3.8 — Investment Appraisal

PART A: INTRODUCTION TO INVESTMENT APPRAISAL

Definition

Investment appraisal (also called capital budgeting) is the process of evaluating proposed capital investments to determine whether they are worthwhile and to compare alternative investment options.

What is a Capital Investment?

A capital investment is spending on non-current assets or projects that will generate returns over multiple years.

Examples	Description
New machinery	Equipment to increase capacity or efficiency
New premises	Factory, warehouse, office, retail outlet
New product development	R&D and launch costs
Technology systems	IT infrastructure, software
Expansion	Opening new locations, entering new markets
Acquisition	Buying another business
Replacement	Replacing worn-out assets

Why Investment Appraisal Matters

Reason	Explanation
Large amounts	Capital investments involve significant sums
Long-term commitment	Decisions are difficult to reverse
Opportunity cost	Capital used here cannot be used elsewhere
Risk	Future returns are uncertain
Strategic impact	Investments shape the business's future
Limited resources	Cannot pursue all possible investments
Accountability	Need to justify decisions to stakeholders

The Investment Decision Process

Step	Description
1. Identify options	What investment opportunities exist?
2. Gather data	Estimate costs, revenues, timing
3. Apply appraisal methods	Calculate payback, ARR, etc.
4. Consider qualitative factors	Non-financial considerations
5. Make decision	Accept, reject, or rank options
6. Implement	Proceed with chosen investment
7. Monitor	Track actual vs expected performance

Key Data Required

Data	Description
Initial investment	Cost of the asset/project at the start
Expected cash flows	Cash inflows and outflows over the life of the investment
Project life	How long the investment will generate returns
Residual value	Expected value at the end of project life
Cost of capital	The required rate of return (for NPV/IRR)

Investment Appraisal Methods

Method	What It Measures
Payback Period	How long to recover the initial investment
Average Rate of Return (ARR)	Average annual profit as a percentage of investment
Net Present Value (NPV)	Value of future cash flows in today's terms (HL)
Internal Rate of Return (IRR)	Discount rate at which NPV equals zero (HL)

This unit covers Payback Period and ARR (SL/HL). NPV and IRR are HL only.

PART B: PAYBACK PERIOD

Definition

The payback period is the length of time it takes for a project to recover its initial investment from its net cash inflows.

Key question answered: "How long until we get our money back?"

Formula

For even (equal) annual cash flows:

$Payback\ Period = \frac{Initial\ Investment}{Annual\ Cash\ Flow}$

For uneven (varying) cash flows:

Calculate the cumulative cash flow until the initial investment is recovered.

Example 1: Even Cash Flows

Data	Amount
Initial Investment	$100,000
Annual Cash Flow	$25,000 (same each year)

$Payback\ Period = \frac{100,000}{25,000} = 4\ years$

Interpretation: The investment will be recovered in 4 years.

Example 2: Uneven Cash Flows

Year	Cash Flow	Cumulative Cash Flow
0	($100,000)	($100,000)
1	$30,000	($70,000)
2	$40,000	($30,000)
3	$50,000	$20,000
4	$40,000	$60,000

Analysis:

After Year 2: Still $30,000 short
After Year 3: $20,000 surplus — payback occurs during Year 3

Calculating exact payback:

$Payback = 2\ years + \frac{30,000\ (remaining)}{50,000\ (Year\ 3\ cash\ flow)}$

$Payback = 2 + 0.6 = 2.6\ years\ (or\ 2\ years\ 7.2\ months)$

Step-by-Step Method for Uneven Cash Flows

Step	Action
1	Calculate cumulative cash flow for each year
2	Identify the year when cumulative cash flow turns positive
3	Note the cumulative cash flow at the end of the previous year
4	Calculate: Payback = Previous year + (Remaining amount / Cash flow in payback year)

Interpreting Payback Period

Payback	Interpretation
Shorter is better	Faster recovery reduces risk
Compare to target	Many businesses set maximum acceptable payback
Compare alternatives	Choose project with shorter payback (all else equal)

Typical targets:

High-tech/fast-changing industries: 2-3 years
Stable industries: 3-5 years
Infrastructure: 5-10 years

Advantages of Payback Period

Advantage	Explanation
Simple	Easy to calculate and understand
Quick	Fast to compute; minimal data needed
Risk focus	Emphasises early cash flows (less uncertain)
Liquidity	Identifies when cash returns
Widely used	Common in business practice
Useful for cash-poor businesses	Prioritises getting money back quickly
Suitable for uncertain environments	When long-term predictions are unreliable
Good screening tool	Quickly eliminates poor investments

Disadvantages of Payback Period

Disadvantage	Explanation
Ignores cash flows after payback	A project may generate significant returns after payback
Ignores profitability	Doesn't measure total return
Ignores timing within payback	$50k in Year 1 + $50k in Year 2 treated same as $10k + $90k
Ignores time value of money	$1 today worth more than $1 in future
Arbitrary target	What is an "acceptable" payback?
Favours short-term	May reject good long-term investments
No clear decision rule	Shorter is better, but how short?

Example: Payback Ignores Cash After Payback

	Project A	Project B
Initial Investment	$100,000	$100,000
Year 1	$50,000	$30,000
Year 2	$50,000	$30,000
Year 3	$10,000	$40,000
Year 4	$10,000	$50,000
Year 5	$10,000	$50,000
Payback	2 years	3 years
Total Cash Flows	$130,000	$200,000

Payback suggests: Project A is better (faster payback)

Reality: Project B generates $70,000 more total cash!

PART C: AVERAGE RATE OF RETURN (ARR)

Definition

The Average Rate of Return (ARR) measures the average annual profit generated by an investment as a percentage of the initial investment (or average investment).

Also called: Accounting Rate of Return, Return on Investment (ROI)

Key question answered: "What is the average annual profit as a percentage of investment?"

Formula

$ARR = \frac{Average\ Annual\ Profit}{Initial\ Investment} \times 100%$

Or (alternative version):

$ARR = \frac{Average\ Annual\ Profit}{Average\ Investment} \times 100%$

Where:

$Average\ Investment = \frac{Initial\ Investment + Residual\ Value}{2}$

Note: The IB typically uses the initial investment version.

Calculating Average Annual Profit

$Average\ Annual\ Profit = \frac{Total\ Profit\ over\ Project\ Life}{Number\ of\ Years}$

Where:

$Total\ Profit = Total\ Cash\ Flows - Initial\ Investment$

Or more precisely:

$Total\ Profit = Total\ Cash\ Inflows - Initial\ Investment - Depreciation$

Important: ARR uses profit, not cash flow. If given cash flows:

$Total\ Profit = Total\ Cash\ Inflows - Initial\ Investment\ (if\ no\ residual\ value)$

$Total\ Profit = Total\ Cash\ Inflows - Depreciation\ (if\ residual\ value\ exists)$

Where:

$Depreciation = Initial\ Investment - Residual\ Value$

Example 1: Basic ARR Calculation

Data	Amount
Initial Investment	$200,000
Project Life	5 years
Total Cash Inflows	$350,000
Residual Value	$0

Step 1: Calculate Total Profit

$Total\ Profit = 350,000 - 200,000 = 150,000$

Step 2: Calculate Average Annual Profit

$Average\ Annual\ Profit = \frac{150,000}{5} = 30,000$

Step 3: Calculate ARR

$ARR = \frac{30,000}{200,000} \times 100% = 15%$

Interpretation: The investment generates an average annual return of 15% on the initial investment.

Example 2: With Residual Value

Data	Amount
Initial Investment	$200,000
Project Life	5 years
Total Cash Inflows	$350,000
Residual Value	$20,000

Step 1: Calculate Depreciation

$Depreciation = 200,000 - 20,000 = 180,000$

Step 2: Calculate Total Profit

$Total\ Profit = 350,000 - 180,000 = 170,000$

Step 3: Calculate Average Annual Profit

$Average\ Annual\ Profit = \frac{170,000}{5} = 34,000$

Step 4: Calculate ARR (using initial investment)

$ARR = \frac{34,000}{200,000} \times 100% = 17%$

Example 3: Using Average Investment

Using the same data as Example 2, but with average investment:

$Average\ Investment = \frac{200,000 + 20,000}{2} = 110,000$

$ARR = \frac{34,000}{110,000} \times 100% = 30.9%$

Note: This method gives a higher ARR. Be consistent and follow the formula specified in the question.

Interpreting ARR

ARR Value	Interpretation
Higher is better	Greater return on investment
Compare to target	Should exceed required rate of return
Compare to cost of capital	Should exceed the cost of financing
Compare alternatives	Choose project with highest ARR (all else equal)
Compare to bank interest	Should exceed what money could earn in bank

Decision Rules for ARR

Rule	Application
Accept if ARR > target rate	Investment is worthwhile
Reject if ARR < target rate	Investment is not worthwhile
Choose highest ARR	When comparing mutually exclusive projects

Advantages of ARR

Advantage	Explanation
Considers all cash flows	Uses total returns over project life
Measures profitability	Shows actual return on investment
Easy to understand	Percentage return is intuitive
Comparable	Can compare to other investments, interest rates
Uses familiar data	Based on profit figures used elsewhere
Accounts for whole life	Considers returns after payback

Disadvantages of ARR

Disadvantage	Explanation
Ignores timing	$100 in Year 1 treated same as $100 in Year 5
Ignores time value of money	Money today worth more than money tomorrow
Uses profit, not cash	Profit can be manipulated; cash is fact
Average hides variation	May have losses in some years, high profits in others
Different calculation methods	Initial vs average investment gives different results
Arbitrary target	What is an "acceptable" ARR?
Ignores project size	20% on $10,000 vs 20% on $1,000,000

Example: ARR Ignores Timing

	Project A	Project B
Initial Investment	$100,000	$100,000
Year 1 Profit	$40,000	$10,000
Year 2 Profit	$30,000	$20,000
Year 3 Profit	$20,000	$30,000
Year 4 Profit	$10,000	$40,000
Total Profit	$100,000	$100,000
Average Annual Profit	$25,000	$25,000
ARR	25%	25%

ARR suggests: Both projects are equal

Reality: Project A is better — it generates more cash earlier, which can be reinvested.

PART D: COMPARING PAYBACK AND ARR

Comparison Table

Aspect	Payback Period	ARR
Measures	Time to recover investment	Average annual return
Result	Time (years/months)	Percentage
Uses	Cash flows	Profit
Cash after payback	Ignores	Includes
Time value of money	Ignores	Ignores
Timing of cash flows	Partially considers	Ignores completely
Risk focus	High (favours quick return)	Lower
Complexity	Simple	Simple
Best for	Risky/uncertain environments	Comparing profitability

When to Use Each Method

Situation	Best Method
High uncertainty	Payback (favour quick returns)
Liquidity concerns	Payback (need cash back quickly)
Long-term strategic	ARR (consider total returns)
Comparing profitability	ARR (percentage return)
Quick screening	Payback (eliminate poor options)
Detailed analysis	Use both (and NPV/IRR if HL)

Example: Different Methods, Different Conclusions

	Project X	Project Y
Initial Investment	$100,000	$100,000
Year 1	$60,000	$20,000
Year 2	$40,000	$30,000
Year 3	$20,000	$50,000
Year 4	$10,000	$60,000
Total Cash Flows	$130,000	$160,000
Payback	2 years	3 years
Total Profit	$30,000	$60,000
Average Annual Profit	$7,500	$15,000
ARR	7.5%	15%

Method	Preferred Project
Payback	Project X (faster)
ARR	Project Y (higher return)

Conclusion: Different methods may lead to different decisions. This is why multiple methods should be used together.

PART E: QUALITATIVE FACTORS IN INVESTMENT DECISIONS

Beyond the Numbers

Investment appraisal methods provide quantitative analysis, but decisions should also consider qualitative factors.

Key Qualitative Factors

Factor	Considerations
Strategic fit	Does it align with business strategy and objectives?
Risk	How uncertain are the cash flow estimates?
Flexibility	Can the investment be adapted if conditions change?
Reputation	How will it affect brand, image, stakeholder perceptions?
Employee impact	Effect on morale, jobs, skills requirements
Customer impact	Effect on service, quality, relationships
Competitive position	How will competitors respond?
Environmental impact	Sustainability, regulations, social responsibility
Legal/Regulatory	Compliance requirements, potential changes
Technology	Risk of obsolescence; future developments
Timing	Is now the right time? Market conditions?
Management capacity	Do we have skills to implement successfully?
Opportunity cost	What else could we do with these resources?
Reversibility	How easily can we exit if it fails?

Risk Assessment

Type of Risk	Examples
Market risk	Demand lower than expected
Technical risk	Technology doesn't work as planned
Cost risk	Costs higher than estimated
Timing risk	Delays in implementation
Competitive risk	Competitor actions reduce returns
Economic risk	Recession, currency changes
Political/Regulatory risk	New laws affect viability

Dealing with Uncertainty

Technique	Description
Sensitivity analysis	Test how changes in assumptions affect results
Scenario planning	Best case, worst case, most likely
Probability analysis	Assign probabilities to outcomes
Shorter payback target	Require faster payback for riskier projects
Higher ARR target	Require higher returns for riskier projects
Conservative estimates	Use pessimistic figures

PART F: LIMITATIONS OF INVESTMENT APPRAISAL

Common Limitations

Limitation	Explanation
Based on estimates	Future cash flows are predictions, not facts
Uncertainty	External factors may change
Ignores qualitative factors	Numbers don't capture everything
Time value (Payback/ARR)	Money today worth more than money tomorrow
Timing issues (ARR)	Doesn't consider when returns occur
Cash after payback	Payback ignores later returns
Different results	Methods may give conflicting answers
Garbage in, garbage out	Results only as good as data
Static analysis	Assumes conditions remain constant
Ignores financing	Doesn't consider how investment is funded

Improving Investment Decisions

Approach	Description
Use multiple methods	Don't rely on just one technique
Consider qualitative factors	Look beyond the numbers
Sensitivity analysis	Test key assumptions
Review and update	Revisit estimates as information changes
Post-investment audit	Compare actual to predicted; learn for future
Involve stakeholders	Get input from those affected
Consider alternatives	Compare with doing nothing; other options

PART G: EXAM APPLICATION

Potential Exam Questions

"Calculate the payback period for the proposed investment and evaluate whether it should proceed." (10 marks)
"Analyse the advantages and disadvantages of using payback period as an investment appraisal method." (10 marks)
"Calculate the average rate of return (ARR) and discuss its usefulness for decision-making." (10 marks)
"Evaluate the view that investment decisions should be based on financial criteria alone." (10 marks)
"Compare and contrast payback period and ARR as investment appraisal methods." (10 marks)
"Discuss the limitations of investment appraisal techniques." (10 marks)

Key Definitions to Memorise

Term	Definition
Investment appraisal	The process of evaluating proposed capital investments to determine their viability
Payback period	The time taken for a project to recover its initial investment from net cash inflows
Average Rate of Return (ARR)	Average annual profit as a percentage of the initial investment
Initial investment	The cost of the asset or project at the start
Net cash flow	Cash inflows minus cash outflows for a period
Cumulative cash flow	Total cash flows accumulated over time
Residual value	Expected value of the asset at the end of its useful life
Time value of money	The concept that money today is worth more than the same amount in the future

Key Formulas

Calculation	Formula
Payback (even cash flows)	Initial Investment / Annual Cash Flow
Payback (uneven cash flows)	Years before recovery + (Remaining amount / Cash flow in payback year)
Total Profit	Total Cash Inflows − Initial Investment (or − Depreciation if residual value)
Average Annual Profit	Total Profit / Number of Years
ARR	(Average Annual Profit / Initial Investment) × 100%

Calculation Tips

Tip	Explanation
Show workings	Marks often given for method, not just answer
State units	Years for payback; % for ARR
Check reasonableness	Does the answer make sense?
Read carefully	Initial vs average investment; profit vs cash flow
Be consistent	Use same method throughout
Label clearly	Make it easy for examiner to follow

Evaluation Frameworks

When evaluating payback:

"Payback is useful for screening but ignores returns after payback..."
"Suitable for uncertain environments where quick recovery is important..."
"Should be used alongside other methods..."
"Does not measure profitability or total return..."

When evaluating ARR:

"ARR measures overall profitability but ignores timing of returns..."
"Useful for comparing investments but arbitrary target rates..."
"Uses accounting profit which can be manipulated..."
"Considers all returns unlike payback..."

When comparing methods:

"Different methods may give different recommendations..."
"The best method depends on the decision context..."
"Multiple methods should be used together for better decisions..."
"Qualitative factors should complement quantitative analysis..."

Sample Calculation Question

Question: A company is considering investing $80,000 in new equipment. The expected cash flows are:

Year	Cash Flow
1	$25,000
2	$30,000
3	$35,000
4	$20,000

Calculate (a) the payback period and (b) the ARR. Recommend whether the investment should proceed if the company requires a payback of 3 years and ARR of 15%.

Answer:

(a) Payback Period

Year	Cash Flow	Cumulative
0	($80,000)	($80,000)
1	$25,000	($55,000)
2	$30,000	($25,000)
3	$35,000	$10,000

Payback occurs in Year 3.

$Payback = 2 + \frac{25,000}{35,000} = 2 + 0.71 = 2.71\ years\ (or\ 2\ years\ 9\ months)$

(b) ARR

Total Cash Inflows = $25,000 + $30,000 + $35,000 + $20,000 = $110,000

Total Profit = $110,000 − $80,000 = $30,000

Average Annual Profit = $30,000 ÷ 4 = $7,500

$ARR = \frac{7,500}{80,000} \times 100% = 9.375%$

(c) Recommendation

Criterion	Target	Actual	Met?
Payback	≤ 3 years	2.71 years	✓ Yes
ARR	≥ 15%	9.375%	✗ No

Recommendation: The investment meets the payback target but fails to meet the ARR target. On financial grounds alone, the investment should be rejected. However, qualitative factors such as strategic importance, competitive necessity, or other non-financial benefits should also be considered before making a final decision.