 Engineering Management & Technopreneurship 101 5.2 Materials Science & Engineering 5.3 Environment Science & Engineering 5.4 Computer-Aided Drawing (CAD) & Engineering Graphics
6 Chapter 6: GEAS - ECE Laws, Ethics & Contracts
6.1 Republic Act No. 9292 (Electronics Engineering Law of 2004) 6.2 ECE Code of Ethics & Professional Conduct 6.3 Contracts, Specifications & National Building Code (PD 1096)
7 Chapter 7: Electronics Engineering - Circuits & Semiconductor Diodes
7.1 DC & AC Circuit Analysis & Network Theorems 7.2 Electromagnetics & Passive Components 7.3 Semiconductor Physics & Diode Circuits 7.4 Power Supply Design & Voltage Regulators
8 Chapter 8: Electronics Engineering - Transistors & Analog Circuits
8.1 BJT Operation, Biasing & Small-Signal Amplifiers 8.2 FET Characteristics, Biasing & Amplifier Circuits 8.3 Multistage Amplifiers, Frequency Response & Power Amplifiers 8.4 Operational Amplifiers & Active Filter Design
9 Chapter 9: Electronics Engineering - Digital Electronics & Control Systems
9.1 Feedback Topologies & Oscillator Circuits 9.2 Boolean Algebra, Logic Gates & Combinational Circuits 9.3 Sequential Logic, Flip-Flops & Microprocessor Architecture 9.4 Industrial Power Electronics & Control System Theory
10 Chapter 10: EST - Communications Fundamentals & Transmission Lines
10.1 Signal Fundamentals, Decibel Calculations & Noise Analysis 10.2 Amplitude Modulation (AM) Principles & Receivers 10.3 Frequency Modulation (FM), Phase Modulation & Discriminators 10.4 Transmission Line Parameters, SWR & Smith Chart
11 Chapter 11: EST - Digital Communications, Wireless & Optical Systems
11.1 Pulse & Digital Modulation Systems 11.2 Data Communications, OSI Model & Protocols 11.3 Antenna Principles & Electromagnetic Wave Propagation 11.4 Optical Fiber, Microwave, Satellite & Philippine NTC Regulations
4.3 Engineering Economics & Financial Analysis
Key Takeaways Explain This Topic AI
Time value of money converts single future sums F = P(1+i)^n using the single payment compound amount factor (F/P, i, n).
Uniform series annual cash flows relate to present worth via P = A [ ( 1 + i ) n − 1 i ( 1 + i ) n ] P = A \left[ \frac{(1+i)^n - 1}{i(1+i)^n} \right] P = A [ i ( 1 + i ) n ( 1 + i ) n − 1 ] using (P/A, i, n).
Depreciation reduces asset book value over recovery life: Straight-Line gives constant d = C − S n d = \frac{C - S}{n} d = n C − S , whereas SYD accelerates early tax deductions.
Net Present Value (NPV) evaluation criteria accepts projects when NPV ≥ 0 \ge 0 ≥ 0 at the Minimum Attractive Rate of Return (MARR).
Capitalized cost C C = C 0 + A i + R C ( 1 + i ) k − 1 CC = C_0 + \frac{A}{i} + \frac{RC}{(1+i)^k - 1} CC = C 0 + i A + ( 1 + i ) k − 1 RC represents the present worth of an asset maintained indefinitely through periodic replacement.
Last updated: July 2026
- 4.3 Engineering Economics & Financial Analysis
- 1. Principles of Engineering Economics & Interest Formulas
Engineering Economics combines engineering decision-making with financial evaluation to select the most cost-effective alternatives over a project's lifecycle.
Simple vs. Compound Interest
Simple Interest : Interest is charged only on the principal amount P P P : I = P ⋅ i ⋅ n , F = P ( 1 + i ⋅ n ) I = P \cdot i \cdot n, \quad F = P(1 + i \cdot n) I = P ⋅ i ⋅ n , F = P ( 1 + i ⋅ n )
Compound Interest : Interest earned in each period is added to the principal to earn interest in subsequent periods: F = P ( 1 + i ) n F = P(1 + i)^n F = P ( 1 + i ) n where P P P is Present Worth, F F F is Future Worth, i i i is interest rate per period, and n n n is number of compounding periods.
Nominal vs. Effective Interest Rates
When an annual nominal interest rate r r r is compounded m m m times per year:
- Period interest rate: i = r m i = \frac{r}{m} i = m r
- Total periods in Y Y Y years: n = m ⋅ Y n = m \cdot Y n = m ⋅ Y
Effective Annual Rate ( i eff i_{\text{eff}} i eff ) : i eff = ( 1 + r m ) m − 1 i_{\text{eff}} = \left(1 + \frac{r}{m}\right)^m - 1 i eff = ( 1 + m r ) m − 1
Continuous Compounding : As m → ∞ m \to \infty m → ∞ , the future worth becomes F = P e r n F = P e^{r n} F = P e r n , and i eff = e r − 1 i_{\text{eff}} = e^r - 1 i eff = e r − 1 .
2. Discrete Cash Flow Equivalence Factors
Equivalence Factor Name Standard Notation Formula
Single Payment Compound Amount ( F / P , i , n ) (F/P, i, n) ( F / P , i , n ) ( 1 + i ) n (1 + i)^n ( 1 + i ) n
Single Payment Present Worth ( P / F , i , n ) (P/F, i, n) ( P / F , i , n ) ( 1 + i ) − n (1 + i)^{-n} ( 1 + i ) − n
Uniform Series Sinking Fund ( A / F , i , n ) (A/F, i, n) ( A / F , i , n ) i ( 1 + i ) n − 1 \frac{i}{(1 + i)^n - 1} ( 1 + i ) n − 1 i
Uniform Series Compound Amount ( F / A , i , n ) (F/A, i, n) ( F / A , i , n ) ( 1 + i ) n − 1 i \frac{(1 + i)^n - 1}{i} i ( 1 + i ) n − 1
Capital Recovery Factor ( A / P , i , n ) (A/P, i, n) ( A / P , i , n ) i ( 1 + i ) n ( 1 + i ) n − 1 \frac{i(1 + i)^n}{(1 + i)^n - 1} ( 1 + i ) n − 1 i ( 1 + i ) n
Uniform Series Present Worth ( P / A , i , n ) (P/A, i, n) ( P / A , i , n ) ( 1 + i ) n − 1 i ( 1 + i ) n \frac{(1 + i)^n - 1}{i(1 + i)^n} i ( 1 + i ) n ( 1 + i ) n − 1
Arithmetic Gradient Present Worth ( P / G , i , n ) (P/G, i, n) ( P / G , i , n ) ( 1 + i ) n − i n − 1 i 2 ( 1 + i ) n \frac{(1+i)^n - i n - 1}{i^2 (1+i)^n} i 2 ( 1 + i ) n ( 1 + i ) n − in − 1
- 3. Project Evaluation Methods
- 1. Present Worth (PW) Method
All cash inflows ( + R t +R_t + R t ) and outflows ( − C t -C_t − C t ) are discounted to t = 0 t=0 t = 0 using the Minimum Attractive Rate of Return (MARR): PW = ∑ t = 0 n R t − C t ( 1 + MARR ) t \text{PW} = \sum_{t=0}^n \frac{R_t - C_t}{(1 + \text{MARR})^t} PW = t = 0 ∑ n ( 1 + MARR ) t R t − C t
Decision Criterion : Accept project if PW ≥ 0 \text{PW} \ge 0 PW ≥ 0 .
2. Annual Worth (AW) Method
Converts all project cash flows into an equivalent uniform annual cash flow over the service life: AW = PW × ( A / P , i , n ) \text{AW} = \text{PW} \times (A/P, i, n) AW = PW × ( A / P , i , n )
Decision Criterion : Accept project if AW ≥ 0 \text{AW} \ge 0 AW ≥ 0 . Useful for comparing mutually exclusive projects with unequal service lives.
3. Internal Rate of Return (IRR / ROR)
The discount rate i ∗ i^* i ∗ at which the Present Worth of cash inflows equals the Present Worth of cash outflows (i.e., PW ( i ∗ ) = 0 \text{PW}(i^*) = 0 PW ( i ∗ ) = 0 ): ∑ t = 0 n R t − C t ( 1 + i ∗ ) t = 0 \sum_{t=0}^n \frac{R_t - C_t}{(1 + i^*)^t} = 0 t = 0 ∑ n ( 1 + i ∗ ) t R t − C t = 0
Decision Criterion : Accept project if IRR ≥ MARR \text{IRR} \ge \text{MARR} IRR ≥ MARR .
4. Capitalized Cost ( C C CC CC )
Capitalized cost is the present worth of an asset that is assumed to provide service perpetually (infinite life n = ∞ n = \infty n = ∞ ): C C = C 0 + A i + R C ( 1 + i ) k − 1 CC = C_0 + \frac{A}{i} + \frac{RC}{(1 + i)^k - 1} CC = C 0 + i A + ( 1 + i ) k − 1 RC
where C 0 C_0 C 0 is initial cost, A A A is annual operating cost, R C RC RC is replacement cost every k k k years, and i i i is interest rate.
4. Asset Depreciation & Tax Accounting
Depreciation is the systematic allocation of an asset's initial cost C C C over its useful recovery life n n n , leaving a salvage value S S S .
Straight-Line Method (SL)
Constant annual depreciation charge d t d_t d t : d t = d = C − S n d_t = d = \frac{C - S}{n} d t = d = n C − S
Book value at end of year t t t : B V t = C − t ⋅ d BV_t = C - t \cdot d B V t = C − t ⋅ d .
Sum-of-the-Years-Digits Method (SYD)
Accelerated depreciation method where annual charge decreases linearly: SOYD = n ( n + 1 ) 2 \text{SOYD} = \frac{n(n + 1)}{2} SOYD = 2 n ( n + 1 ) d t = ( C − S ) × n − t + 1 SOYD d_t = (C - S) \times \frac{n - t + 1}{\text{SOYD}} d t = ( C − S ) × SOYD n − t + 1
Declining Balance Method (DB / DDB)
Fixed percentage rate k k k applied to the beginning book value B V t − 1 BV_{t-1} B V t − 1 :
k = 1.5 n k = \frac{1.5}{n} k = n 1.5 (150% Declining Balance) or k = 2.0 n k = \frac{2.0}{n} k = n 2.0 (200% Double Declining Balance)
- d t = k ⋅ B V t − 1 d_t = k \cdot BV_{t-1} d t = k ⋅ B V t − 1
- B V t = C ( 1 − k ) t BV_t = C(1 - k)^t B V t = C ( 1 − k ) t
- 5. Break-Even Analysis & Inflation
- Break-Even Analysis
Determines the production volume Q Q Q where Total Revenue T R TR TR equals Total Cost T C TC TC : T R = P ⋅ Q , T C = F C + V C ⋅ Q TR = P \cdot Q, \quad TC = FC + VC \cdot Q TR = P ⋅ Q , TC = FC + V C ⋅ Q Q BE = F C P − V C Q_{\text{BE}} = \frac{FC}{P - VC} Q BE = P − V C FC
where F C FC FC is fixed costs, V C VC V C is variable cost per unit, and P P P is selling price per unit.
Inflation Adjustment
If market interest rate is i i i and annual inflation rate is f f f , the real (inflation-free) interest rate i ′ i' i ′ is: ( 1 + i ) = ( 1 + i ′ ) ( 1 + f ) ⟹ i = i ′ + f + i ′ f (1 + i) = (1 + i')(1 + f) \implies i = i' + f + i' f ( 1 + i ) = ( 1 + i ′ ) ( 1 + f ) ⟹ i = i ′ + f + i ′ f