fi3300_chapter10
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FI3300
Corporate FinanceSpring Semester 2010
Dr. Isabel Tkatch
Assistant Professor of Finance
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Quiz # 3 - next week
Time Value of Money calculations
The frequency of compounding
Capital budgeting rules (today)
45 60 minutes
Mostly multiple choice questions
Bring your calculators (IRR and loan amortization only financial calculator!)
Formulas? Maybe (one page one side)
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Learning objectives
Explain the purpose and importance of capital budgeting
Determine whether a new project should be accepted using the following rules:
net present value (NPV)
internal rate of return (IRR)
profitability index (PI)
payback period (PBP)
Explain which decision rule should be used to maximize shareholder wealth
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Example
You are contemplating the purchase of a rental property. The property consists of 12 apartments, each of which fetches a rent of $600 per month.
The cost of maintaining the entire property is $1,800 per month.
The effective monthly discount rate is 1%.
The property has an economic life of ten years and can be sold for $500,000 at the end of its life.
1. What is the maximum that you would pay for this property?
2. What if the owner is selling for $500,000?
CF1 = = CF119 = (600 x 12) 1800 = 5,400
CF120 = 5,400 + 500,000
R_eff_monthly = 1%
PV = 376,382,82+151,497.40 = 527,880.21
NPV = 527,880.21 500,000 >0 Accept project (buy)
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The Net Present Value (NPV)
Write down the CF stream
cash inflows are positive
cash outflows are negative
Use the risk adjusted cost of capital to calculate
NPV = PV (CF stream)
Note: we say net present value because we subtract the PV of cash outflows (costs, investment) from the PV of cash inflows (benefits).
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The Net Present Value (NPV) rule
The goal of capital budgeting:
Find a decision rule that will maximize shareholder wealth
The NPV rule:
Accept project if NPV > 0
If we accept a project with NPV > 0
increase shareholder wealth
If we accept a project with NPV < 0
decrease shareholder wealth
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Assumptions
Assumption 1 (magnitude preference):
all else equal, investors prefer to have more money rather than less
Assumption 2 (timing preference):
all else equal, investors prefer to get the money sooner (today) rather than later (in the future)
Assumption 3 (risk preference):
all else equal, investors prefer a safe CF to a risky CF (they are risk-averse)
Assumption 4 (managements goal):
The primary goal of the firms management is to maximize shareholder wealth
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Good Capital Budgeting Decision Rules
Criterion 1:
Does the NPV rule consider ALL CFs?
Criterion 2:
Does the NPV rule consider CFs timing?
Criterion 3:
Does the NPV rule consider CFs riskiness?
Criterion 4:
Is the NPV rule consistent with managements primary goal - maximizing shareholders wealth?
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Profitability Index (PI)
Write down the CF stream
cash inflows
cash outflows (investment)
Use the risk adjusted cost of capital to calculate:
Note that PI is a ratio while NPV is a difference
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The Profitability Index (PI) rule
PI (ratio) rule intuition: look for projects with
PV(cash inflows) > PV(cash outflows)
If PI > 1 Accept project
If PI = 1 indifference
If PI < 1 Reject project
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The Net Present Value (NPV) rule
NPV (difference) rule intuition: look for projects with
PV(cash inflows) > PV(cash outflows)
If NPV > 0 Accept project
If NPV = 0 indifference
If NPV < 0 Reject project
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Example apply NPV and PI
You are contemplating the purchase of a rental property. The property consists of 12 apartments, each of which fetches a rent of $600 per month.
The cost of maintaining the entire property is $1,800 per month.
The effective monthly discount rate is 1%.
The property has an economic life of ten years and can be sold for $500,000 at the end of its life.
1. What is the maximum that you would pay for this property?
2. What if the owner is selling for $500,000?
PV(cash inflows):
CF1 = = CF119 = (600 x 12) = 7,200
CF120 = 7,200 + 500,000
r_eff_monthly = 1%
PV(inflows) = 501,843.76 + 151,497.39 = 653,341.15
PV(cash outflows):
CF1 = = CF120 = 1,800
CF0 = 500,000
r_eff_monthly = 1%
PV = 125,460.94 + 500,000 = 625,460.94
PI = 653,341.15 / 625,460.94 = 1.045 Accept project (buy)
NPV = 653,341.15 - 625,460.94 = 27,880.21 >0 Accept project (buy)
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Example
Consider the mutually exclusive projects A and B
NPV(A) __ NPV(B) Choose project ____
PI(A) __ PV(B) Choose Project ____
Which rule should we use?
ProjectPV(inflows)PV(outflows)PINPVA$110,000$100,000B$315,000$300,000NPV(A) = 110,000 100,000 = 10,000 < 15,000 = 315,000 300,000 = NPV(B) Choose B
PI(A) = 110,000 / 100,000 = 1.1 < 1.05 = 315,000 / 300,000 = PI(B) Choose A
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Good Capital Budgeting Decision Rules
Criterion 1:
Does the PI rule consider ALL CFs?
Criterion 2:
Does the PI rule consider CFs timing?
Criterion 3:
Does the PI rule consider CFs riskiness?
Criterion 4:
Is the PI rule consistent with managements primary goal - maximizing shareholders wealth?
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The Internal Rate of Return (IRR)
Write down the CF stream
cash inflows and cash outflows (investment)
Set NPV = 0 and solve for the cost of capital (r):
Note: use a trial-and-error algorithm to find IRR.
If NPV>0 then we used r < IRR
If NPV=0 then we used r = IRR
If NPV IRR
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The Internal Rate of Return (IRR) rule
IRR is a yield what we earn, on average, per year. Compare the IRR to the required (risk-adjusted) rate of return
If IRR > required risk-adjusted return
Accept project
If IRR = required risk-adjusted return
Indifference
If IRR < required risk-adjusted return
Reject project
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Example apply IRR
You are contemplating the purchase of a rental property. The property consists of 12 apartments, each of which fetches a rent of $600 per month.
The cost of maintaining the entire property is $1,800 per month.
The effective monthly discount rate is 1%.
The property has an economic life of ten years and can be sold for $500,000 at the end of its life.
1. Calculate IRR if the owner is selling for $500,000
2. Compare IRR to the cost of capital and decide whether to accept / reject the project.
PV(cash inflows):
CF1 = = CF119 = (600 x 12) 1,800 = 5,400
CF120 = 5,400 + 500,000
CF0 = -500,000
r_eff_monthly = 1%
Write down the formula for NPV, including the investment (CF0), the annuity and the future selling value.
Find IRR such that NPV=0. We know that 1% implied a positive NPV IRR must be ABOVE 1%.
IRR = 1.08% > 1% accept the project.
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NPV and IRR (conventional projects)
FI 3300 - Corporate Finance Y.C.Loon
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Textbook application: NPV & IRR
A firm considers an investment of $1,200 in a project that yields cash flows of $500 in the first year, $600 in the second year and $700 in the third year.
The annual risk adjusted cost of capital is 10%.
Compute the project NPV and IRR and decide whether to accept or reject.
FI 3300 - Corporate Finance Y.C.Loon
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Apply the NPV, IRR and PI rules
Assume the following CF stream and an annual risk adjusted cost of capital of 11%.
Compute the NPV, IRR, PI and decide whether the project should be accepted or rejected.
Datet=0t=1t=2t=3t=4T=5CF-1,000400400400500500FI 3300 - Corporate Finance Y.C.Loon
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Verify that NPV = 603.58, IRR = 31.79%, PI = 1.60358
Since NPV>0, IRR>11% and PI>1, accept the project
PI = (603.58 + 1,000)/1,000 = 1.60358
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Example
A five-year project, if taken, will require an initial investment of $120,000. The expected end-of-year cash inflows are as follows:
If the appropriate cost of capital for this project is 11%, which of the following is a correct decision?
a. Reject the project because NPV = -$30,507, which is less than 0
b. Reject the project because IRR is 10.04%, which is less than the cost of capital, 11%
c. Both a and b are correct
d. Accept the project because IRR is positive
e. None of the above
Datet=0t=1t=2t=3t=4T=5CF30,00042,00042,00028,00012,000FI 3300 - Corporate Finance Y.C.Loon
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Answer: B.
NPV = -2,608.9095
IRR = 10.04117%
The lesson here is to know why you accept/reject a project. Option A is the correct decision but for the wrong reason. So the answer is option B because it gives the correct decision for the right reason.
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Textbook Example
The firms cost of capital for the following project is 12%.
The project will require an initial investment of $6 million and generate cash flows of $750,000 per year for ever.
Compute the NPV, IRR and PI of the project.
FI 3300 - Corporate Finance Y.C.Loon
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Verify that NPV=$250,000, IRR=12.5%, PI=1.0417
NPV:
CF0 = -6,000,000
The cash inflow stream is a perpetuity. The FC cannot give you the answer. Use the perpetuity formula to find the PV of CIF.
PV of CIF = 750,000/0.12 = 6,250,000
Therefore, NPV = 6,250,000 6,000,000 = 250,000
PI = 6,250,000/6,000,000= 1.0417
For IRR, again make use of the perpetuity formula, we want,
750,000/r = 6,000,000
Re-arranging,
R = 750,000/6,000,000 = 0.125 or 12.5%
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IRR technical problems: Example 1
Consider a project that yields (pays) a cash flow of $120 on date t=0 and requires an outflow (investment) of $100 to be paid on date t=1. The discount rate is 10%.
Calculate the NPV and IRR and decide whether to accept / reject.
FI 3300 - Corporate Finance Y.C.Loon
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NPV = 120 (100/1.1) = 29.09
IRR = -16.67
IRR:
120 (100/(1+IRR)) = 0
1+IRR = 100/120
IRR = 100/120 -1 = -0.16667
Using the FC, Enter N = 1, PV = 120, PMT = 0, FV = - 100, I/Y = ? in the calculator. We obtain an IRR of - 16.667 percent.
Think about what the irr is. It is the rate that equates PV of CIF with PV of COF. In this example, to make the two equal, 100/(1+IRR) must = 120, with a positive interest rate, this is not possible. The only way is to have a negative IRR, so that 100 is divided by a number between 0 and 1. this can yield 120. specifically, with IRR=-0.16667, the division is equal to 100.
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IRR technical problems: Example 2
Consider the following project cash flows:
Suppose the discount rate is 70%. Verify that NPV = $32.53
What about the IRR?
Datet=0t=1t=2CF-$400$2,500-$3,000FI 3300 - Corporate Finance Y.C.Loon
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There are two IRRs for this project: 61.98%, 363%. Look at the NPV profile (next slide).
Using the BA II Plus, students will get the first IRR = 61.98%, but this is misleading.
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NPV and the required rate of return
Figure 11.3: Project NPV profile.
Cash flows at t = 0, 1, 2 are -$400, $2,500, -$3,000.
FI 3300 - Corporate Finance Y.C.Loon
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IRR and Conventional Projects
Conventional project:
1. Starts with an investment: outflows, one or more negative CFs
2. Ends with inflows, positive CFs
3. There is only one sign change only one transition from negative to positive CFs
USE the IRR rule only for conventional projects!
FI 3300 - Corporate Finance Y.C.Loon
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IRR and Unconventional Projects
Unconventional project:
1. May start with a positive CF rather than an investment (outflow, negative CF)
2. May end with negative CFs - outflows, not inflows
3. There may be more than one sign change more than one transition from negative to positive CFs or positive to negative CFs
If the project is not conventional the IRR rule has to be modified. Use the NPV rule!
FI 3300 - Corporate Finance Y.C.Loon
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Example: scale differences
Consider the mutually exclusive projects A and B and assume an annual cost of capital of 5%
NPV(A) __ NPV(B) Choose project ____
IRR(A) __ IRR(B) Choose Project ____
PI(A) __ PV(B) Choose Project ____
Which rule should we use?
Datet=0t=1t=2t=3CF(A)-$1,000,000$400,000$400,000$400,000CF(B)-$1$0.40.40.5Project:AB
NPV89,2990.1757
IRR9.7010%13.7789%
PI1.08931.1757
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Good Capital Budgeting Decision Rules
Criterion 1:
Does the IRR rule consider ALL CFs?
Criterion 2:
Does the IRR rule consider CFs timing?
Criterion 3:
Does the IRR rule consider CFs riskiness?
Criterion 4:
Is the IRR rule consistent with managements primary goal - maximizing shareholders wealth?
+ technical problems if the project is not conventional
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The Pay-Back Period (PBP)
The payback period for a project is the length of time it take to get your initial investment back. It is the time from the initial cash outflow to the time when the projects cash inflows add up to the initial cash outflow.
Example: if the initial investment is $100,000 and the projects CF stream is as follows, PBP = _____
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Datet=1t=2t=3t=4T=5CF30,00042,00042,00028,00012,000ACC. CF -
The Pay-Back Period (PBP) rule
Firms usually specify an arbitrary number of periods (t) as the maximum time-to-payback. The PBP decision rule is:
If PBP < t Accept project
If PBP = t Indifference
If PBP > t Reject project
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Textbook example: PBP
Calculate the payback period for the following projects, which project will you accept if you require a maximum of 3 years to payback?
Datet=0t=1t=2t=3t=4T=5CF(A)-9,0002,0003,0004,0005,0006,000CF(B)-11,0002,0003,0004,0005,0006,000FI 3300 - Corporate Finance Y.C.Loon
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Verify that PBP for A = 3 years, PBP for B = 3.4 years
(assume cash flows occur evenly throughout the year)For B: Note that at the end of three years, 9,000 of the cost of the project (11,000) are recovered leaving 2,000 to be recovered.
In the fourth year, the cash inflow is 5,000. Thus it would take the first (2000/5000) = 0.4 fraction of the year to recover the remaining cost of the project. The payback period is, therefore, 3.4 years. The assumption is that cash flows are received evenly throughout the year. Suppose that, on the other hand, cash flows from the project were received only at the end of each year. In this case, the payback period for project B would not be 3.4 years but 4 years.
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Example: PBP compared with NPV
Assume the firm uses two years as the critical number of periods to payback and the cost of capital is 10%.
Calculate the NPV and PBP for the two projects.
NPV(A) __ NPV(B) Choose project ____
PBP(A) __ PBP(B) Choose Project ____
Which rule should we use?
Datet=0t=1t=2T=3CF(A)-1,00050051010CF(B)-1,0000099,000,000FI 3300 - Corporate Finance Y.C.Loon
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Good Capital Budgeting Decision Rules
Criterion 1:
Does the PBP rule consider ALL CFs?
Criterion 2:
Does the PBP rule consider CFs timing?
Criterion 3:
Does the PBP rule consider CFs riskiness?
Criterion 4:
Is the PBP rule consistent with managements primary goal - maximizing shareholders wealth?
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The Discounted Pay-Back Period (DPBP)
The discounted payback period for a project is the length of time it take to get your initial investment back in terms of discounted future CFs.
Example: if the initial investment is $100,000, the cost of capital is 2% and the projects CF stream is as follows, DPBP = _____
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Datet=1t=2t=3t=4T=5CF30,00042,00042,00028,00012,000PV(CF)ACC. PV(CF) -
The Discounted Pay-Back Period rule
Firm usually specify an arbitrary number of periods (t) as the maximum time-to-discounted-payback. The Discounted PBP decision rule they is:
If Discounted PBP < t Accept project
If Discounted PBP = t Indifference
If Discounted PBP > t Reject project
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Discounted PBP example
Suppose that the discount rate is 10%. Project A has the following cash flows. Find As discounted PBP.
Datet=1t=2t=3t=4CF-9,0003,0006,0009,000PV(CF)ACC. PV(CF)FI 3300 - Corporate Finance Y.C.Loon
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DCF = discounted cash flows
2,727 = 3,000/1.1
4,959 = 6,000/(1.1)2
6,762 = 9,000/(1.1)3
The last row in the table above is the cumulative discounted cash flows, 2,727 + 4,959 = 4,297 and so on.
The discounted payback period is, = 2 + (9,000 7,686)/6,762 = 2 + 0.194 = 2.194 yrs
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Good Capital Budgeting Decision Rules
Criterion 1:
Does the Discounted PBP rule consider ALL CFs?
Criterion 2:
Does the Discounted PBP rule consider CFs timing?
Criterion 3:
Does the Discounted PBP rule consider CFs riskiness?
Criterion 4:
Is the Discounted PBP rule consistent with managements primary goal - maximizing shareholders wealth?
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Why the PBP criterion exists?
PBP is widely used by corporations
It is used as a secondary project selection criterion
Example: the firm may require a project to have
(1) positive NPV first and also
(2) satisfy some payback criterion.
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Summary 1: Description
RuleDescriptionNPVNPV = PV (CF stream) = PV(cash inflows) PV(cash outflows)IRRThe cost of capital ,r , that makes NPV = 0PIPI = PV(cash inflows) / PV(cash outflows)D. PBPThe time it take to get your initial investment back, in terms of discounted future CFs -
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Summary 2: Rules
RuleAccept project if Reject project ifNPVNPV > 0NPV < 0IRRIRR > cost of capital, rIRR < cost of capital, rPIPI > 1PI < 1D. PBPD. PBP < # of years (arbitrary number)D. PBP > # of years (arbitrary number) -
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Summary 2: Rule quality
Criterion \ RuleNPVIRRPIDisc. PDP1. Does the rule consider ALL CFs?X2. Does the rule consider CFs timing?3. Does the rule consider CFs riskiness?4. Is the rule consistent with maximizing shareholders wealth?XXXPV (cash outflows)
PV (cash inflows)
PV (cash inflows)
PV
NPV =-
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PI =
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PV (cash inflo
PV (cash
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PV (cash inflows)
PV (cash o
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12
0
12
......0
(1)(1)(1)(1)
t
T
tT
CF
CFCFCF
NPVCF
IRRIRRIRRIRR
=++++++=
++++
600
500
400
300
200
100
0
-1000
-800
-600
-400
-200
0
200
Discount rate
NPV
IRR?