1 ĐẠI HỌC HOA SEN Khoa Kinh tế Thương mại
Oct 30, 2014
4
References
• Fundamentals of Corporate Finance, Brealey et al., McGraw Hill, 5th edition, USA, 2007.
• Foundation of Financial Management, Block & Hirt, McGraw Hill, 12th edition,USA, 2008.
• Other relevant materials.
5
Chapter 5: NET PRESENT VALUE and OTHER INVESTMENT
CRITERIA
• Main Contents:
1. Net Present Value
2. Other Investment Criteria
3. Examples of mutually exclusive projects
4. Capital rationing
5. A last look
6
I. NET PRESENT VALUE
•An investor intends to invest a project which has a following cash flow:
01
-$350,000
$400,000
??? Should he invest in this project ? Assuming that he could invest in a 1 year-US Treasury note of 7%
…calculate NPV NPV = PV of cash flow – required investment
•PV = $373,832 •NPV = $23,832 ACCEPT the project
7
I. NET PRESENT VALUE (cont’d)
1 year-US Treasury note of 7%
Opportunity cost of capital
�NPV – present value of cash flows minus required investment
8
I. NET PRESENT VALUE (cont’d)
�Risk and Present Value
… the investment is more risky than investing a 1 year-treasury note of 7%
…the investment is as risky as investing a stock with rate of return of 12%
01
-$350,000
$400,000
•NPV with rate of return of 12% = $7,143 < $23,832
A risky dollar is worth less than a safe one
10
I. NET PRESENT VALUE (cont’d)
�Value long-lived projects
… the investment with an opportunity cost of capital of 7% and has a cash flow:
01
-$350,000
$16,000
•NPV = ?
2
$16,000
3
$466,000
12
I. NET PRESENT VALUE (cont’d)
�Value long-lived projects (cont’d)
In case that the investor decides to sell this project by selling 1,000 stocks
What is the price of one stock ?
•Price per share: $409.3
01
-$350,000
$16
2
$16
3
$466
•Net gain: ~ $59,300
13
I. NET PRESENT VALUE (cont’d)
�Using NPV rule to choose among projects
Project A and B are Mutual exclusive projects
Project A
What would I
choose ?
Project B
Select the project whose NPV is higher!!
15
II. OTHER INVESTMENT CRITERIA
…time until cash flows recover the initial investment in the project
�Payback period
Payback rule
…a project should be accepted if its payback period is less than a specified cutoff period
WHAT IF ?
A or B ??NPV < 0, the payback period = 1NPV > 0, the payback period = 2
NPV > 0, the payback period = 2
Project B
A or B ??NPV > 0, the payback period = 1
Select…Project A
16
II. OTHER INVESTMENT CRITERIA
Which project should you choose if you don’t care NPV ?
�Payback period (cont’d)
…calculate Discounted Payback
17
II. OTHER INVESTMENT CRITERIA
�Payback period (cont’d)
•Discounted Payback
How long must the project last in order to offer a positive NPV ?
Steps to calculate Discounted Payback
1 Calculate the PV of the cash flow
2 Add each PV up to be equal with initial investment
18
II. OTHER INVESTMENT CRITERIA
�Internal rate of return (IRR)
…selecting project whose IRR is higher than the opportunity cost of capital
??? How to calculate the IRR ?
Setting NPV = 0 and calculate the IRR
IRR is the discount rate at which NPV = 0
19
IRR > opportunity cost of capital
II. OTHER INVESTMENT CRITERIA
�Internal rate of return (IRR)
NPV is POSITIVE
IRR < opportunity cost of capital
NPV is NEGATIVE
21
II. OTHER INVESTMENT CRITERIA
�Internal rate of return (IRR)
Supposing that you have a project with the following relevant cash flow:
…calculate IRR
22
II. OTHER INVESTMENT CRITERIA
�Some pitfalls with the IRR
is not the opportunity cost
is the profitability of a project
23
II. OTHER INVESTMENT CRITERIA
�Some pitfalls with the IRR
•Pitfall 1: Lending or Borrowing
???D and E have the same attraction ?
Not exactly !!!!!
D
E What received today is repaid more and more tomorrow
You are in borrowing with high interest rate
What paid today is received more and more tomorrow
You are in lending with high interest rate
24
II. OTHER INVESTMENT CRITERIA
�Some pitfalls with the IRR (cont’d)
•Pitfall 2: Multiple Rate of Return
-$40+$15+$15+$15+$15-$22
C5C4C3C2C1C0
Cash flow
…the project has two IRRs
25
II. OTHER INVESTMENT CRITERIA
�Some pitfalls with the IRR (cont’d)
•Pitfall 2: Multiple Rate of Return (cont’d)
Solution Modified IRR
1 Combining last two cash flows into one PV of year 4
2 If the PV is negative, combining last three cash flows into one PV of year 3
�Steps to calculate modified IRR (applied for a 4-year project):
3 If the PV is still negative, combining last four cash flows into one PV of year 2and so on
4If the PV is positive, making a new modified cash flow and calculate the modified IRR
26
II. OTHER INVESTMENT CRITERIA
�Some pitfalls with the IRR (cont’d)
•Pitfall 2: Multiple Rate of Return (cont’d)
IRR = 12.53%0)1(98.10
11522 2 =
+
+
+
+−
IRRIRR
r = 10%
27
II. OTHER INVESTMENT CRITERIA
�Some pitfalls with the IRR (cont’d)
•Pitfall 3: Mutually exclusive projects
…the higher IRR does not mean the higher NPV
29
II. OTHER INVESTMENT CRITERIA
�Some pitfalls with the IRR (cont’d)
•Pitfall 4: Mutually exclusive projects involving different outlays
Misranking as comparing projects with the same lives but different outlays
IRR mistakenly favor small projects with high rates of return but low NPVs
30
III. EXAMPLES OF MUTUALLY EXCLUSIVE PROJECTS
Timing decision
Long and short lived equipment
Replacement decision
31
III. EXAMPLES OF MUTUALLY EXCLUSIVE PROJECTS (cont’d)
When should the company invest in new computer system ?
�Investment timing
NPV >0, invest in new computer system now,
madam ?
Not now. Next year’s computer will be
cheaper!!!
•Several years later, the project cannot be launched, the business of company ……
Not now, next year…
Not now, next year…
Financial Manager
32
III. EXAMPLES OF MUTUALLY EXCLUSIVE PROJECTS (cont’d)
�Investment timing (cont’d)
•A new computer system can last for 4 years
…choosing an investment time that results in the highest NPV today
34
III. EXAMPLES OF MUTUALLY EXCLUSIVE PROJECTS (cont’d)
�Long versus short lived equipment
…selecting two machines with the same function:
Which machine should Samsung choose ?
…calculating the Equivalent Annual Annuity
…and select the machine that has the lowest Equivalent Annual Annuity
…the cash flow per period with the same PV as the cost of buying and operating a machine
35
III. EXAMPLES OF MUTUALLY EXCLUSIVE PROJECTS (cont’d)
�Long versus short lived equipment (cont’d)
…selecting two machines with the same function:
Machine Fshould be selected
36
III. EXAMPLES OF MUTUALLY EXCLUSIVE PROJECTS (cont’d)
�Replacing an Old Machine
•…will be last in 2 more years
•…cost $12,000 per year to operate
CURRENT MOTO
•…will be last in 5 years
•…cost $8,000 per year to operate
NEW MOTO
Which moto should you choose ?Higher than 12
Continue using the current moto
38
IV. CAPITAL RATIONING
�Soft rationing
Capital rationing
Limit set on the amount of funds available for investment
•…constrains on spending
•…under certain circumstances can be violated
•…or even viewed as constituting targets rather than absolute limits
39
IV. CAPITAL RATIONING (cont’d)
�Hard rationing
•…a capital budget must be adhered
•…applied as company has limited resources
40
IV. CAPITAL RATIONING (cont’d)
�Hard rationing (cont’d)
•Company’s total resources: $20 million
•Opportunity cost of capital : 10%
•Company has the following project proposals: