Comparison and Selection among Alternatives Created By Eng.Maysa Gharaybeh

Quiz 1, 2, 7, 15,19, 20, 22, 26, 36, 40.

The objective of chapter 6 is

to evaluate correctly capital

investment alternatives when

the time value of money is a

key influence.

Making decisions means

comparing alternatives.

In this chapter we examine feasible design

alternatives.

The decisions considered are those selecting

from among a set of mutually exclusive

alternatives (when selecting one excludes the

choice of any of the others).

Principle 2 from Chapter 1. The alternative that requires the minimum investment of

capital and produces satisfactory functional results will be

chosen(the base alternative)

unless the incremental capital associated with an alternative

having a larger investment can be justified with respect to its

incremental benefits.

The alternative requiring the least investment is the base alternative.

For alternatives that have a larger

investment than the base…

If the extra benefits obtained by investing additional

capital are better than those that could be obtained from

investment of the same capital elsewhere in the

company at the MARR, the investment should be made.

(Please note that there are some cautions when

considering more than two alternatives, which will be

examined later.)

Types of Alternatives Investment alternatives (capital & Revenue)

Cost alternatives (Negative & salvage value) same expected revenue

Ensuring Comparable Basis

Rule 1. When revenues and other economic benefits are present(Investment alternatives ), select alternative that has greatest positive equivalent worth at i %= MARR% and satisfies project requirements.

Rule 2. When revenues and economic benefits are not present(Cost alternatives ), select alternative that minimizes cost.

In Other Words:

Select the alternative that gives you

the most money!

For investment alternatives the PW of all cash flows must be positive, at the MARR, to be attractive. Select the alternative with the largest PW.

For cost alternatives the PW of all cash flows will be negative. Select the alternative with the largest (smallest in absolute value) PW.

Example: Investment Alternative

Use a MARR of 10% and useful life of 5 years to select

between the investment alternatives below.

Alternative

A B

Capital investment -$100,000 -$125,000

Annual revenues less expenses $34,000 $41,000

Both alternatives are attractive, but Alternative B provides

a greater present worth, so is better economically.

Cost alternative example

Use a MARR of 12% and useful life of 4 years to select

between the cost alternatives below.

Alternative

C D

Capital investment -$80,000 -$60,000

Annual expenses -$25,000 -$30,000

Alternative D costs less than Alternative C, it has a greater

PW, so is better economically.

PW(10%)A= 9,738$

PW(10%)B= 10,131$

PW(10%)B-A = 393$

Investment

Alternative

PW(10%)C= -477,077$

PW(10%)D= -463,607$

PW(10%)D-C = 13,470$

Cost

Alternative

with selvage

value

Determining the study period.

A study period (or planning horizon) is the time period over which mutually exclusive alternatives are compared, and it must be appropriate for the decision situation.

mutually exclusive alternatives can have equal lives (in which case the study period used is these equal lives), or they can have unequal lives, and at least one does not match the study period.

The equal life case is straightforward.

Useful Lives of all Alternatives is Equal to the Study Period

1. Equivalent worth methods

2. Rate of return methods

1.Equivalent Worth Methods

If : PWA (i) < PWB (i)

Then

AWA (i) < AWB (i)

and

FWA (i) < FWB (i)

Select Alternative B

Example: When lives are equal adjustments to cash flows are not

required. The MEAs can be compared by directly comparing

their equivalent worth (PW, FW, or AW) calculated using the

MARR. The decision will be the same regardless of the

equivalent worth method you use. For a MARR of 12%, select

from among the MEAs below.

Alternatives

A B C D

Capital investment -$150,000 -$85,000 -$75,000 -$120,000

Annual revenues $28,000 $16,000 $15,000 $22,000

Annual expenses -$1,000 -$550 -$500 -$700

Market Value

(EOL)

$20,000 $10,000 $6,000 $11,000

Life (years) 10 10 10 10

Selecting the best alternative.

Present worth analysis select Alternative A (but C is close).

Annual worth analysis—the decision is the same.

Using rates of return is

another way to compare

alternatives.

The return on investment (rate of return) is a popular

measure of investment performance.

Selecting the alternative with the largest rate of return

can lead to incorrect decisions do not compare the

IRR of one alternative to the IRR of another

alternative.

Remember, the base alternative must be attractive

(rate of return greater than the MARR), and the

additional investment in other alternatives must itself

make a satisfactory rate of return on that increment.

The Incremental Investment

Analysis Procedure. Arrange (rank order) the feasible alternatives based on

increasing capital investment.

Establish a base alternative.

Cost alternatives the first alternative is the base.

Investment alternatives the first acceptable alternative

(IRR>MARR) is the base.

Iteratively evaluate differences (incremental cash flows) between alternatives until all have been considered.

a. If incremental cash flow between next alternative and current alternative is acceptable, choose the next.

b. Repeat, and select as the preferred alternative the last one for which the incremental cash flow was acceptable

Example 6-4 A B C D E F

Capital 900 1,500 2,500 4,000 5,000 7,000

Annual R – Annual E

150 276 400 925 1,125 1,425

IRR 10.6% 13% 9.6% 19.1% 18.3% 15.6%

The alternative is arranged based on increasing capital investment.

IRR for alternative (C) 9.6<MARR(10%)

Then C is rejected

A is the base alternative then we will compare A with B

A Δ(B-A) Δ(D-B)

Δ(E-D)

Δ(F-E)

ΔCapital

900

Δ(Annual R – Annual E)

150

IRRΔ 10.6%

Is increment justified

Yes

B is better then A because the additional capital investment gives IRR >MARR(16.4%>10%)

Then we will compare B with D since C is rejected from the beginning

A Δ(B-A) Δ(D-B)

Δ(E-D)

Δ(F-E)

ΔCapital

900 600

Δ(Annual R – Annual E)

150 126

IRRΔ 10.6% 16.4%

Is increment justified

Yes Yes

D is better then B because the additional capital investment gives IRR >MARR(22.6%>10%)

Then we will compare D with E

A Δ(B-A) Δ(D-B)

Δ(E-D)

Δ(F-E)

ΔCapital

900 600 2,500

Δ(Annual R – Annual E)

150 126 649

IRRΔ 10.6% 16.4% 22.6%

Is increment justified

Yes Yes Yes

E is better then D because the additional capital investment gives IRR >MARR(15.1%>10%)

Then we will compare E with F

A Δ(B-A) Δ(D-B)

Δ(E-D)

Δ(F-E)

ΔCapital

900 600 2,500 1,000

Δ(Annual R – Annual E)

150 126 649 200

IRRΔ 10.6% 16.4% 22.6% 15.1%

Is increment justified

Yes Yes Yes Yes

F is NOT better then E because the additional capital investment gives IRR < MARR(8.1%>10%)

Then E is the best alternative

A Δ(B-A) Δ(D-B)

Δ(E-D)

Δ(F-E)

ΔCapital

900 600 2,500 1,000 2,000

Δ(Annual R – Annual E)

150 126 649 200 300

IRRΔ 10.6% 16.4% 22.6% 15.1% 8.1%

Is increment justified

Yes Yes Yes Yes No

Three Errors Common To Incremental Investment Analysis Procedure Applied To IRR

Choosing the feasible Alternative with:

1. the highest overall IRR on total cash flow (choose D)

A B C D E F

Capital 900 1,500 2,500 4,000 5,000 7,000

Annual R – Annual E

150 276 400 925 1,125 1,425

IRR 10.6% 13% 9.6% 19.1% 18.3% 15.6%

Three Errors Common To Incremental Investment Analysis Procedure Applied To IRR

Choosing the feasible Alternative with: 2.the highest IRR on an incremental capital investment(choose

D-B instead of E-D)

A Δ(B-A) Δ(D-B)

Δ(E-D)

Δ(F-E)

ΔCapital

900 600 2,500 1,000 2,000

Δ(Annual R – Annual E)

150 126 649 200 300

IRRΔ 10.6% 16.4% 22.6% 15.1% 8.1%

Is increment justified

Yes Yes Yes Yes No

Three Errors Common To Incremental Investment Analysis Procedure Applied To IRR

3.the largest capital investment that has an IRR greater than or equal to the MARR (choose F)

A B C D E F

Capital 900 1,500 2,500 4,000 5,000 7,000

Annual R – Annual E

150 276 400 925 1,125 1,425

IRR 10.6% 13% 9.6% 19.1% 18.3% 15.6%

Incremental analysis must be used with rate of return methods to ensure the best alternative is selected

Comparing MEAs with Unequal lives.

• Repeatability assumption

• Coterminated assumption

Rate of Return with unequal lifes A B

Capital investment $3,500 $5,00

Annual cash flow 1,255 1,480

Useful life 4 6

When the repeatability applies 1.we need to find the AW of each alternative over it’s own useful life 2.Find the interest rate that make them equal AW A(i*%) = AW B(i*%) -3,500(A/i*%,4) +1,255 = -5,000(A/i*%,6) +1,480 Trail and error i= 26% >MARR (10%) the increment is justified and B is preferred

Useful life > Study period

The imputed Market Value Technique

i. e find the estimated market value at any year that is before the end of the useful life

MVT = PW at EOY T of remaining CR amounts + PW at EOY T of original market value at end of useful life

Example

If the capital investment is 47,600 useful life = 9 years market value at the end of 9 years = $5,000 find the market value et the end of 5 years if MARR = 20%

Step 1 : CR = 47,000 (A/P,20%,9) – 5,000(A/F,20%,9)

Step 2 : PW at EOY 5 of the remaining CR

PW(20%) CR = CR (P/A, 20%,4) = $29,949

Step 3 : PW at EOY 5 of MV 9

PW(20%) MV = 5,000 (P/F, 20%,4) = $2,412

The estimated market value at EOY 5 =

MV 5 = PW(20%) CR + PW(20%) MV = 29,949 + 2,412 = 32,361