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Corporate Finance ­FIN 622
VU
Lesson 10
METHODS OF PROJECT EVALUATIONS
The following topics will be discussed in this hand out.
Methods of Project evaluations:
Internal Rate of Return ­ IRR
Associated topics to be covered:
NPV vs. IRR
Criticism of IRR
The Internal Rate of Return (IRR)
The IRR is the discount rate at which the NPV for a project equals zero. This rate means that the present
value of the cash inflows for the project would equal the present value of its outflows.
The IRR is the break-even discount rate.
The IRR is found by trial and error.
Where r = IRR
IRR of an annuity:
Where:
Q (n, r) is the discount factor
Io is the initial outlay
C is the uniform annual receipt (C1 = C2 =....= Cn).
Example:
What is the IRR of an equal annual income of $20 per annum which accrues for 7 years and costs $120?
=6
Net present value vs. Internal rate of return:
Independent vs. dependent projects
NPV and IRR methods are closely related because:
i)
both are time-adjusted measures of profitability, and
ii)
Their mathematical formulas are almost identical.
So, which method leads to an optimal decision: IRR or NPV?
a) NPV vs. IRR: Independent projects
Independent project: Selecting one project does not preclude the choosing of the other.
With conventional cash flows (-|+|+) no conflict in decision arises; in this case both NPV and IRR lead to
the same accept/reject decisions.
Mathematical proof: for a project to be acceptable, the NPV must be positive, i.e.
Similarly for the same project to be acceptable:
Where R is the IRR.
Since the numerators Ct are identical and positive in both instances:
* Implicitly/intuitively R must be greater than k (R > k);
* If NPV = 0 then R = k: the company is indifferent to such a project;
* Hence, IRR and NPV lead to the same decision in this case.
b) NPV vs. IRR: Dependent projects
NPV clashes with IRR where mutually exclusive projects exist.
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Corporate Finance ­FIN 622
VU
Example:
Agritex is considering building either a one-storey (Project A) or five-storey (Project B) block of offices on a
prime site. The following information is available:
Initial Investment Outlay Net Inflow at the Year End
Project A -9,500
11,500
Project B -15,000
18,000
Assume k = 10%, which project should Agritex undertake?
= $954.55
= $1,363.64
Both projects are of one-year duration:
IRRA:
$11,500 = $9,500 (1 +RA)
= 1.21-1
Therefore IRRA = 21%
IRRB:
$18,000 = $15,000(1 + RB)
= 1.2-1
Therefore IRRB = 20%
Decision:
Assuming that k = 10%, both projects are acceptable because:
NPVA and NPVB are both positive
IRRA > k AND IRRB > k
Which project is a "better option" for Agritex?
If we use the NPV method:
NPVB ($1,363.64) > NPVA ($954.55): Agritex should choose Project B.
If we use the IRR method:
IRRA (21%) > IRRB (20%): Agritex should choose Project A.
Differences in the scale of investment
NPV and IRR may give conflicting decisions where projects differ in their scale of investment. Example:
Years
0
1
2
3
Project A -2,500 1,500 1,500 1,500
Project B -14,000 7,000 7,000 7,000
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Corporate Finance ­FIN 622
VU
Assume k= 10%.
NPVA = $1,500 x PVFA at 10% for 3 years
= $1,500 x 2.487
= $3,730.50 - $2,500.00
= $1,230.50.
NPVB == $7,000 x PVFA at 10% for 3 years
= $7,000 x 2.487
= $17,409 - $14,000
= $3,409.00.
IRRA =
= 1.67.
Therefore IRRA = 36% (from the tables)
IRRB =
= 2.0
Therefore IRRB = 21%
Decision:
Conflicting, as:
·  NPV prefers B to A
·  IRR prefers A to B
NPV
IRR
Project A $ 3,730.50 36%
Project B $17,400.00 21%
To show why:
i)
The NPV prefers B, the larger project, for a discount rate below 20%
ii)
The NPV is superior to the IRR
a) Use the incremental cash flow approach, "B minus A" approach
b) Choosing project B is tantamount to choosing a hypothetical project "B minus A".
0
1
2
3
Project B
- 14,000 7,000 7,000 7,000
Project A
- 2,500 1,500 1,500 1,500
"B minus A" - 11,500 5,500 5,500 5,500
IRR"B Minus A"
= 2.09
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Corporate Finance ­FIN 622
VU
= 20%
c) Choosing B is equivalent to: A + (B - A) = B
d) Choosing the bigger project B means choosing the smaller project A plus an additional outlay of
$11,500 of which $5,500 will be realized each year for the next 3 years.
e) The IRR"B minus A" on the incremental cash flow is 20%.
f)  Given k of 10%, this is a profitable opportunity, therefore must be accepted.
g) But, if k were greater than the IRR (20%) on the incremental CF, then reject project.
h) At the point of intersection,
NPVA = NPVB or NPVA - NPVB = 0, i.e. indifferent to projects A and B.
i)  If k = 20% (IRR of "B - A") the company should accept project A.
This justifies the use of NPV criterion.
Advantage of NPV:
It ensures that the firm reaches an optimal scale of investment.
Disadvantage of IRR:
·  It expresses the return in a percentage form rather than in terms of absolute dollar returns, e.g. the
IRR will prefer 500% of $1 to 20% return on $100. However, most companies set their goals in
absolute terms and not in % terms, e.g. target sales figure of $2.5 million.
The timing of the cash flow
The IRR may give conflicting decisions where the timing of cash flows varies between the 2 projects.
Note that initial outlay Io is the same.
0
1
2
Project A
- 100 20
125.00
Project B
- 100 100
31.25
"A minus B" 0
- 80 88.15
Assume k = 10%
NPV IRR
Project A
17.3 20.0%
Project B
16.7 25.0%
"A minus B" 0.6
10.9%
IRR prefers B to A even though both projects have identical initial outlays. So, the decision is to accept A,
that is B + (A - B) = A.
The horizon problem
NPV and IRR rankings are contradictory. Project A earns $120 at the end of the first year while project B
earns $174 at the end of the fourth year.
0
1
2
3
4
Project A
-100 120 -
-
-
Project B
-100 -
-
-
174
Assume k = 10%
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Corporate Finance ­FIN 622
VU
NPV IRR
Project A 9
20%
Project B 19
15%
Decision:
NPV prefers B to A.
IRR prefers A to B.
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Table of Contents:
  1. INTRODUCTION TO SUBJECT
  2. COMPARISON OF FINANCIAL STATEMENTS
  3. TIME VALUE OF MONEY
  4. Discounted Cash Flow, Effective Annual Interest Bond Valuation - introduction
  5. Features of Bond, Coupon Interest, Face value, Coupon rate, Duration or maturity date
  6. TERM STRUCTURE OF INTEREST RATES
  7. COMMON STOCK VALUATION
  8. Capital Budgeting Definition and Process
  9. METHODS OF PROJECT EVALUATIONS, Net present value, Weighted Average Cost of Capital
  10. METHODS OF PROJECT EVALUATIONS 2
  11. METHODS OF PROJECT EVALUATIONS 3
  12. ADVANCE EVALUATION METHODS: Sensitivity analysis, Profitability analysis, Break even accounting, Break even - economic
  13. Economic Break Even, Operating Leverage, Capital Rationing, Hard & Soft Rationing, Single & Multi Period Rationing
  14. Single period, Multi-period capital rationing, Linear programming
  15. Risk and Uncertainty, Measuring risk, Variability of return–Historical Return, Variance of return, Standard Deviation
  16. Portfolio and Diversification, Portfolio and Variance, Risk–Systematic & Unsystematic, Beta – Measure of systematic risk, Aggressive & defensive stocks
  17. Security Market Line, Capital Asset Pricing Model – CAPM Calculating Over, Under valued stocks
  18. Cost of Capital & Capital Structure, Components of Capital, Cost of Equity, Estimating g or growth rate, Dividend growth model, Cost of Debt, Bonds, Cost of Preferred Stocks
  19. Venture Capital, Cost of Debt & Bond, Weighted average cost of debt, Tax and cost of debt, Cost of Loans & Leases, Overall cost of capital – WACC, WACC & Capital Budgeting
  20. When to use WACC, Pure Play, Capital Structure and Financial Leverage
  21. Home made leverage, Modigliani & Miller Model, How WACC remains constant, Business & Financial Risk, M & M model with taxes
  22. Problems associated with high gearing, Bankruptcy costs, Optimal capital structure, Dividend policy
  23. Dividend and value of firm, Dividend relevance, Residual dividend policy, Financial planning process and control
  24. Budgeting process, Purpose, functions of budgets, Cash budgets–Preparation & interpretation
  25. Cash flow statement Direct method Indirect method, Working capital management, Cash and operating cycle
  26. Working capital management, Risk, Profitability and Liquidity - Working capital policies, Conservative, Aggressive, Moderate
  27. Classification of working capital, Current Assets Financing – Hedging approach, Short term Vs long term financing
  28. Overtrading – Indications & remedies, Cash management, Motives for Cash holding, Cash flow problems and remedies, Investing surplus cash
  29. Miller-Orr Model of cash management, Inventory management, Inventory costs, Economic order quantity, Reorder level, Discounts and EOQ
  30. Inventory cost – Stock out cost, Economic Order Point, Just in time (JIT), Debtors Management, Credit Control Policy
  31. Cash discounts, Cost of discount, Shortening average collection period, Credit instrument, Analyzing credit policy, Revenue effect, Cost effect, Cost of debt o Probability of default
  32. Effects of discounts–Not effecting volume, Extension of credit, Factoring, Management of creditors, Mergers & Acquisitions
  33. Synergies, Types of mergers, Why mergers fail, Merger process, Acquisition consideration
  34. Acquisition Consideration, Valuation of shares
  35. Assets Based Share Valuations, Hybrid Valuation methods, Procedure for public, private takeover
  36. Corporate Restructuring, Divestment, Purpose of divestment, Buyouts, Types of buyouts, Financial distress
  37. Sources of financial distress, Effects of financial distress, Reorganization
  38. Currency Risks, Transaction exposure, Translation exposure, Economic exposure
  39. Future payment situation – hedging, Currency futures – features, CF – future payment in FCY
  40. CF–future receipt in FCY, Forward contract vs. currency futures, Interest rate risk, Hedging against interest rate, Forward rate agreements, Decision rule
  41. Interest rate future, Prices in futures, Hedging–short term interest rate (STIR), Scenario–Borrowing in ST and risk of rising interest, Scenario–deposit and risk of lowering interest rates on deposits, Options and Swaps, Features of opti
  42. FOREIGN EXCHANGE MARKET’S OPTIONS
  43. Calculating financial benefit–Interest rate Option, Interest rate caps and floor, Swaps, Interest rate swaps, Currency swaps
  44. Exchange rate determination, Purchasing power parity theory, PPP model, International fisher effect, Exchange rate system, Fixed, Floating
  45. FOREIGN INVESTMENT: Motives, International operations, Export, Branch, Subsidiary, Joint venture, Licensing agreements, Political risk