Capital Budgeting Techniques

1- Fundamentals of Financial Management

by

James C. Van Horne

John M. Wachowicz, Jr.

2- Economic Decision Analysis

by

W.J. Fabrycky

G.J. Thuesen

.

INTRODUCTIONGrowing competitiveness of manufacturing and service organizations necessitates the optimal use of capital resources. A systematic evaluation of costs and benefits of technical business projects requires an understanding of basic concepts of economic evaluation by the engineers who manage these projects and organizations. In most cases more than one options are feasible. An economic evaluation of each to determine the internal rate of return

or benefit to cost ratio, enables the managers to make decisions. The knowledge of the basic economic concepts and principles also helps the engineers/managers in day to day management of the operations of private and public business organizations, state corporations. Government departments and even non profit organizations.

Given the necessary information, a method has to be found for evaluating the profitability of new estimates. In selecting a suitable criteria, the following two fundamental principles should be kept in view.

1.The Bigger the Better Principle

Other things being equal, bigger benefits are preferable over smaller ones.

Project Evaluation Criteria

2. The Bird in Hand Principle

Other things being equal, early benefits are preferable than later benefits.

There are four basic methods to assess the economic viability of a project:

• Payback Period (PBP)

• Internal Rate of Return (IRR)

• Net Present Value (NPV)

• Profitability Index (PI)

Proposed Project Data

Julie Miller is evaluating a new project for her firm Basket Wonders (BW). She has determined that the after- tax cash flows for the project will be $ 10,000, $ 12,000, $ 15.000, $ 10,000 and $ 7,000 respectively for each of the years 1 through 5. The initial cash outlay will be $ 40,000.

Payback Period (PBP)

PBP is the period of time required for the cumulative expected cash flows from an investment project to equal the initial cash outflows.

0 1 2 3 4 5

-40 K 10 K 12 K 15 K 10 K 7K

Payback Period (PBP)Solution-1

PBP is the period of time required for the cumulative expected cash flows from an investment project to equal the initial cash outflows.

0 1 2 3 4 5

-40 K 10 K 12 K 15 K 7K

10K 22K 37K 47K 54K Cumulative Inflows

(a)

(d)10 K

(c)

(-b)

Payback Solution

PBP = a + (b-c) / d

= 3 + (40 – 37) / 10

= 3 + (3) / 10

= 3.3 Years

Payback Period (PBP)Solution-2

PBP is the period of time required for the cumulative expected cash flows from an investment project to equal the initial cash outflows.

0 1 2 4 5

-40 K 10 K 12 K 15 K 10 K 7K

-40 K -30 K -18 K 7 K 14 K -b

c

a

3

-3KCumulative Cash flows

Payback Period (PBP)Solution-2

PBP = 3 + ( 3 K ) / 10 K

= 3.3 Years

We take absolute value of last negative cumulative cash flow values.

PBP Acceptance Criterion

The management of Basket Wonders has set a max PBP of 3.5 years for this project.

Should this project be accepted?Yes the Project should be accepted! The firm will receive back the initial cash outlay in less than 3.5 Years

( 3.3 Years<3.5 Years Max)

• Advantages of PBP

The PBP is used to rank the investment alternatives. Projects having the shortest payback period are given the highest ranking or preferred the most.

The method is simple to understand and easy to calculate. It basically calculates the time period in which investment in the project is likely to be recovered. The method is also widely used for projects with high risk and uncertainty. The shorter the PBP, the faster

the uncertainty associated with the project is resolved. It is also helpful in those type of projects which are subject to rapid technological changes (rapid technological obsolescence) because it reduces the possibility of loss through obsolescence.

•Disadvantages of PBP

Investments are however not made just to recover the capital. The true worth of an investment is that how much income it

generates after the original investment has been paid back. Since PBP method ignores inflows after payback period, it discriminates against projects which generate substantial cash inflows in later years. Further it concentrates more on the recovery of the capital, without paying attention to the ultimate profitability of the investment.

Internal Rate of Return(IRR)

IRR is the discount rate that equates the present value of the future net cash flows from an investment project with the project’s initial cash outflow.

IRR Solution ( Try 10% )

Find the interest rate (IRR) that causes the discounted cash flows to equal $ 40,000

IRR Solution ( Try 15 % )

.10 41,444 ------------a

.15 36,841 ------------bIRR 40,000 ------------c.05 -4,603 -------------dIRR-.10 40,000-41,444 = -1,444

IRR Solution Interpolate

IRR Acceptance Criterion

The management of BW has determined that the hurdle rate is 13% for projects of this type.

Should this project be accepted?No! The firm will receive 11.57% for each dollar invested in this project at a cost of 13% (IRR < Hurdle Rate)

• Advantages of IRR

1.It ranks the projects according to their IRR and present value of the future net cash flows. A project with higher IRR is selected from among several projects.

2.It considers the cash flow stream in its entirety.

• Disadvantages of IRR

The IRR value cannot distinguish between lending and borrowing , and therefore a higher IRR need not necessarily be a desirable yardstick for selecting a project.

Net present Value (NPV)

NPV is the present value of an investment project’s net cash flows minus the project’s initial cash out flow.

NPV = PV - ICO

NPV SolutionBasket Wonders has determined that the appropriate discount rate (K) for this project is 13%

NPV Solution

NPV Acceptance Criterion

The management of BW has determined that the required rate is 13% for projects of this type.

Should this project be accepted?No! The NPV is negative. This means that this project is reducing shareholder’s wealth. So (Rejected as NPV<0)

• Advantages of NPV

1.It takes into consideration the time value of money as it is based on the principal that the sum of money today has a higher value than an equivalent amount after a year from now.

2.It considers the return from the project in its entirety in evaluation of the capital expenditure.

• Disadvantages of NPV

1.It is not an easy method to understand and computation of NPV is also difficult.

2.It requires data on discount rate.

Profitability Index (PI)PI is the ratio of the present value of a project’s future net cash flows to the project’s initial cash out flow.

PI Acceptance Criterion

Should this Project be accepted?

No! The PI is less than 1.00. This means that the project is not profitable.(Rejected as PI <1.00)

Evaluation Summary

Basket Wonders Independent Project

Method Project Comparison Decision

PBP 3.3 3.5 Accepted

IRR 11.57% 13% Rejected

NPV ($1,428) $0 Rejected

PI 0.96 1 Rejected

Available Projects for BW6Project ICO ($) IRR (%) NPV ($) PI

A 500 18 50 1.10B 5,000 25 6,500 2.30C 5,000 37 5,500 2.10D 7,500 20 5,000 1.67E 12,500 26 500 1.04F 15,000 28 21,000 2.40G 17,500 19 7,500 1.43H 25,000 15 6,000 1.24

Choosing by IRRs for BW

Project ICO ($) IRR (%) NPV ($) PI

C 5,000 37 5,500 2.10

F 15,000 28 21,000 2.40

E 12,500 26 500 1.04

Projects C, F, and E have the three largest IRRs.The resulting increase in shareholder wealth is $ 27,000 with a $ 32, 500 outlay.

Choosing by NPVs for BW

Project ICO ($) IRR (%) NPV ($) PI

F 15,000 28 21,000 2.40

G 17,500 19 7,500 1.43

Projects F, and G have the two largest NPVs.The resulting increase in shareholder wealth is $ 28,500 with a $ 32, 500 outlay.

Choosing by PIs for BW

Project ICO ($) IRR (%) NPV ($) PI

F 15,000 28 21,000 2.40

B 5,000 25 6,500 2.30

C 5,000 37 5,500 2.10

D 7,500 20 5,000 1.67

Projects F, B, C and D have the four largest PIs.The resulting increase in shareholder wealth is $ 38,000 with a $ 32, 500 outlay.

Summary of Comparison

Method Projects Accepted Value Added

C F, B, C and D $ 38,000

F F and G $ 28,500

E C, F and E $ 27, 000

PI generates the greatest increase in shareholder wealth when a limited capital budget exists for a single period.

The Benefit - Cost Ratio

Many types of engineering projects particularly aimed to provide public utilities and services such as health, education, water supply, power supply, transport, irrigation and flood control etc financed and controlled by the government, require different decision criteria. Profitability, or rate on investment is not the objective of public engineering projects. The output of such projects may or may not earn revenue to liquidate the

investment and operation costs. The government finances these projects out of tax revenues, donations, and loans at low interest rate. A popular method of deciding upon the economic justification of a public project is to compute the benefit-cost ratio. The ratio may be expressed as :

B-C Ratio =

Where the benefits and costs are present or equivalent annual amounts computed using the

cost of money. Thus the B-C ratio reflects the user’s equivalent dollar benefits and the sponsor’s equivalent dollar cost. If the ratio is 1, the equivalent benefits and the equivalent cost are equal. This represents the minimum justification for expenditure by the government.

Benefits are defined to mean all the advantages , less any disadvantage to the user. Similarly costs are defined to mean all costs, less any saving, that will be incurred by the sponsor. Such savings are not benefits to users, but are reductions in cost to the government.

In addition to this economic criteria many qualitative, social and political factors also influence decisions of public utility projects. The objectives of these projects include protection of health, life, provision of services (at no profit) and provision of jobs. The benefit cost ratio in terms of present worth (PW) may be expressed as:

where PW(B) is the present worth of benefits,

I is the initial investment of the project,

PW(O&M) is the present worth of the operation and maintenance costs,

Modified B/C ratio is also used frequently:

A ratio of modified B/C = 1 or more is considered favorable for a project.

Determine the B/C ratio for a project with the following data:

Initial Cost = Rs. 50(M)

Project Life = 20 years

Salvage Value = Rs. 6(M)

Yearly Benefit(B) = Rs 12(M)

Yearly O & M Cost = Rs. 3(M)

Interest Rate = 12%

(Capital Expense)

Capital Recovery Factor @ (12%, 20)

= 0.1339

Firstly we determine the Capital recovery Cost as per following:

Capital Recovery Cost

= (Initial Cost – Salvage Value) CRF

+ (Salvage Value) (capital expense)

= (50,000,000 – 6,000, 000) (0.1339)

+ (6,000,000 ) x (0.12)

= 5,891,600 + 720,000

= Rs. 6,611,600

Conventional B/C Ratio =

= 1.2485 > 1

Modified B/C Ratio =

= 1.361 > 1

The B/C Ratio being greater than 1 favors the project.

Capital recovery Factor for 12 % , 20 years:

• Capital Recovery

An asset such as a machine is a unit of capital. Such a unit of capital loses value over a period of time in which it is used in carrying out the productive activities of an enterprise. This loss of value of an asset represents the actual piecemeal consumption or expenditure of capital.

Two monetary transactions are associated with the procurement and eventual retirement of a capital asset: its first cost and salvage value. From these amounts it is possible to derive a

simple formula for the equivalent annual cost of the asset for use in economic studies. Let

P = first cost of the asset,

F = estimated salvage value,

n = estimated service life in years

Then the annual cost of the asset may be expressed as the annual equivalent first cost less the equivalent salvage value. This equivalent amount represents the amount that an asset must earn each year if the invested capital is to be

recovered along with a return on the investment.

The expression capital Recovery with return is

An asset with a first cost of $ 5,000 has an estimated life of 5 years and an estimated salvage value of $ 1,000. For an interest rate of 6 % , the annual equivalent cost is

It should be recognized that the cost of an asset is made up of the cost resulting from the loss in value plus the cost of interest on unrecovered capital. The asset in this example suffered a loss, in value of $ 800 per year for 5 years. In addition, the annual equivalent cost of interest on the unrecovered capital was $ 202 per year for 5 years.

Capital assets are purchased in the belief that they will earn more than they cost. One part of

the prospective earning is considered to be capital recovery.

Capital invested in an asset is recovered in the form of incoming derived from the services rendered by the asset and from its sale at the end of its useful life. If the asset provided services valued at $ 800 per year during its life, and if $ 1,000 were received from its sale, a total of $ 5,000 would be recovered.

A second part of the prospective earning will be considered to be return.

Since capital invested in an asset is ordinarily recovered piecemeal, it is necessary to consider the interest on the unrecovered balance as a cost of ownership. Thus an investment in an asset is expected to result in income sufficient not only to recover the amount of the original investment, but also to provide for a return on the diminishing investment remaining in the asset at any time during its life. This gives rise to the phrase capital recovery with return.

The following example illustrates the use of capital recovery with return in an annual equivalent comparison.

A national distribution firm is considering alternative arrangement for adding an additional warehouse to their present distribution system. The warehouse is to be constructed on a parcel of land owned by the firm. The firm can either own the warehouse themselves or lease it from another company that specializes in buildings and leasing buildings. If the firm decides to own the warehouse, they must pay $ 2,000,000 for

its construction. Annual property taxes in this case are expected to be $ 50 per thousand of the appraised value. In this city the appraised value is 40 % of the amount paid for the construction. Annual maintenance costs, and insurance are anticipated to be $ 100,000 and $ 4,000, respectively.

If the building is leased, the firm will make an annual payment of $ 400,000. The lessor will be responsible for all property taxes, insurances & maintenance costs. All other costs will be handled the same for either the lessor or buy

arrangement. The firm expects to utilize the warehouse for the next 10 years, at which time it is estimated that the building could be sold for $ 800,000. The firm uses a minimum attractive rate of return of 15 %.

Buy Building

Capital recovery Cost

Capital Recovery Cost $ 359,160

Property Tax (2,000,000)(0.40)( 50 / 1,000) 40,000

Maintenance Cost 100,000

Insurance Cost 4,000

Annual Equivalent Cost $ 503,160

Lease Building

Annual Lease Payment $ 400,000

Annual Equivalent Cost $ 400,000

If the distribution system firm has the option of

of investing its funds at 15 %, leasing will save $ 103,160 ($ 503, 160 - $ 400,000) per year in equivalent dollars. Note that over the 10 years period the Buy option requires net expenditure of $ 2,640,000 (1,200,000 + 144,000 x 10), whereas the lease option requires expenditure of $ (400,000 x 10) = $ 4,000,000. Again it is evident that when money has a time value it is not the total expenditure that are significant but when those expenditures occur.

Q.No.1

An investment proposal requires an investment of Rs. 50,000. The cash flow expected to be generated in different years is as follows:

Year-1: Rs. 20,000, Year-2: Rs. 22,000, Year-3: Rs. 12, 000: Year-4: 12,000: Year-5: Rs. 10,000.

Should the proposal be accepted if the maximum acceptable PBA is 3 years? Draw the Time Line showing the ICO and cash flows.

Q.No.2

A company is trying to decide which of the two equipments A or B to be installed. Each of the equipment cost Rs. 150, 000. Earning after taxation is expected to be as follows:

Indicate which of the equipment would be chosen on the basis of PBP of ranking investment proposed?

Year Equipment-A (Rs in thousands) Equipment-B (Rs in thousands

1 35 15

2 45 35

3 55 45

4 35 65

5 25 45

Q. No.3

An investment proposal requires an investment of Rs. 70,000. The cash flows expected to be generated in different years is as follows:

Calculate the IRR of the Project. (What is the approximate IRR?)

Year Cash Flows ( Amount in Rs.)

1 12,000

2 15,000

3 18,000

4 21,000

5 26,000

Q.No.4

A company is trying to decide which of the two machines A or B to be purchased. Each will involve an investment of $.10,000.The expected net incremental cash flow is given below:

The company’s cost of capital is 10 %. Calculate the IRR of the Machines. Which one is as per target?

Year Machine-A (Amount in dollars) Machine-B (Amount in dollars)

1 5,000 2,000

2 4,000 3,000

3 2,000 5,000

4 2,000 4,000

Q.No.5

A company is deciding to choose between two mutually exclusive projects A & B. Project-A requires an investment of Rs. 400,000 and is expected to generate cash flow of Rs. 140,000 per annum for 4 years of life, whereas Project-B requires an initial investment of Rs. 450,000 and has a life of 6 years & is expected to generate a cash flow of Rs. 100,000 per year. Which proposal should be accepted based on NPV criterion? Assume 6 % rate of investment.

Q. No.6

Basket Wonder firm is evaluating a new project. They have determined that the after tax cash flows for the project will be $ 12000, $ 15000, $ 18000, $ 21000 and $ 2500 respectively for each of the years one through five. The initial cash outlay is $ 70000. What is the payback period (PBP) of this project? The management of Basket Wonders has set a maximum PBP of 3.5 years for projects of this type. Should this project be accepted on the basis of PBP?

What is the internal rate of return (IRR)?

The management of BW has determined that the hurdle rate is 12 % for projects of this type. Should this project be accepted on the basis of IRR?