16 Present Worth Concept Overview
PRESENT WORTH | CONCEPT OVERVIEW The TOPIC of PRESENT WORTH can be referenced on page 131 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing.
CONCEPT INTRO: When we have a number of various receipts and disbursements strung across a period of time, we are able to convert them all, regardless of when they take place in time, in to one unique equivalent Present Value. The FORMULAS for PRESENT WORTH can be referenced in the TABLE of ENGINEERING ECONOMICS FACTORS under the SUBJECT of ENGINEERING ECONOMICS on page 131 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. We can compare single or multiple alternative scenarios using the following procedure: 1. Define the various Benefits and costs identified for the single or multiple alternatives (Investment) and the period of the entire investment. 2. Select a desired value for the return on investment or discount rate. This will typically be given in the problem as an interest rate. 3. Using the Present Worth formulas in the table on page 131 of the NCEES Supplied Reference Handbook. 4. If the present worth isnβt greater than zero, than chances are it is not a good investment because that is telling you that future costs will be greater than future benefits for that particular investment.
Made with
by Prepineer | Prepineer.com
It has been established in previous lessons that money does not have the same value at different points in time. For this reason, we need tools, tables, formulas, and various economic factors to reference when it is necessary to compare two complex alternatives. When we have a number of various receipts and disbursements strung across a period of time, we are able to convert them all, regardless of when they take place in time, in to one unique equivalent Present Value. This is useful analysis to employ when comparing various investment alternatives, when the future benefits of those alternatives and other factors are known. The goal of a Present Worth problem is to convert a series of costs and benefits over a period of time in to one equivalent present time value. We may be given a problem that requests that we convert just one series of transactions, or we may be given a problem where we are asked to compare two unique investments, each with individual periods, interest rates, and transactions.
Made with
by Prepineer | Prepineer.com
CONCEPT EXAMPLE: A construction company wants to purchase a new earthmover. The mover costs $125,000 now to purchase and is projected to save them $17,000 in annual rent, have an annual maintenance cost of $15,000, and a salvage value of $25,000 at the end of its lifespan, 12 years. Assuming 8% interest, would the investment be beneficial to the company? A. -$200,000 B. -$100,000 C. $100,000 D. $200,000
Made with
by Prepineer | Prepineer.com
SOLUTION: The goal is to determine what the present value would be of all the future money receipts and disbursements of this particular investment. In this problem, there is an initial investment that is made as well as various other costs and benefits over the lifespan of the piece of equipment. The FORMULAS for PRESENT WORTH can be referenced in the TABLE of ENGINEERING ECONOMICS FACTORS under the SUBJECT of ENGINEERING ECONOMICS on page 131 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. We can determine the present worth of this investment by using the functional notation versions of the Present Worth formulas and referencing the Compound Interest Tables provided in the NCEES Supplied Reference Handbook. As mentioned earlier, as Engineering Economic problems get more complicated, it is best to get comfortable using the functional notation version of the equations and referencing the Compound Interest Tables as it will lead to a much more efficient use of your time. The first step in solving this problem is to define the identified costs and benefits as well as the overall period of the investment:
Made with
by Prepineer | Prepineer.com
In this problem we are given: β’ π΄π΄" =$17,000 (Plus, a savings from rent)
β’ S = $25,000 (Plus, a savings at the end of the lifespan) β’ P = -$125,000 (Minus, a cost to purchase) β’ π΄π΄# =-$15,000 (Minus, a cost to maintain) β’ n = 12 years
The next step is to determine the desire rate of return. In this problem, we are given an interest rate of: i = 8% We now need to determine which present worth formulas we need to solve this problem. We have 3 items that need to be converted to a present worth, one annual benefit (π΄π΄" ), one annual cost (π΄π΄# ), and one Future Cost (S). Therefore, referencing the table provided in the Reference Handbook, we will use the Uniform Series Present Worth Formula written in functional notation for a Present Worth, which is: ππ = π΄π΄(ππ/π΄π΄, ππ, ππ)
And the Single Payment Present Worth formula, which is: ππ = πΉπΉ(ππ/πΉπΉ, ππ, ππ)
Made with
by Prepineer | Prepineer.com
The terms (ππ/π΄π΄, ππ, ππ) and (ππ/πΉπΉ, ππ, ππ) can be defined using the given values (i, n) and
the Compound Interest Tables provided in the NCEES Supplied Reference Handbook. The FACTOR TABLE for an INTEREST RATE of 8% can be referenced under the SUBJECT of ENGINEERING ECONOMICS on page 136 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. Referencing the Compound Interest Table for i=8% in the NCEES Supplied Reference Handbook, we reference the appropriate values for n (Left Column) for P/A and work our way horizontally and find that:
Made with
by Prepineer | Prepineer.com
For the Uniform Series Present Worth Formula written in functional notation as Present Worth is ππ = π΄π΄(ππ/π΄π΄, ππ, ππ), the economic factor is determined to be: (ππ/π΄π΄, 8%, 12) = 7.5361
Referencing the Compound Interest Table for i=8% in the NCEES Supplied Reference Handbook, we reference the appropriate values for n (Left Column) for P/F and work our way horizontally and find that:
Made with
by Prepineer | Prepineer.com
For the Uniform Gradient Present Worth Formula written in functional notation as Present Worth is ππ = πΊπΊ(ππ/πΉπΉ, ππ, ππ), the economic factor is determined to be: (ππ/πΉπΉ, 8%, 12) = 0.3971
The total Present Worth of all the future money receipts and disbursements of this particular investment will be: ππ = βππ + π΄π΄(ππ/π΄π΄, ππ, ππ) β π΄π΄(ππ/π΄π΄, ππ, ππ) + πΉπΉ(ππ/πΉπΉ, ππ, ππ)
Plugging these values in to the equations we get: ππ = β$125,000
ππ = $17,000(7.3561) = $128,114
ππ = β$15,000(7.3561) = $113,042
ππ = $25,000(0.3971) = $9,928
ππ = β$125,000 + $128,114 β $113,042 + $9,928 = β$100,000
The present worth of all the investments over the 12-year period is -$100,000, therefore, it wouldnβt be a wise investment without further investigation in to other benefits.
Therefore, the correct answer choice is B. β$ππππππ, ππππππ.
Made with
by Prepineer | Prepineer.com
CONCEPT INTRO: When we have a number of various receipts and disbursements strung across a period of time, we are able to convert them all, regardless of when they take place in time, in to one unique equivalent Present Value. The FORMULAS for PRESENT WORTH can be referenced in the TABLE of ENGINEERING ECONOMICS FACTORS under the SUBJECT of ENGINEERING ECONOMICS on page 131 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. We can compare single or multiple alternative scenarios using the following procedure: 1. Define the various Benefits and costs identified for the single or multiple alternatives (Investment) and the period of the entire investment. 2. Select a desired value for the return on investment or discount rate. This will typically be given in the problem as an interest rate. 3. Using the Present Worth formulas in the table on page 131 of the NCEES Supplied Reference Handbook. 4. If the present worth isnβt greater than zero, than chances are it is not a good investment because that is telling you that future costs will be greater than future benefits for that particular investment.
Made with
by Prepineer | Prepineer.com
It has been established in previous lessons that money does not have the same value at different points in time. For this reason, we need tools, tables, formulas, and various economic factors to reference when it is necessary to compare two complex alternatives. When we have a number of various receipts and disbursements strung across a period of time, we are able to convert them all, regardless of when they take place in time, in to one unique equivalent Present Value. This is useful analysis to employ when comparing various investment alternatives, when the future benefits of those alternatives and other factors are known. The goal of a Present Worth problem is to convert a series of costs and benefits over a period of time in to one equivalent present time value. We may be given a problem that requests that we convert just one series of transactions, or we may be given a problem where we are asked to compare two unique investments, each with individual periods, interest rates, and transactions.
Made with
by Prepineer | Prepineer.com
CONCEPT EXAMPLE: A construction company wants to purchase a new earthmover. The mover costs $125,000 now to purchase and is projected to save them $17,000 in annual rent, have an annual maintenance cost of $15,000, and a salvage value of $25,000 at the end of its lifespan, 12 years. Assuming 8% interest, would the investment be beneficial to the company? A. -$200,000 B. -$100,000 C. $100,000 D. $200,000
Made with
by Prepineer | Prepineer.com
SOLUTION: The goal is to determine what the present value would be of all the future money receipts and disbursements of this particular investment. In this problem, there is an initial investment that is made as well as various other costs and benefits over the lifespan of the piece of equipment. The FORMULAS for PRESENT WORTH can be referenced in the TABLE of ENGINEERING ECONOMICS FACTORS under the SUBJECT of ENGINEERING ECONOMICS on page 131 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. We can determine the present worth of this investment by using the functional notation versions of the Present Worth formulas and referencing the Compound Interest Tables provided in the NCEES Supplied Reference Handbook. As mentioned earlier, as Engineering Economic problems get more complicated, it is best to get comfortable using the functional notation version of the equations and referencing the Compound Interest Tables as it will lead to a much more efficient use of your time. The first step in solving this problem is to define the identified costs and benefits as well as the overall period of the investment:
Made with
by Prepineer | Prepineer.com
In this problem we are given: β’ π΄π΄" =$17,000 (Plus, a savings from rent)
β’ S = $25,000 (Plus, a savings at the end of the lifespan) β’ P = -$125,000 (Minus, a cost to purchase) β’ π΄π΄# =-$15,000 (Minus, a cost to maintain) β’ n = 12 years
The next step is to determine the desire rate of return. In this problem, we are given an interest rate of: i = 8% We now need to determine which present worth formulas we need to solve this problem. We have 3 items that need to be converted to a present worth, one annual benefit (π΄π΄" ), one annual cost (π΄π΄# ), and one Future Cost (S). Therefore, referencing the table provided in the Reference Handbook, we will use the Uniform Series Present Worth Formula written in functional notation for a Present Worth, which is: ππ = π΄π΄(ππ/π΄π΄, ππ, ππ)
And the Single Payment Present Worth formula, which is: ππ = πΉπΉ(ππ/πΉπΉ, ππ, ππ)
Made with
by Prepineer | Prepineer.com
The terms (ππ/π΄π΄, ππ, ππ) and (ππ/πΉπΉ, ππ, ππ) can be defined using the given values (i, n) and
the Compound Interest Tables provided in the NCEES Supplied Reference Handbook. The FACTOR TABLE for an INTEREST RATE of 8% can be referenced under the SUBJECT of ENGINEERING ECONOMICS on page 136 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. Referencing the Compound Interest Table for i=8% in the NCEES Supplied Reference Handbook, we reference the appropriate values for n (Left Column) for P/A and work our way horizontally and find that:
Made with
by Prepineer | Prepineer.com
For the Uniform Series Present Worth Formula written in functional notation as Present Worth is ππ = π΄π΄(ππ/π΄π΄, ππ, ππ), the economic factor is determined to be: (ππ/π΄π΄, 8%, 12) = 7.5361
Referencing the Compound Interest Table for i=8% in the NCEES Supplied Reference Handbook, we reference the appropriate values for n (Left Column) for P/F and work our way horizontally and find that:
Made with
by Prepineer | Prepineer.com
For the Uniform Gradient Present Worth Formula written in functional notation as Present Worth is ππ = πΊπΊ(ππ/πΉπΉ, ππ, ππ), the economic factor is determined to be: (ππ/πΉπΉ, 8%, 12) = 0.3971
The total Present Worth of all the future money receipts and disbursements of this particular investment will be: ππ = βππ + π΄π΄(ππ/π΄π΄, ππ, ππ) β π΄π΄(ππ/π΄π΄, ππ, ππ) + πΉπΉ(ππ/πΉπΉ, ππ, ππ)
Plugging these values in to the equations we get: ππ = β$125,000
ππ = $17,000(7.3561) = $128,114
ππ = β$15,000(7.3561) = $113,042
ππ = $25,000(0.3971) = $9,928
ππ = β$125,000 + $128,114 β $113,042 + $9,928 = β$100,000
The present worth of all the investments over the 12-year period is -$100,000, therefore, it wouldnβt be a wise investment without further investigation in to other benefits.
Therefore, the correct answer choice is B. β$ππππππ, ππππππ.
Made with
by Prepineer | Prepineer.com
