Capital investment appraisal

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Capital investment appraisal

As investments involve large resources, wrong

investment decisions are very expensive to correct Managers are responsible for comparing and

evaluating alternative projects so as to allocate

limited resources and maximize the firm’s wealth Basic techniques of making capital investment

appraisal for evaluating proposed capital

investment projects

Investment appraisal methods

Considering the time value of

money concept Ignoring the time value of money concept

•Net present value

•Internal rate of return

•Payback period

•Accounting rate of return

Net present value method

Time value of money

When facing different investment proposals, the

management should choose the project that can

generate the greatest addition of value to the

company For example,

Project A Project B Initial investment $100 $100

Cash inflow at end of year

At first sight, some may think that project B is

better because it has a higher cash inflow

However, the time value of money concept states that a dollar today is always worth more than a

dollar in the future

The two projects are of equal value to the

company because their present values are the same

After taking timing of cash flow into consideration,

Project A Project B Present value of cash flow

(interest rate is 10% per annum) 110 121

(1+10%) (1+10%)2

= $100 $100 The two projects are of equal value to the company because their present values are the same

Factors leading to the changes in value of money

Opportunity cost of money

Erosion of purchasing power due to inflation

Uncertainty and risk

Opportunity cost of money

Opportunity cost of money refers to the cost

incurred or income forgone by not using the

money for other purpose

For surplus cash, the opportunity cost is the

interest income forgone by investing the cash in

other investments or depositing it in the bank

Erosion of purchasing power due

to inflation

Inflation refers to the continual increase in the

general price level of goods or services

During a period of inflation, prices of goods

increase while the purchasing power of money

decrease The purchasing power of a dollar today

is greater than that of the future

Uncertainty and risk

Investors tend to avoid risk The uncertainty

involved in future cash inflows is much higher

than that in present cash inflows

If the level of risk rises, investors will expect a

higher return as compensation.

For example, suppose an investor expects $100 for return now After adding a 10% risk premium, he will expect $110 one year later

Discounting

According to the time value of money concept, a

dollar in one year is not worth the same as a dollar

in anther year.

In evaluating a multi-year investment, cash

inflows and outflows are generated in different

years

It is necessary to convert the cash flows for

different years into a common value at a common point of time , either at present or in the future

Discounting is the process of reducing future cash flows to present values with the use of an interest rate

Example

John has won a lucky draw He is deciding whether to receive the Prize money of $3000 today or the following set of cash flows over the next three years:

Net present value method

Net present value method

Net present value (NPV) method is a process that uses the discounted cash flow of a project to

determine whether the rate of return on that

project is equal to, higher than, or lower than the

desired rate of return

With the NPV method, we can compare the return

on investment in capital projects with the return on

an alternative equal risk investment in securities

traded in financial market

3 Interpreting the NPV derived as follows:

NPVs Comments Reasons

<0 Reject the project The rate of return from the project is

small than the rate of return from an equivalent risk investment

=0 Indifferent to accept

or reject the project

The rate of return from the project is

equal to the rate of return from an equivalent risk investment

>0 Accept the project The rate of return from the project is

greater than the rate of return from an equivalent risk investment

Highest Accept the project If various project are considered, the

project with highest positive NPV should be chosen

Example

A company is considering making several investments in the

Production facilities for the new products with an estimated useful

Life of four years The cash inflows and outflows are listed as follows:

Project

Initial investment 900000 1000000 303730 1500000Cash inflow

(a) Calculate the NPV of each investment and determine whether

to accept it or not (assuming the company has unlimited

resources)

(b) If the company has limited resources, determine which

investment should be accepted by referring to the highest NPV

(b) With limited resources, the company should only accept project A

because it generates the highest NPV

Internal rate of return

Internal rate of return

The internal rate of return is the annual percentage return achieved by a project, of which the sum of discounted cash inflow over the life of the project

is equal to the sum of discounted cash outflows

If the IRR is used to determine the NPV of a

project, the NPV will be zero.

The company will accept this project only if the

IRR is equal to or higher than the minimum rate of return or the cost of capital

Calculation procedures

1. By trial and error, find out the discount rate that

will give a zero NPV

2. If the NPV is positive, try a higher discount rate in

order to give a negative NPV and vice versa

NPV = FV(1+r)11 FV+ (1+r)2 FV2 + (1+r)3 FV3 + (1+r)n n - I

0 = 0

3 After getting one positive NPV and one negative

NPV, use interpolation to find out the rate

giving zero NPV

IRR = L + P

P – N (H – L)

Where L = Discount rate of the low trial

H = Discount rate of the high trial

P = NPV of cash flows of the low trial

N = NPV of cash flows of the high trial

4 In evaluating an investment project, the IRR is

compared with the management’s predetermined rate

< lowest acceptable level of return Reject NPV<0

= lowest acceptable level of return Accept NPV=0

> Lowest accepted level of return Accept NPV>0

considered, the highest IRR should

Example

A project costs $400 and produces a regular cash inflow of $200 at the end of each of the next three years Calculate the IRR If the minimum rate of return is 15 %, suggest with reason whether you Should accept the project or not

IRR = L + P

P – N (H – L)

Where L = Discount rate of the low trial

H = Discount rate of the high trial

P = NPV of cash flows of the low trial

N = NPV of cash flows of the high trial

Payback period

Payback period

Payback period is the period of time it takes for a company to recover its initial investment in a

project

The method measures the time required for a

project’s cash flow to equalize the initial

investment

Acceptance criterion

< predetermined cutoff period Accept the project

> Predetermined cutoff period Reject the project

Example

A company is considering making the following mutually exclusiveInvestments in the production facilities for the new products with an Estimated useful life of four years The cash inflow and outflows areListed as follows:

Project A : 3 years Project B: 2 years

Project B takes only two years to recover its initial investment With

Advantages of payback period

Easy to adopt

Facilities further evaluation

 After obtaining an acceptable payback period, the project will be evaluated by other financial capital budgeting techniques

Disadvantages of Payback period

Ignore the cash flows after payback period

Adopt an arbitrary standard for the payback period Ignores the timing of cash flow

Discounted payback period

The payback period method is criticized for

ignoring the timing of cash flows, therefore

discounted cash flows are used to calculate the

discounted payback period

Example

A company is considering making the following mutually exclusiveinvestments in the production facilities for the new products with an estimated useful life of four years The cash inflow and outflows arelisted as follows:

Accounting rate of return

Accounting rate of return

The accounting rate of return compares the

average accounting profit with the average

investment cost of project

The accounting profit can be expressed either

before tax or after tax

Calculation procedures

ARR = Average net profit per year (over the life of the project)Average investment cost

Average net profit per year = No of life of the projectTotal profit

Average investment cost = Initial investment 2

In evaluating an investment project, the ARR of the project is

compared with a predetermined minimum acceptable accounting Rate of return:

< minimum acceptable rate Reject project

= minimum acceptable rate Accept project

> minimum acceptable rate Accept project

Highest Choose highest ARR

Acceptance criterion

Example

A company is considering whether to buy specialized machines

For a new production line The purchase price of machinery is

$400000 and its estimated useful life is four years There is no scrap

Value after four years

The project income statements:

Average net income = 51000+68000+59500+765004 = $63750Average investment = 400000+0 2 = $200000

The cost of machinery is $400000 at the beginning

The cost of machinery is $0 at the end as depreciation is provided

On straight line method and there is no scrap value

ARR = $63750$200000 = 31.875%

Since the ARR is 31.875%, which is higher than the minimum

Acceptable rate of 20%, the company should invest in the new machinery

Advantages of ARR

It is easy to understand and compute

It avoids using gross figures Therefore, it enables comparisons to be made between projects with

different useful lives

Disadvantages of ARR

It ignores the time value of money

ARR method seems to be less reliable than the

NPV method It adopts the accounting profit

instead of cash flows calculation The change of

depreciation method may also alter the accounting profit