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Questions and Answers
In Case 1, the capitalized cost (CC) is calculated using the formula CC = FC + ______
In Case 1, the capitalized cost (CC) is calculated using the formula CC = FC + ______
P
In Case 2, the capitalized cost (CC) is given by the formula CC = FC + ______
In Case 2, the capitalized cost (CC) is given by the formula CC = FC + ______
X
The formula for calculating the present worth of a gradient is PG = G(P/G, i%, n) = ______
The formula for calculating the present worth of a gradient is PG = G(P/G, i%, n) = ______
[(1+i)^n-1/i]-n}(1+i)^-n
A bond is defined as a financial security note issued by businesses, corporations, or ______
A bond is defined as a financial security note issued by businesses, corporations, or ______
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One method for bond retirement involves creating a ______ fund where periodic deposits are made.
One method for bond retirement involves creating a ______ fund where periodic deposits are made.
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ENGINEERING ECONOMY is the analysis and evaluation of factors affecting the economic success of engineering ______.
ENGINEERING ECONOMY is the analysis and evaluation of factors affecting the economic success of engineering ______.
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SIMPLE INTEREST is based only on the ______.
SIMPLE INTEREST is based only on the ______.
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The formula for calculating future worth is represented as ______ = P(1+ni).
The formula for calculating future worth is represented as ______ = P(1+ni).
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ORDINARY SIMPLE INTEREST is computed on the basis of 12 months of ______ days each.
ORDINARY SIMPLE INTEREST is computed on the basis of 12 months of ______ days each.
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EXACT SIMPLE INTEREST considers the actual number of days in a given year, which is ______ days for a normal year.
EXACT SIMPLE INTEREST considers the actual number of days in a given year, which is ______ days for a normal year.
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The formula for discount is represented as D = ______ - P.
The formula for discount is represented as D = ______ - P.
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The interest deducted in advance is known as ______.
The interest deducted in advance is known as ______.
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Rate of ______ is the discount on one unit of principal for one unit of time.
Rate of ______ is the discount on one unit of principal for one unit of time.
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The formula d = 1 – (1 + ______)^-1 defines the rate of discount in relation to the rate of interest.
The formula d = 1 – (1 + ______)^-1 defines the rate of discount in relation to the rate of interest.
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Compound interest can be described as ‘interest on top of ______.'
Compound interest can be described as ‘interest on top of ______.'
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In cash flow diagrams, ↑ represents receipts or positive cash flow while ↓ symbolizes ______.
In cash flow diagrams, ↑ represents receipts or positive cash flow while ↓ symbolizes ______.
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The formula F = P(1 + i)^n calculates the future amount of money, where P is the present worth or ______.
The formula F = P(1 + i)^n calculates the future amount of money, where P is the present worth or ______.
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The nominal rate of interest specifies the rate of interest and the number of ______ periods in one year.
The nominal rate of interest specifies the rate of interest and the number of ______ periods in one year.
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The effective rate of interest, given by the formula ERi = (1 + i)^m - 1, reflects the actual rate earned on the ______ during a one-year period.
The effective rate of interest, given by the formula ERi = (1 + i)^m - 1, reflects the actual rate earned on the ______ during a one-year period.
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Continuous compounding assumes that cash payments occur once per year but compounding is ______ throughout the year.
Continuous compounding assumes that cash payments occur once per year but compounding is ______ throughout the year.
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In the formula P = F(1 + i)^-n, P refers to the ______ worth or principal.
In the formula P = F(1 + i)^-n, P refers to the ______ worth or principal.
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Annuities are a series of equal payments occurring at equal intervals of time, and there are two types: ordinary annuity and ______ annuity.
Annuities are a series of equal payments occurring at equal intervals of time, and there are two types: ordinary annuity and ______ annuity.
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The formula for finding the future worth of an annuity when A is given is F = A{[(1+i)n – 1] / ______}.
The formula for finding the future worth of an annuity when A is given is F = A{[(1+i)n – 1] / ______}.
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The equation of value is established by setting the sum of the values of one set of obligations to the sum of the values on the same date of ______ set of obligations.
The equation of value is established by setting the sum of the values of one set of obligations to the sum of the values on the same date of ______ set of obligations.
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In a perpetual annuity, the payments continue ______.
In a perpetual annuity, the payments continue ______.
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The capitalized cost of any property includes its first cost and the present worth of all costs for ______, operation, and maintenance.
The capitalized cost of any property includes its first cost and the present worth of all costs for ______, operation, and maintenance.
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The formula for finding the present worth of an annuity when A is given is P = A{[1-(1+i)-n ] / ______}(1+i)-n.
The formula for finding the present worth of an annuity when A is given is P = A{[1-(1+i)-n ] / ______}(1+i)-n.
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The future worth of a deferred annuity when A is given can be calculated using the formula F = A{[(1+i)n – 1] / i}(1+i)______.
The future worth of a deferred annuity when A is given can be calculated using the formula F = A{[(1+i)n – 1] / i}(1+i)______.
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In financial calculations, F represents the ______ worth of an annuity.
In financial calculations, F represents the ______ worth of an annuity.
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This method is also called the constant percentage method or the ______ Formula.
This method is also called the constant percentage method or the ______ Formula.
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The decline rate, k, must always be less than ______.
The decline rate, k, must always be less than ______.
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In the Double Declining Balance Method, the decline rate, k, is replaced by ______/L.
In the Double Declining Balance Method, the decline rate, k, is replaced by ______/L.
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The Service-Output Method assumes that depreciation is directly proportional to the quantity of ______ of the property.
The Service-Output Method assumes that depreciation is directly proportional to the quantity of ______ of the property.
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Depletion cost is the reduction of the value of a certain natural resource due to the gradual ______ of its contents.
Depletion cost is the reduction of the value of a certain natural resource due to the gradual ______ of its contents.
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The Unit or Factor Method depends on the initial cost of the property and the number of ______ in the property.
The Unit or Factor Method depends on the initial cost of the property and the number of ______ in the property.
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The Rate of Return (ROR) Method measures the effectiveness of an ______ of capital.
The Rate of Return (ROR) Method measures the effectiveness of an ______ of capital.
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If the computed ROR is greater than the ROR______, the proposed investment is justified.
If the computed ROR is greater than the ROR______, the proposed investment is justified.
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If the excess of annual cash inflows over annual cash outflows is 0, the proposed investment is justified using the ______ method.
If the excess of annual cash inflows over annual cash outflows is 0, the proposed investment is justified using the ______ method.
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The Payback Period is the length of time required to recover the first cost of an investment from the net cash flow, calculated in ______ years.
The Payback Period is the length of time required to recover the first cost of an investment from the net cash flow, calculated in ______ years.
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In the ROR on additional investment method, if the ROR on additional investment is ______ than the ROR required, the alternative is more economical.
In the ROR on additional investment method, if the ROR on additional investment is ______ than the ROR required, the alternative is more economical.
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The alternative with the least ______ cost is usually chosen in the Annual Cost method.
The alternative with the least ______ cost is usually chosen in the Annual Cost method.
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All cash flows must be converted to an equivalent uniform annual cost in the ______ method.
All cash flows must be converted to an equivalent uniform annual cost in the ______ method.
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In the Present Worth Cost method, the alternative with the least ______ should be selected.
In the Present Worth Cost method, the alternative with the least ______ should be selected.
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The alternative with the shortest payback period is adopted, as per the ______ method.
The alternative with the shortest payback period is adopted, as per the ______ method.
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The break-even point is the value of the variable for which the costs of the ______ will be equal.
The break-even point is the value of the variable for which the costs of the ______ will be equal.
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Study Notes
Engineering Economy
- Engineering economy is the analysis and evaluation of factors affecting the economic success of engineering projects. Its goal is to make recommendations for the best use of capital.
Formulas in Engineering Economy
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Simple Interest: Interest calculated only on the principal. Used for short-term loans.
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I = Pni (1)
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F = P(1+ni) (2)
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I = interest
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P = principal/present worth
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n = number of interest periods
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i = interest rate per period
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F = future worth/accumulated amount
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Ordinary Simple Interest: Interest calculated based on 12 months of 30 days each (360 days/year).
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n = d/360
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n=number of interest periods
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d = number of days principal is invested
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Exact Simple Interest: Interest is computed using the exact number of days in a year (365 for a normal year, 366 for a leap year).
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n = d/365 (normal year)
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n = d/366 (leap year)
Discount
- Discount is the interest deducted in advance.
- Discount = Future Worth - Present Worth
- D = F - P (3)
- Rate of discount = d = 1 - (1+i)⁻¹ (4)
- i = interest rate
- d = discount rate
Compound Interest
- Compound interest is interest calculated on the initial principal plus accumulated interest. Used often for longer periods.
Cash Flow Diagrams
- Graphical representation of cash flows over time
- ↑ = cash inflow
- ↓ = cash outflow
Rate of Interest
- Cost of borrowing money or amount earned by a unit principal per unit time.
- Nominal Rate: The basic annual interest rate. Specifies the rate and number of interest periods in a year.
- i / r / m
- i = rate of interest per interest period
- r = nominal rate of interest
- m = number of compounding periods per year
- Effective Rate: The true rate of interest earned over a one-year period.
- ERi = (1+i)m - 1
- ERi = effective rate of interest
Continuous Compounding
- Interest is compounded continuously throughout the year.
- F=Pe^rt
Equation of Value
- Setting the sum of values of one set of obligations at a date equal to the sum of the values of another set at the same date
Annuities
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A series of equal payments occurring at equal intervals.
- Ordinary Annuity: Payments made at the end of each period.
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Formula examples
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F = A[(1+i)n-1)/i] (11)
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P = A[1-(1+i)-n]/i] (12)
- Deferred Annuity: Payments start after a specified number of periods.
Perpetuity
- Annuity with payments that continue indefinitely.
- P = A/i (15)
Capitalized Cost
- Sum of first cost, and present worth of all replacement, operation, and maintenance costs for a long period or forever.
- Case 1 (no replacement): CC=FC+P (16)
- Case 2 (replacement only): CC = FC + X (17)
- X = S/(1+i) -1 (18)
Gradient
- A series of payments or receipts increasing or decreasing by a constant amount every period.
- Example formula: P = PA + PG (19)
Capital Financing with Bonds
- Businesses borrow long-term funds; notes specifying repayment terms.
- Bond value = present worth of all future returns
- Methods of bond retirement: 1.Issuing new bonds 2.Sinking fund
Depreciation
- Decrease in value of a physical property over time.
- Types of Depreciation:
- Physical
- Functional
- Methods of Depreciation:
- Straight-Line Method: loss in value is proportional to the age
- Types of Depreciation:
- d = (Co - Cn)/n (22)
- dn = (Co - Cl)/(Σdigits)(n) (34)
Depletion
- Reduction in value of natural resources (mines, oil, quarries) due to extraction.
- Methods of Computing Depletion Charge:
- Unit or Factor Method
- Percentage or Depletion Allowance Method
Investment of Capital
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Rate of Return (ROR) Method
- Measures investment effectiveness. If computed ROR ≥ required ROR, proposed investment is justified.
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Annual Worth Method
- includes interest as a cost; if annual cash inflows ≥ annual costs, investment is justified
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Present Worth(PW) Method**
- Calculates the present value of cash flows; if PW ≥ 0, investment is justifiable.
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Payback Period Method
- Time to recover initial investment from net cash flow.
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Comparing Alternatives:
- ROR on additional investment,
- Annual Cost (AC) Method,
- Equivalent Uniform Annual Cost (EUAC) Method,
- Present Worth Cost (PWC) Method
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Methods for Break-Even Analysis*
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Break-even point (BEP)= the value of the variable for which the costs of the alternatives are equal
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Description
Test your understanding of key concepts in Engineering Economy including capitalized cost, present worth, bonds, and interest. This quiz covers formulas and definitions essential for evaluating the economic success of engineering projects. Perfect for students looking to reinforce their knowledge in this field.
