Fundamentals of Management Accounting

Investment Appraisal Techniques

Fundamentals of Management Accounting

Class Slides Ian Wilson

Explain the process of long term investments

Calculate the Net Present Value (NPV), Internal Rate of Return(IRR) & Payback for an Investment

In the course to date, we have focused on COSTS & CASH FLOWS that relate to normal & typical BUSINESS COSTS & EXPENSES.

This is called REVENUE Expenditure

Typically, Materials, Labour, Rent, Rates, Insurance etc fall into this category.

A business will also need to purchase & fund ASSETS TANGIBLE ASSETS, typically items such as:

Computers, Machinery, Premises & Vehicles

This is called:

CAPITAL EXPENDITURECAPITAL EXPENDITURECAPITAL EXPENDITURECAPITAL EXPENDITURE

A business will have to decide IF it can afford to purchase ASSETS & what benefit & Financial Return those Assets will create

As such, Managers have to:

1. PLAN buy the asset

2. MAKE a DECISION is it the right asset

3. CONTROL against that Decision will it give an actual return as we expect?

This process is called:

PROJECT APPRAISALPROJECT APPRAISALPROJECT APPRAISALPROJECT APPRAISAL

Management accountants are involved heavily in this process, guiding managers to the right outcome:

Techniques used could beTechniques used could beTechniques used could beTechniques used could be:

1. Net Present Value (NPV)

2. Internal rate of Return (IRR)

3. Payback

Before a Company can look at a specific asset, it has to consider the relevant costs associated with the project.

To do this, it must understand the FUTURE CASH FLOWS associated with the life time of the asset:

The purchase cost today year 0

The following years income generated by the Asset:

Year 1, Year 2 etc & at the end of the term and disposal proceeds

We can now see an important aspect of this process developing:

Cash Flows take place over a longer time period, often 3 years, 5 years or even longer

Premises may be used for 20+ years, a vehicle for 10 years and so on

Over time money changes in value

You will have to consider the Time Value of Money

What is thisWhat is thisWhat is thisWhat is this?

Based on the concept that money received now is worth more than the same sum received in one years time or at another time in the future.

When capital expenditure projects are evaluated, it is appropriate to decide whether the investment will make enough profit to allow for the time value of money as capital is tied up over time.

$1000 received NOW is worth MORE than $1000 received in say, 2 years time.

WhyWhyWhyWhy?

1. Inflation

2. Uncertainty & Risk

3. Opportunities to Invest

You need to learn some key terms also:

Simple InterestSimple InterestSimple InterestSimple Interest:

Simple interest involves adding interest to an invested capital sum of money, whereby the interest that is added each period is added to the capital sum only and not to the interest earned in previous periods.

Simple interest formula Simple interest formula Simple interest formula Simple interest formula ::::FV = PV (1 + rn)

You need to understand the Key:

See the next slide:

Simple interest formula FV = PV (1 + rn)

WhereWhereWhereWhere:

1. FV = Future Value after n periods

2. PV = Present or Initial Value

3. r = Rate of Interest per period

4. n = Number of periods

$1,000 is invested at the start of year 1 and simple interest is added each year at 10% per annum.

How much income will the investment generate by the end of Year 2?

Answer:

1. Initial investment $1,000

2. Interest year 1 $1,000 x 10% $100

3. Interest year 2 $1,000 x 10% $100

4. Value at end of year 2 $1,200

Compound interest is a system that adds interest each year to both the original capital PLUS any interest added to date.

Compound interest formula Compound interest formula Compound interest formula Compound interest formula ::::FV = PV (1 + r)n

WhereWhereWhereWhere:

1. FV = Future Value after n periods

2. PV = Present or Initial Value

3. r = Rate of Interest per period

4. n = Number of periods

$1,000 is invested at the start of year 1 and compound interest is added each year at 10% per annum.

Calculate the value of the investment at the end of Year 3.

Answer on next Slide:

Initial investment $1,000

Interest year 1 $1,000 x 10% $100

Value end of year 1 $1,100

Interest year 2 $1,100 x 10% $110

Value end of year 2 $1,210

Interest year 3 $1,210 x 10% $121

Value end of year 3 $1,331

Yes! Apply the formulaYes! Apply the formulaYes! Apply the formulaYes! Apply the formula:

Remember:

FV = PV (1 + r)n

FV = $1000 x (1+0.10)3

FV = $1331

Present Present Present Present Values (Values (Values (Values (PVs):PVs):PVs):PVs):

This calculates the present value (at year 0) of all cash flows, & sums them to give the NPV. If this value is positive, the investment goes ahead.

In other wordsIn other wordsIn other wordsIn other words:

The value at time 0 of a future cash flow, having taken account of the time value of money. In investment appraisal, it represents the maximum an investor would be willing to invest for a future cash inflow given a specified required return

Discounted Cash Flow(DCF)Discounted Cash Flow(DCF)Discounted Cash Flow(DCF)Discounted Cash Flow(DCF):

DCF is a technique that takes into account the timing of cash flows & allows comparison between cash flows arising at different points in time.

Compounding Compounding Compounding Compounding ReReReRe----capcapcapcap:

Compounding calculates the future value of a given sum of money

FV = PV (1 + r)n

where FV = Future Value after n periods

PV = Present or Initial Value

r = Rate of Interest per period

n = Number of periods

Final reFinal reFinal reFinal re----capcapcapcap:

Compounding: we move from a present value to a future value by adding compound interest each year

DiscountingDiscountingDiscountingDiscounting::::

Discounting is the reverse of compounding we start at the future value and work back to the present value.

PV = FV (1 + r)n

WhereWhereWhereWhere:

PV = present value

FV = future value

r = rate of interest

n = number of periods

Compounding:

Discounting:

YEAR 0 YEAR 1

What do they containWhat do they containWhat do they containWhat do they contain?

Periods n for 15 years, by single year

Discount rate r, r = a %, 1 to 20%

Read off the years/periods & discount rate & you get a factor, something to multiply your cash flow by to get the:

PRESENT VALUE, ie the value in todays terms for a cash flow in the future

You can calculate your own factors with a formula:

1

1+r^n

Say r = 10%, substitute 0.10 into the formula in your calculator:

1

1+ 0.1^n

= 0.909 = the same answer as your tables

How do we deal with timescales of many years, ie n=2, or n=3 etc?.

You have to use to the power of for each year.

2 years = power of 2, n=2

3 years = power of 3, n=3

Your calculator has a ^ key for you to do this

10% on 2 years would be:

1

1 + 0.1 power 2 = 0.826

See page 132: find the present value of $80,000 at the end of year 5

Remember your formula for

FV = PV (1 + r)n

Substitute into the formula:

FV = $80,000, r = 10%

FV = 80000

(1+.10)5

= $49674 invested today to get $80000 in 5 years time

The answer again:

PV = FV/(1 + r)n

PV = 80,000 / (1 + 0.1)5

PV = 80,000 / 1.61051 = $49,674

NPV looks at the comparison of how much cash will an investor get back from an investment compared to how much cash they have had to pay for the investment.

Everything is compared in present value terms.

The techniques is used to evaluate whether or not a project should be accepted.

There are Three steps to follow:

1. Step 1: sort out the numbering of the years between the investment & each future value

2. Step 2: decide what Cost of capital to use & find discount factors

3. Step 3: multiply each future value by the relevant discount factor to give the present values

Decision CriteriaDecision CriteriaDecision CriteriaDecision Criteria:

If the investment has a positive NPV then the project should be accepted (negative -rejected).

A positive NPV means that the project will increase the wealth of the company by the amount of the NPV at the current cost of capital

A company is evaluating a project that has the following cash flows:

Machine to be purchased on January 1 2011: for $50,000

You are given Net Cash Flows for 2011 to 2014.

The Company can borrow money at 10%

Is the project worthwhile?

Use the template on page 133

YearYearYearYear Cash FlowCash FlowCash FlowCash Flow Discount FactorDiscount FactorDiscount FactorDiscount Factor@ 10%@ 10%@ 10%@ 10%

Present ValuePresent ValuePresent ValuePresent Value

0 ($50,000) 1.000 ($50,000)

1 $20,000 0.909 $18,180

2 $10,000 0.826 $8,260

3 $20,000 0.751 $15,020

4 $15,000 0.683 $10,245

5

Net Present Value: $1,705

The rate of interest (discount) at which the NPV = 0

If the IRR is greater than the cost of capital the project should be accepted, because this suggests that the NPV is positive at the cost of capital

Look at Exercise 3

You will need the linear interpolation formula:

Lets look at this example:

What is it?What is it?What is it?What is it?

The length of time it takes for cash inflows from trading to pay back the initial Investment in Year 0

Is your payback period right or wrong?

The answer is you dont know unless you have a Target.

What is the Target?, measure against that.

It depends!

How do we calculate it?How do we calculate it?How do we calculate it?How do we calculate it?

This is the length of time it takes for cash inflows from trading to pay back the

initial investment.

Payback period = Initial investment / Annual inflow

A company invests in a project with an initial cash outflow of $100,000. Cash inflows resulting from the project are $40,000 per annum.

Calculate the payback period.

Payback period = $100,000 / $40,000 =

2.5 years

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