程序代写 AF3625 Engineering Economics

AF3625 Engineering Economics

Engineering Economics
Topic 7: Evaluating a Single Project

Copyright ©2012 by , Inc.
Upper Saddle River, 07458
All rights reserved.
Engineering Economy, Fifteenth Edition
By William G. Sullivan, Elin M. Wicks, and C.

Minimum attractive rate of return (MARR)
Present worth (PW)
Future worth (FW)
Annual worth (AW)
Capitalized worth (CW)
Topic 7: Evaluating a Single Project

Copyright ©2012 by , Inc.
Upper Saddle River, 07458
All rights reserved.
Engineering Economy, Fifteenth Edition
By William G. Sullivan, Elin M. Wicks, and C.

Proposed capital projects can be evaluated in several ways:
Present worth (PW)
Future worth (FW)
Annual worth (AW)
Internal rate of return (IRR) to be introduced in Topic 8

To be acceptable or worth-investing, a capital project must provide a return that reaches a minimum level established by the organization –
Minimum Attractive Rate of Return (MARR).
How to Evaluate A Capital (or Investment) Project

Copyright ©2012 by , Inc.
Upper Saddle River, 07458
All rights reserved.
Engineering Economy, Fifteenth Edition
By William G. Sullivan, Elin M. Wicks, and C.

The Determination of MARR

A firm has to decide whether to invest and how many projects to invest.
It will first invest in the project that brings the highest marginal benefit measured by the rate of profit.
Suppose a firm has 9 projects (A to I) available as shown below in descending order of their profitability.
Note that the amount of investment required for each project is different.

Copyright ©2012 by , Inc.
Upper Saddle River, 07458
All rights reserved.
Engineering Economy, Fifteenth Edition
By William G. Sullivan, Elin M. Wicks, and C.

The upward-sloping curve is the supply of financial resources.
It is upward sloping because the cost of financial capital will rise when more financial resources are needed.
Projects A and B together only need $25 million, which can be financed by retained earnings at much lower cost.
If the firm needs to raise more money to invest in more projects, then it may have to borrow from the bank paying higher interest rates.
Given the supply curve of financial capital, only Projects A to F will be selected based on the cost-benefit analysis.

The Determination of MARR

Copyright ©2012 by , Inc.
Upper Saddle River, 07458
All rights reserved.
Engineering Economy, Fifteenth Edition
By William G. Sullivan, Elin M. Wicks, and C.

Present Worth (PW) Method
The present worth method may be used the most often.
The present worth (PW) is found by discounting all cash inflows and outflows to the present time at an interest rate that is generally the MARR.
According to the CBA criterion, a project is worth-investing as long as its benefit ≥ its cost  A non-negative PW for an investment project indicates that it is acceptable (its rate of return or profit ≥ MARR).

Copyright ©2012 by , Inc.
Upper Saddle River, 07458
All rights reserved.
Engineering Economy, Fifteenth Edition
By William G. Sullivan, Elin M. Wicks, and C.

Consider a project that has an initial investment of $50,000 and returns of $18,000 per year for the next four years. If the MARR is 12%, is this a good investment (“To Do or Not To Do”)?
PW = ‒$50,000 + $18,000 (P/A, 12%, 4)
= ‒$50,000 + $18,000 (3.037)
= $4,666  This is a good investment!
Example of PW Method

Copyright ©2012 by , Inc.
Upper Saddle River, 07458
All rights reserved.
Engineering Economy, Fifteenth Edition
By William G. Sullivan, Elin M. Wicks, and C.

Bond is an IOU (debt contract) that the buyer (lender) agrees to lend a specific amount to the issuer (borrower that can be a government or a corporation) for a specific period of time.
In return, the buyer/bondholder will receive periodic interest payments and get back the principle when the issuer redeems the bond at its maturity.
Not all buyers of newly issued bonds hold them until maturity. Instead, they may sell the bonds on the bond market before maturity.
How much such “second-hand” bonds can be sold for depends on the market interest rate at the time of the transaction.

Application of PW Method –
Market Values of Bonds

Copyright ©2012 by , Inc.
Upper Saddle River, 07458
All rights reserved.
Engineering Economy, Fifteenth Edition
By William G. Sullivan, Elin M. Wicks, and C.

A corporate bond was issued two years ago at a par value (or face value) of $10,000 for a period of 5 years.
The bond rate or coupon rate is 6% annually and the interest is paid twice a year (i.e. the bondholder will be paid $300 of interest every 6 months until the maturity of the bond).
Now this bond is available for sale on the market. If you are interested in this investment opportunity, what will be the maximum amount you are willing to pay for the bond if the market interest rate (i.e. the best alternative rate of return you can get) is 4% per year?
Market Value of (Second-hand) Bonds
– Self Exercise 1 in Self Study Notes Unit 7

First draw the cash flow diagram.

Copyright ©2012 by , Inc.
Upper Saddle River, 07458
All rights reserved.
Engineering Economy, Fifteenth Edition
By William G. Sullivan, Elin M. Wicks, and C.

Market Value of (Second-hand) Bonds
– Self Exercise 1 in Self Study Notes Unit 7

Copyright ©2012 by , Inc.
Upper Saddle River, 07458
All rights reserved.
Engineering Economy, Fifteenth Edition
By William G. Sullivan, Elin M. Wicks, and C.

Think! Why would you be willing to pay more than the face value of the bond, which is $10,000, although you can only receive the interest payments for the remaining 3 years but not 5 years?
Market Value of (Second-hand) Bonds
– Self Exercise 1 in Self Study Notes Unit 7

Consider the best alternative available. If you invest $10,000 now for 3 years, how much interest will you receive in each of the next 3 years on top of the $10,000 you’ll get back 3 years later.

Copyright ©2012 by , Inc.
Upper Saddle River, 07458
All rights reserved.
Engineering Economy, Fifteenth Edition
By William G. Sullivan, Elin M. Wicks, and C.

Imagine if you could buy the bond at $10,000, then you would have a promised rate of return of 3% every 6 months.
If you invest $10,000 in the best alternative, you will only get 2% every 6 months.
Which one will you prefer? How about other investors?
Higher return offered by the bond
A great demand for the bond
The bond price will be driven higher until the actual rate of return on the bond is equivalent to the market interest rate of 4%.
Market Value of (Second-hand) Bonds
– Self Exercise 1 in Self Study Notes Unit 7

Copyright ©2012 by , Inc.
Upper Saddle River, 07458
All rights reserved.
Engineering Economy, Fifteenth Edition
By William G. Sullivan, Elin M. Wicks, and C.

When you pay $10,560.42 to buy the bond now, this cash outflow will be economically equivalent to the cash inflows promised by the bond at the market rate of 4%.
The PW derived earlier is an equilibrium price of the bond at the market interest rate of 4% per year.
How much will you be willing to pay for the bond if the market interest rate is now 8% per year (i.e. 4% every 6 months)?
Market Value of (Second-hand) Bonds
– Self Exercise 1 in Self Study Notes Unit 7

Market prices of bonds are inversely related to market interest rate.
This is true for all fixed-income assets.

Copyright ©2012 by , Inc.
Upper Saddle River, 07458
All rights reserved.
Engineering Economy, Fifteenth Edition
By William G. Sullivan, Elin M. Wicks, and C.

Governments usually issue bonds as an additional source of finance other than taxes.
The latest iBond Series Retail Bonds Due 2024 has a minimum denomination of HK$10,000 and a term of three years.
The semi-annual interest payments are linked to average annual inflation in , subject to a minimum interest rate of 2.00%. The principal amount will be repaid in full (i.e. 100%) by the HKSAR Government at maturity.
Investors who hold 2024 iBond through Securities Clearing Company Limited (HKSCC) directly or through their securities broker may trade 2024 iBond through SEHK.

Copyright ©2012 by , Inc.
Upper Saddle River, 07458
All rights reserved.
Engineering Economy, Fifteenth Edition
By William G. Sullivan, Elin M. Wicks, and C.

Mr. Chan wants to buy a bond. It has a face value of $50,000, a bond rate of 6% (nominal), payable semi-annually (twice a year), and matures in 10 years. Mr. Chan wants to earn a nominal interest of 8% (i.e. 4% every 6 months). What is the maximum price Mr. Chan will be willing to pay for the bond?
Exercise on Bond Value
The maximum price is the equilibrium price of the bond:
PW = $50,000 (P/F, 4%, 20) + 0.03($50,000)(P/A, 4%, 20)

Copyright ©2012 by , Inc.
Upper Saddle River, 07458
All rights reserved.
Engineering Economy, Fifteenth Edition
By William G. Sullivan, Elin M. Wicks, and C.

Interest rate = 4%

Mr. Chan wants to buy a bond. It has a face value of $50,000, a bond rate of 6% (nominal), payable semi-annually (twice a year), and matures in 10 years. Mr. Chan wants to earn a nominal interest of 8%. What is the maximum price Mr. Chan will be willing to pay for the bond?
Exercise on Bond Value
The maximum price is the equilibrium price of the bond:
PW = $50,000 (P/F, 4%, 20) + 0.03($50,000)(P/A, 4%, 20)
= $50,000(0.4564) + $1,500(13.590)
= $(22,820 + 20,385)

An investment project can also be evaluated on the basis of its future worth (FW).
FW is the future equivalent of all cash inflows and outflows derived at the end of the project life or the study period at an interest rate that is generally the MARR.
The same decisions will be made using the FW and PW methods.
A non-negative FW for an investment project indicates that the project is acceptable (its rate of profit ≥ MARR).

Future Worth (FW) Method

A $45,000 investment in a new conveyor system is projected to improve throughput and increasing revenue by $14,000 per year for five years. The conveyor will have an estimated market value of $4,000 at the end of five years. Using FW and a MARR of 12%, is this a good investment?
FW = -$45,000(F/P, 12%, 5)+$14,000(F/A, 12%, 5)+$4,000
= -$45,000(1.7623)+$14,000(6.3528)+$4,000
= $13,635.70  This is a good investment!
Example of FW Method

Interest rate = 12%

A $45,000 investment in a new conveyor system is projected to improve throughput and increasing revenue by $14,000 per year for five years. The conveyor will have an estimated market value of $4,000 at the end of five years. Using FW and a MARR of 12%, is this a good investment?
FW = ‒$45,000(F/P, 12%, 5)+$14,000(F/A, 12%, 5)+$4,000
= ‒$45,000(1.7623)+$14,000(6.3528)+$4,000
= $13,635.70  This is a good investment!
Do Self Exercise 2 in Self-study Notes Unit 7.
Example of FW Method

What exactly does the value of PW or FW mean?
Objective of every firm: profit maximization
Positive profit  increase the wealth or value of the firm
In the long run, a firm will commit to a new project only if it is expected to increase its wealth or value.*
It is difficult to evaluate the worthiness of long-term investment projects year by year.
We estimate PW or FW to decide

PW and FW are zero PW and FW are positive PW and FW are negative
All the receipts are sufficient to pay for all expenses and compensate investors or suppliers of financial resources at an acceptable rate of profit or interest (represented by MARR). After paying the rewards to all the factors of production including the entrepreneur (who is the major investor), there is still a positive amount remaining to add value to the wealth of the firm. The firm’s value will be adversely affected by the project and therefore it should be rejected.

Refer to Example 2 in Self-study notes Unit 7 for information of Project Balance.
“To do or not to do?”

The AW of an investment project is a series of equal periodic (usually annual) amounts that is equivalent to the cash inflows and outflows of the project derived for a stated study period at an interest rate that is generally the MARR.
The AW is usually derived from the annual equivalent revenue or savings ( ) minus annual equivalent expenses ( ), less its annual capital recovery (CR) amount.

If AW ≥ 0, the project is economically justified, i.e. acceptable or worth-considering.
If AW < 0, the project should be rejected. Annual Worth (AW) Method Copyright ©2012 by , Inc. Upper Saddle River, 07458 All rights reserved. Engineering Economy, Fifteenth Edition By William G. Sullivan, Elin M. Wicks, and C. Capital Recovery (CR) CR is the annual equivalent cost of the capital invested CR covers the following items: Loss in value of the asset (depreciation) Forgone interest on invested capital (at MARR) CR distributes the initial cost (I) and the salvage value (S) across the life of the asset. CR(i%) = I (A/P, i%, N) – S (A/F, i%, N) Copyright ©2012 by , Inc. Upper Saddle River, 07458 All rights reserved. Engineering Economy, Fifteenth Edition By William G. Sullivan, Elin M. Wicks, and C. A project requires an initial investment of $45,000, has a salvage value of $12,000 after six years, incurs annual expenses of $6,000, and provides an annual revenue of $18,000. Using a MARR of 10%, determine the AW of this project. Example of AW Method AW(10%) = – – CR(10%) CR(10%) = $45,000(A/P, 10%, 6) - $12,000(A/F, 10%, 6) Copyright ©2012 by , Inc. Upper Saddle River, 07458 All rights reserved. Engineering Economy, Fifteenth Edition By William G. Sullivan, Elin M. Wicks, and C. Interest rate = 10% Copyright ©2012 by , Inc. Upper Saddle River, 07458 All rights reserved. Engineering Economy, Fifteenth Edition By William G. Sullivan, Elin M. Wicks, and C. A project requires an initial investment of $45,000, has a salvage value of $12,000 after six years, incurs annual expenses of $6,000, and provides an annual revenue of $18,000. Using a MARR of 10%, determine the AW of this project. Since the AW is positive, the project is a good investment. Example of AW Method CR(10%) = $45,000(A/P, 10%, 6) - $12,000(A/F, 10%, 6) = $45,000(0.2296) - $12,000(0.1296) AW(10%) = $(18,000 - 6,000 – 8,777) = $3,223 AW(10%) = – – CR(10%) Copyright ©2012 by , Inc. Upper Saddle River, 07458 All rights reserved. Engineering Economy, Fifteenth Edition By William G. Sullivan, Elin M. Wicks, and C. Capitalized worth (CW) method is a revised version of the PW method required to evaluate a project that lasts for an infinite length of time. If a project involves no inflows but only expenses (outflows) are considered, its CW is sometimes referred to as the capitalized cost. The CW method is especially useful in problems involving endowments and public projects with indefinite lives. Capitalized Worth (CW) Method Recall that the PW of a uniform series of payments A, evaluated at i% of interest per period for N periods, is A(P/A, i%, N). As N becomes very large, the (P/A) term approaches 1/i, we have CW(i%) = PW(i%)N = = Copyright ©2012 by , Inc. Upper Saddle River, 07458 All rights reserved. Engineering Economy, Fifteenth Edition By William G. Sullivan, Elin M. Wicks, and C. Consider the following cash flow diagram that describes an infrastructural project considered by the government. Given that the initial capital cost is $1,900,000 and the infinite annual upkeep cost is $25,000, if the MARR for the government remains at 8% forever, how much money should the government raise now to finance this series of cash outflows? Example of CW Method This is Example 5 in Self-study Notes Unit 7. * You must do Self Exercise 3 to practice the use of effective interest rate for a compounding period longer than one year. Copyright ©2012 by , Inc. Upper Saddle River, 07458 All rights reserved. Engineering Economy, Fifteenth Edition By William G. Sullivan, Elin M. Wicks, and C. )6%,2,/(AP )6%,2,/(FP = $[300  5.6014 + 10,000  0.8880] = $10,560.42 )6%,4,/(AP )6%,4,/(FP = $[300  5.2421 + 10,000  0.7903] = $9,475.63 /docProps/thumbnail.jpeg 程序代写 CS代考加微信: powcoder QQ: 1823890830 Email: powcoder@163.com

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