Investment appraisal is a quantitative process used by managers to evaluate the profitability of
investment decisions. It compares the expected future returns on projects with the costs,
considering nonfinancial issues.
Quantitative Investment Appraisal
• Initial capital cost: Cost of buildings and equipment.
• Estimated life expectancy: 'useful life' of an asset.
• Residual value: Assets sold at end of useful lives, increasing cash inflow.
• Forecasted net cash flows: Expected returns from investment less annual operating cost.
Quantitative Methods of Investment Appraisal
• Payback period: A project's payback period is four years, compared to alternative investments.
• Accounting rate of return: The average rate of return is used to determine the payback period.
Payback Method
• For a $2 million project, the payback period is four years.
• Year 0 is the time period when the investment is made, with a negative cash flow.
• The forecast annual net cash flows and cumulative cash flows show the running total of net
cash flows.
• Payback is expected at the end of the fourth month of the third year.
• At the end of year 2, $50 000 is needed to repay the remainder of the initial investment.
Project Payback Importance
• Managers can rank alternative projects based on payback period.
• Payback period can be compared with a business cut-off time period.
• Longer payback periods increase interest payments.
• Speedier paybacks make capital available for other projects.
• Longer payback periods increase investment uncertainty due to potential external changes.
• Quick paybacks reduce uncertainties for risk-averse managers.
• Cash flows received in the future have less real value due to inflation.
• Quicker return of money increases its real value.
Accounting Rate of Return Overview
• Also known as average rate of return.
• Helps in making investment decisions.
Project Annual Return Rate (ARR) Importance
• Indicates a business's average annual return of 20% over the investment's lifespan.
• Compares with other projects' ARR.
• Sets the minimum expected return, known as the criterion rate.
• Determines the annual interest rate on loans.
• If ARR is less than the interest rate, it's not worth investing in the project.
Quantitative Techniques: Discounted Cash Flow
• Managers may struggle with comparing projects with different ARR and payback periods due
to conflicting results from two basic investment appraisal methods.
• A third method, discounted cash flow, considers both the size of net cash flows and their
timing.
• The decision to accept a payment today is based on three reasons: immediate spending,
potential savings at the current interest rate, and certainty of the cash today.
• Discounting reduces the value of future cash flows to their present value in today's terms,
based on the rate of interest.
• The present-day value of $1100 received in one year's time is calculated to compare
investment projects considering today's value of their returns.
EXAMPLE:
Textile Company plans investment
A textile business is planning an investment programme to overcome a problem of demand
exceeding capacity. It is considering two alternative projects involving new machinery. The
initial investments and future cash outflows are given in Table. In both cases, it is assumed that
the machinery is sold for its residual capital value and 15% is Criterion Rate Return.
Year Project X Project Y
0 ($50 000) ($80 000)
1 $25 000 $45 000
2 $20 000 $35 000
3 $20 000 $17 000
4 $15 000 $10 000
5 $10 000 $5 000
For Project X (including residual value of $5000)
For Project Y (including residual value of $2000)
1 Calculate the payback for both projects.
2 Explain which project should be selected if payback is the only criterion used, and why.
3 Calculate the ARR for both projects.
4 The business has a cut-off or criterion rate of 15% for all new projects. Would either project
be acceptable with this restriction?
5 Taking both the results of payback and ARR together, which project would you advise the
business to invest in and why?
6 What additional information would help you advise the business on the more suitable project
The textile company is evaluating two projects (X and Y) to expand capacity. Here's the
analysis using payback period and accounting rate of return (ARR):
1. Payback Period Calculation
Project X: 2.25 years
Cumulative cash flow turns positive in year 3:
(-50,000) + 25,000 + 20,000 = -5,000 (end of Year 2)
Year 3 cash flow: $20,000 → Payback = 2 + (5,000/20,000) = 2.25 years
Project Y: 2.0 years
Cumulative cash flow reaches breakeven in Year 2:
(-80,000) + 45,000 + 35,000 = 0 → 2 years
2. Project Selection Based on Payback
Project Y would be preferred under payback criteria, as it recovers the initial investment faster
(2.0 vs. 2.25 years). This reduces exposure to long-term risks and improves liquidity.
3. ARR Calculation
Metric Project X Project Y
Total Cash Inflows $90,000 $112,000
Average Annual Profit ($90,000 - $50,000)/5 = $8,000 ($112,000 - $80,000)/5 = $6,400
ARR ($8,000/$50,000) × 100 = 16% ($6,400/$80,000) × 100 = 8%
4. 15% Criterion Rate Evaluation
Project X: 16% ARR (exceeds 15% cutoff) → Acceptable
Project Y: 8% ARR (below cutoff) → Rejected
5. Combined Analysis Recommendation
While Project Y has better liquidity (shorter payback), Project X is the clear choice because:
Only X meets the 15% profitability benchmark
Higher ARR indicates better long-term returns
Payback difference (0.25 years) is relatively small compared to the significant ARR
advantage
6. Additional Information Needed
Key missing factors for a comprehensive decision:
1. Time Value of Money Metrics: NPV and IRR calculations
2. Risk Profile: Equipment reliability differences
3. Capacity Expansion Scale: Which project better addresses demand gaps
4. Long-term Market Trends: Sustainability of increased demand
5. Operational Costs: Maintenance differences between machinery
The company should prioritize Project X but validate with discounted cash flow analysis before
finalizing.
Net Present Value (NPV) Calculation Using Discounted Cash Flow Formula
To answer the questions and replace the use of "discount factor" with the explicit discounted
cash flow formula, let's clarify the process and apply it to the example provided.
Discounted Cash Flow Formula
The present value (PV) of a future cash flow is calculated as:
CF
PV =
¿¿
Where:
CF = Cash Flow in year n
r = Discount rate (here, 8% or 0.08)
n = Year (time period)
Step-by-Step NPV Calculation
1. Calculate the Present Value for Each Year Using the Formula
o Year 0: P V 0= −10,000
¿¿
o Year 1: P V 1= 5,000
¿¿
4,000
o Year 2: P V 2=
¿¿
3,000
o Year 3: P V 3=
¿¿
2,000
o Year 4: P V 4 =
¿¿
2. Sum the Present Values of All Cash Flows (Years 1–4)
Total discounted cash flows=P V 1+ P V 2 + P V 3 + PV 4
¿ 4,629.63+ 3,429.36+2,382.51+1,470.13=11,911.63
3. Subtract the Initial Investment
NPV=(Total discounted cash flows)+ P V 0
¿ 11,911.63−10,000=1,911.63
Example:
A company is evaluating two projects, Location A and Location B, with the following cash
flows (all figures in $000):
Year Location Location B ($000)
A ($000)
0 (12) (12)
1 3 6
2 4 5
3 5 3
4 6 2
5 5 5
Assuming a 10% discount rate, which project has a higher NPV?
A) Location A
B) Location B
C) Both projects have equal NPV
D) Location A (Correct Answer) if PV =Cash¿Flow
¿
Location A
Year Cash Flow ($000) Discounted Cash Flow ($000)
0 (12) −12.00
1 3 3
≈ 2.73
1.10
2 4 4
2
≈ 3.31
1.10
3 5 5
3
≈ 3.76
1.10
4 6 6
4
≈ 4.10
1.10
5 5 5
5
≈ 3.10
1.10
Total NPV for Location A:
−12+2.73+3.31+3.76+ 4.10+3.10=$ 5.00
Location B
Year Cash Flow ($000) Discounted Cash Flow ($000)
0 (12) −12.00
1 6 6
≈ 5.45
1.10
2 5 5
2
≈ 4.13
1.10
3 3 3
3
≈ 2.25
1.10
4 2 2
4
≈1.37
1.10
5 5 5
5
≈ 3.10
1.10
Total NPV for Location B:
−12+5.45+ 4.13+2.25+1.37+3.10=$ 4.30
Conclusion
Location A NPV: $5,000
Location B NPV: $4,300
Answer D is correct because Location A has a higher NPV.
Example:
Discounting cash flows
1 Calculate the present-day values of the following cash flows:
a $10 000 expected in four years’ time at a prevailing rate of interest of 10%
b $2 000 expected in six years’ time at a prevailing rate of interest of 16%
c $6 000 expected in one year’s time at a prevailing rate of interest of 20%.
2 The following net cash flows have been forecast by a manufacturer for the purchase of a
labour saving machine:
Year Net cash flows ($)
0 (15 000)
1 8 000
2 10 000
3 5 000
4 5 000
a Calculate the simple payback period.
b Discount all cash flows at a discount rate of 10%.
c Calculate the NPV.
1. Calculate Present-Day Values
a) $10,000 in 4 years at 10%
10,000
PV =
¿¿
b) $2,000 in 6 years at 16%
2,000
PV =
¿¿
c) $6,000 in 1 year at 20%
6,000
PV =
¿¿
2. Labour-Saving Machine Analysis
a) Simple Payback Period
Year Net Cash Flow ($) Cumulative Cash Flow ($)
0 -15,000 -15,000
1 8,000 -7,000
2 10,000 3,000
Payback occurs in Year 2.
7,000
Payback =1+ =1.7
10,000
b) Discounted Cash flow @ 10%
Year Net Cash Flow ($) Discounted Cash Flow ($)
0 -15,000 −15,000
1 8,000 8,000
=7,272.73
1.10
2 10,000 10,000
2
=8,264.46
1.10
3 5,000 5,000
3
=3,756.57
1.10
4 5,000 5,000
4
=3,415.07
1.10
c) Net Present Value (NPV)
NPV=−15,000+ 7,272.73+8,264.46+3,756.57+ 3,415.07=$ 7,708.83
Positive NPV
Part 1: Present Values
a) $6,830.13
b) $821.04
c) $5,000
Part 2: Machine Investment
a) Payback: 1.7 years
b) Discounted Cash Flows:
o Year 1: $7,272.73
o Year 2: $8,264.46
o Year 3: $3,756.57
o Year 4: $3,415.07
c) NPV: $7,708.83 (profitable investment).
Investment Appraisal Decisions
Quantitative Results and Impact
• Quantitative appraisal methods focus on capital return speed and profit.
• Investment criteria include payback within three years, accounting rate of return of at least
15%, and net present value of at least 15% of the original capital invested.
Qualitative Factors and Their Impact
• Environmental pressure groups may force businesses to consider sensitive developments.
• Local planning officers must weigh costs and benefits of planned undertakings.
• Business objectives may be resisted if customer service is threatened.
• Workforce impact may be reversed if automated machinery replacements are implemented.
• Managers' risk acceptance varies.
