University of the Aegean School of Business Studies
University of the Aegean School of Business Studies Shipping, Trade & Transport Dpt. MA Shipping, Trade & Transport e-course Advanced Corporate Finance THEODORE SYRIOPOULOS Professor of Finance Department of Shipping, Trade & Transport School of Business Studies UNIVERSITY OF THE AEGEAN 2 A, Korai street, 82100 Chios, Greece, Tel. : 22710 35 861, 6944 911 787 e-mail: tsiriop@aegean. gr http: //www. stt. aegean. gr/Syriopoulos. En. asp ADVFIN
INVESTMENT DECISIONS TOOLS
Background n A Good investment decision n …raises current market value of firm’s equity thereby creating value for firm’s owners…. 6
Background n A Capital budgeting involves n comparing amount of cash spent on an investment today… with cash inflows expected from it in the future 7
Background n Discounting is the mechanism used to account for. . the time value of money n converts future cash flows into today’s equivalent value (called present value or discounted value) 8
Background n Apart from the timing issue, there is also risk associated with future cash flows n probability that cash flows to be realized in future may not be the expected ones 9
Time Value of Money 10
Time Value of Money § assume we consider money is a ‘commodity’ what is the PRICE of MONEY ? ? ? n 1 dollar TODAY ≠ 1 dollar TOMORROW ! n only possible to compare or combine values at… SAME POINT IN TIME ! 11
Time Value of Money Compounding the FUTURE value of a present amount of money PV FV Discounting the PRESENT value of a future amount of money FV PV 12
Time Value of Money n receiving $1 today is worth more than $1 in the future n n this is due to opportunity costs opportunity cost of receiving $1 in the future is the interest we could have earned if we had received the $1 sooner Today Future 13
Compounding n compounding translate $1 today into its equivalent in the future Today Future ? 14
Discounting • discounting translate $1 in the future into its equivalent today Today Future ? 15
Present Value vs. Future Value n When express the value in terms of dollars today Present Value (PV) of the investment n When express it in terms of dollars in the future Future Value (FV) of the investment. 16
Basic Rules on Time Value of Money n Financial decisions often require combining cash flows or comparing values n 3 rules govern these processes 17
Future Value & Compounding General equation to find Future Value : where: FVn = PV = k = n = future value of investment at the end of period n original principal (P 0) or present value the rate of interest period, which is often a year the number of periods 18
Example: Future Value of € 100 You leave € 100 invested in the bank savings account at 10% interest for 5 years. How much would you have in the bank at the end of 5 years? 19
Example on Compounding n Problem n What is the Future Value in 3 -years of the following cash flows if compounding rate = 5%? ? 20
Example on Compounding n n Solution or 21
Present Value & Discounting General equation to find Present Value Discount Factor 22
Present Value & Discounting Suppose you are interested in buying a BMW 330 Sports Coupe a year from now. You estimate that the car will cost € 40 000. If your local bank pays 5% interest on savings deposits, how much will you need to save to buy the car? 23
Present Value & Discounting • The further in the future the money will be received, the less it is worth today • The higher the discount rate, the lower the present value of money 24
The Capital Investment Process 25
The Capital Investment Process n Capital investment decision (capital budgeting decision, capital expenditure decision) involves four steps: n identification n evaluation n selection n implementation n audit 26
The Capital Investment Process n Investment proposals are also often classified according to the difficulty in estimating the key valuation parameters n required investments n replacement investments n expansion investments n diversification investments 27
The Capital Investment Process 28
Net Present Value Rule for Value Creating Investments
A One-Period Investment Problem: n How much should we invest now in a savings account with a 6% interest rate…. if we want to receive $11, 000 in 1 -year? 30
A One-Period Investment n Answer: $ 11. 000 x (1/(1+0, 06)1) = $11, 000 x 0. 9434 = $10, 377 discount RATE =k discount FACTOR = 1/(1 + k)n Inversely: $10, 377 + $10, 377 x 6% = $11, 000 or 11, 000 1. 06 = $10, 377 31
A One-Period Investment n at 6%. . . we should be indifferent between… $10, 377 vs. at 6%. . . now $11, 000 in 1 -year the two cash flows are equivalent 32
A One-Period Investment n The difference between… Present Value of future cash flow & initial outlay is called the Net Present Value (NPV) 33
Cash-Flow Time Line : 1 -period project Timeline: linear representation of the timing of potential cash flows Drawing timeline of cash flows helps visualize the financial problem CF 1 = interest rate: 10% CF 0 = Case: 1 - investing $10, 000 in a parcel of land now; expectation: it could be sold for $11, 000 next year; expected return on this investment = 10% - if more than 10% can be earned on a comparable or alternative investment, we should NOT buy the land. 34
Time Line for Multiple-Period Investments The General Case 2 illustrates the case of a multiple-period investment & presents the general NPV formula 35
Valuing a Stream of Cash Flows… Present Value of a Cash Flow Stream: 36
Decomposing the NPV Rule 37
Decomposing the NPV Rule 38
NPV Rule n ACCEPT investment if: NPV > 0 n REJECT investment if: NPV < 0 n INDIFFERENT investment if: NPV = 0 39
Case Study Sunlight Manufacturing Company 40
Applying NPV Rule to a capital investment decision n NPV application - industrial investment project: n Case: Sunlight Manufacturing Company considers adding a new product to its existing line • assumption: inputs have already been estimated (i. e. investment cash flows & cost of capital) 41
Case Study: Sunlight Manufacturing Company Investment Project: adding a new product to existing line 9 42
Calculation of PV for Sunlight Manufacturing Company Case study: Sunlight Manufacturing Company considers adding a new product to its existing line : Initial Capital Outflow = $ 10, 000 Investment horizon = 5 - years Cash-flow stream: CF 1 = $ 8, 320, 000 CF 2 = $ 8, 220, 000 CF 3 = $ 6, 920, 000 CF 4 = $ 5, 540, 000 CF 5 = $ 4, 660, 000 discount rate = 9% 43
Calculation of PV for Sunlight Manufacturing Company 1 Present value of CF 1 = $8, 320, 000 ×(1 + 0. 09)1 = $8, 320, 000 × 0. 9174 = $7, 633, 028 1 Present value of CF 2 = $8, 220, 000 × 0. 8417 = $6, 918, 610 (1 + 0. 09)2 1 Present value of CF 3 = $6, 920, 000 × 0. 7722 = $5, 343, 510 (1 + 0. 09)3 1 Present value of CF 4 = $5, 540, 000 × 0. 7084 = $3, 924, 675 (1 + 0. 09)4 1 Present value of CF 5 = $4, 660, 000 × 0. 6499 = $3, 028, 680 5 (1 + 0. 09) project cash-flows discount factor Total Present Value at 9% $26, 848, 503 discount rate Net Present Value (NPV) cumulative present value $16, 848, 503 Initial Ouflow CF 0 = - $ 10, 000 44
NPV in Mutually Exclusive Projects- example 45
NPV Mutually Exclusive Projects- example 46
Why NPV rule is a Good Investment yardstick n NPV rule is a good investment rule because: n measures value creation n reflects timing of project’s cash flows n takes into account project risk n additivity property 47
Adjustment for Risk of project’s cash flows n Risk adjustment is made through the project’s discount rate n because investors are risk averse… they will require a higher return from riskier investments 48
NPV vs. discount rate NPV inverse relationship by discounting the project’ cash flows at a higher rate the project’s NPV will decrease NPV 1 NPV 2 r 1 r 2 > r 1 r 2 discount rate NPV 2 < NPV 1 49
Cash Flows for 2 investments with CF 0 = $1 mln. k = 0. 12 Investment C - k = 0. 15 Investment D END OF YEAR INVESTMENT C INVESTMENT D 1 CF 1 = $300, 000 2 CF 2 = 300, 000 3 CF 3 = 300, 000 4 CF 4 = 300, 000 5 CF 5 = 300, 000 $1, 500, 000 Total Cash Flows 2 investments - same initial cash outlay - same cumulative cash flows - same cash flow profile BUT: different cost of capital 50
PV of cash flows for Investment C END OF YEAR INVESTMENT C OPPORTUNITY COST OF CAPITAL = 12% 1 PV($300, 000) = $300, 000 × 0. 8929 = $267, 857 2 PV($300, 000) = 300, 000 × 0. 7972 = 239, 158 3 PV($300, 000) = 300, 000 × 0. 7118 = 213, 534 4 PV($300, 000) = 300, 000 × 0. 6355 = 190, 655 5 PV($300, 000) = 300, 000 × 0. 5674 = 170, 228 Total Present Values $1, 081, 432 51
PV of cash flows for Investment D END OF YEAR INVESTMENT D OPPORTUNITY COST OF CAPITAL = 15% 1 PV($300, 000) = $300, 000 × 0. 8696 = $260, 869 2 PV($300, 000) = 300, 000 × 0. 7561 = 226, 843 3 PV($300, 000) = 300, 000 × 0. 6575 = 197, 255 4 PV($300, 000) = 300, 000 × 0. 5718 = 171, 526 5 PV($300, 000) = 300, 000 × 0. 4972 = Total Present Values 149, 153 $1, 005, 646 52
Limitations of NPV criterion n NPV criterion can be adjusted for some situations n it ignores the opportunities to make changes to projects as time passes and more information becomes available n NPV rule is a take-it-or-live-it rule 53
Alternatives to the NPV Rule
Background n Four alternatives to NPV method: n ordinary payback period n discounted payback period n internal rate of return n profitability index 55
Background n Output: n 4 four alternatives to NPV method & how to calculate them n how to apply alternative rules to screen investment proposals n major shortcomings of alternative rules n why these rules are still used even though they are not as reliable to NPV rule 56
Projects examined n 6 different investment projects • investment time-horizon: • initial outlay: n 5 -year $ 1. 0 mln. each alternative is evaluated as to whether it satisfies the conditions of a good investment decision: • does it adjust for timing of cash flows? • does it take risk into consideration? • does it maximize firm’s equity value? 57
Expected Cash-Flow Streams & Cost of Capital: Investments A & B INVESTMENTS A & B END OF YEAR INVESTMENT A INVESTMENT B 1 $600, 000 $100, 000 2 300, 000 3 100, 000 600, 000 4 200, 000 5 300, 000 $1, 500, 000 10% $191, 399 $112, 511 Total Cash Flows Cost of Capital NPV 58
Expected Cash-Flow Streams & Cost of Capital: Investments C & D INVESTMENTS C & D END OF YEAR INVESTMENT C INVESTMENT D 1 $250, 000 2 250, 000 3 250, 000 4 250, 000 5 250, 000 $1, 250, 000 5% 10% $82, 369 –$52, 303 Total Cash Flows Cost of Capital NPV 59
Expected Cash-Flow Streams & Cost of Capital: Investments E & F INVESTMENTS E & F END OF YEAR INVESTMENT E INVESTMENT F 1 $325, 000 $ 325, 000 2 325, 000 3 325, 000 4 325, 000 5 325, 000 975, 000 $1, 625, 000 $2, 275, 000 10% $232, 006 $635, 605 Total Cash Flows Cost of Capital NPV 60
The Payback Period 61
The Payback Period n a project’s payback period is… the number of periods required for sum of project’s cash flows to equal its initial cash outlay n usually measured in years 62
Expected & Cumulative Cash Flows for Investment A Project A: Initial outlay = $1, 000; investment horizon = 5 years END OF YEAR A’s cash outlay was $1, 000; this amount is fully recovered at the end of year 3 EXPECTED CASH FLOWS CUMULATIVE CASH FLOWS 1 $600, 000 $ 600, 000 2 300, 000 900, 000 3 cut-off period 4 100, 000 1, 000 200, 000 1, 200, 000 5 300, 000 1, 500, 000 63
Payback Period for 6 Investments INVESTMENT Payback period (in years) A B C D E 3. 00 4. 00 3. 08 F 3. 08 64
The Payback Period Rule According to this rule: n a project is acceptable if its payback period is shorter than or equal to the cutoff period n for mutually exclusive projects, the one with shortest payback period should be accepted 65
Comparison of 2 Investments with same NPV & different payback periods END OF YEAR Now INVESTMENT A INVESTMENT G –$1, 000, 000 1 600, 000 2 300, 000 200, 000 3 100, 000 300, 000 4 200, 000 300, 000 5 300, 000 666, 740 NPV (AT 10%) $191, 399 PAYBACK PERIOD 3 YEARS 4 YEARS 66
The Discounted Payback Period 67
The Discounted Payback Period or Economic Payback Period n Number of periods required for the sum of present values of project’s expected cash flows to equal its initial cash outlay n Compared to ordinary payback periods… • discounted payback periods are longer • may result in a different project ranking 68
Discounted Payback Period Calculations for Investment A Project A: END OF YEAR Initial cash outflow = $1, 000; investment horizon = 5 years EXPECTED CASH FLOWS DISCOUNT FACTOR AT 10% PRESENT VALUE CUMULATIVE PRESENT VALUE OF CASH FLOWS 1 $600, 000 0. 9091 $545, 455 2 300, 000 0. 8264 247, 934 793, 389 3 100, 000 0. 7513 75, 131 868, 520 4 200, 000 0. 6830 136, 603 1, 005, 123 5 300, 000 0. 6209 186, 276 1, 191, 399 Cut-off period = 4 th year 69
Discounted Payback Periods for 6 Investments INVESTMENT Discounted payback period (in years) A B 3. 96 4. 40 C D E 4. 58 >5 3. 86 F 3. 86 70
The Discounted Payback Period Rule n the discounted payback period rule says that a project is acceptable n n if discounted payback period is shorter or equal to cutoff period among several projects, the one with the shortest period should be accepted 71
The Internal Rate of Return (IRR) 72
Internal Rate of Return (IRR) n A project's internal rate of return (IRR) is the discount rate that makes project NPV = 0 n An investment’s IRR summarizes its expected cash flow stream with a single rate of return - called internal rate 73
IRR for 6 Investments INVESTMENT IRR A B C 19. 05% 13. 92% 7. 93% D E F 7. 93% 18. 72% 28. 52% 74
The IRR Rule n n Based on IRR, a project should be: ACCEPT if: IRR > its cost of capital REJECT if: IRR < its cost of capital if a project’s IRR < its cost of capital the project does not earn its cost of capital should be rejected 75
The IRR Rule n adjustment for risk? • IRR rule accounts for investments risk indirectly by comparing investment’s IRR with its cost of capital • IRR of C (7. 93%) > cost of capital (5%) should be accepted • IRR of D (7. 93%) < cost of capital (10%) should be rejected 76
The IRR Rule n maximization of firm’s equity value? • NPV profile shows an inverse relationship between NPV vs. discount rate 77
NPV vs. discount rate inverse relationship NPV by discounting the project’ cash flows at a higher rate the project’s NPV will decrease NPV 1 NPV 2 r 1 r 2 > r 1 r 2 discount rate NPV 2 < NPV 1 78
NPV of Investment E for various discount rates DISCOUNT RATE NPV(E) 0% 5% 10% $625, 000 $407, 080 $232, 006 15% $89, 450 20% 25% 30% –$28, 051–$125, 984 –$208, 440 79
The NPV Profile of Investment E for discount rates < 18. 72%, project's NPV > 0; for discount rates > 18. 72%, project’s NPV < 0 • according to IRR rule, E should be accepted if IRR > its cost of capital • E should be rejected if IRR < its cost of capital • when NPV >0, IRR > cost of capital; • when NPV < 0 I RR < cost of capital 80
Why do managers prefer IRR to NPV Rule? n IRR calculation requires only a single input (the cash flow stream) n BUT: applying IRR rule still requires input - cost of capital n most managers find IRR easier to understand 81
Why do managers prefer IRR to NPV Rule? n Advice: n compute both a project’s IRR & NPV n n If they agree If they disagree use IRR rule trust NPV rule 82
The Profitability Index (PI) 83
The Profitability Index (PI) n The profitability index n benefit-to-cost ratio equal to ratio of n present value of a project’s expected cash flows to its initial cash outlay 84
Cash Flows, PVs & NPVs 3 -Investments of unequal size with k= 0. 10 INVESTMENT E INVESTMENT F INVESTMENT G (1) Initial cash outlay (CF 0) Year-one cash flow (CF 1) Year-two cash flow (CF 2) $1, 000 800, 000 500, 000 $500, 000 200, 000 510, 000 $500, 000 100, 000 700, 000 (2) Present value of CF 1 and CF 2 at 10% $1, 140, 496 $603, 306 $669, 421 Net present value = (2) – (1) $140, 496 $103, 306 $169, 421 85
Profitability Indexes 3 -Investments of unequal size INVESTMENT E INVESTMENT F (1) Initial cash outlay $1, 000 $500, 000 (2) Present value of future cash-flow stream $1, 140, 496 $603, 306 $669, 421 (3) Profitability index = (2) (1) $1, 140, 496 $1, 000 = 1. 14 $603, 306 $500, 000 = 1. 21 INVESTMENT G $669, 421 $500, 000 = 1. 34 Pr. Ix. G > Pr. Ix. F > Pr. Ix. E 86
Profitability Indexes for 6 Investments INVESTMENT Profitability index A B C D E 1. 19 1. 11 1. 08 0. 95 1. 23 F 1. 64 87
Comparison of 2 mutually exclusive Investments with different initial cash outlays & expected cash flows END OF YEAR Now INVESTMENT A INVESTMENT K –$1, 000 –$2, 000 1 600, 000 100, 000 2 300, 000 3 100, 000 600, 000 4 200, 000 5 300, 000 2, 100, 000 NPV (at 10%) Profitability Index $191, 399 $230, 169 1. 12 K has same useful life (5 years), same cost of capital (10%) as A, but requires twice the initial cash outlay & has a different cashflow stream A has a higher profitability index than K-thus, the PI rule is not consistent with the firm’s value maximization goal 88
Use of Profitability Index Rule n PI is a relative measure of an investment’s value n NPV is an absolute measure n Thus, the PI rule can be a useful substitute for NPV rule when presenting a project’s benefits per dollar of investment 89
The Profitability Index Rule n According to PI rule a project should be: ACCEPT if PI >1 REJECT if PI < 1 90
Comparison of Investment choice methods Investment Decision Criterion Appraisal Method ACCEPT REJECT NPV IRR PI PBP DPBP >0 <0 >κ <κ >1 <1 > cut-off period < cut-off period > dsc cut-off period < dsc cut-off period 91
Capital-Budgeting Techniques Used by Business Firms 92
End of Session 93
- Slides: 93