fi3300_chapter10

FI3300
Corporate Finance

Spring 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)


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





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$300,000
NPV(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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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)


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





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.


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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-1,000400400400500500

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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=5CF30,00042,00042,00028,00012,000

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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.


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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.


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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-$3,000

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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.


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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!


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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!


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Example: scale differences

Consider the mutually exclusive projects A and B and assume an annual cost of capital of 5%


IRR(A) __ IRR(B) Choose Project ____

PI(A) __ PV(B) Choose Project ____

Datet=0t=1t=2t=3CF(A)-$1,000,000$400,000$400,000$400,000CF(B)-$1$0.40.40.5
Project:AB

NPV89,2990.1757

IRR9.7010%13.7789%

PI1.08931.1757

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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)-11,0002,0003,0004,0005,0006,000

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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.


PBP(A) __ PBP(B) Choose Project ____

Datet=0t=1t=2T=3CF(A)-1,00050051010CF(B)-1,0000099,000,000

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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)

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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


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?XXX
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fi3300_chapter10

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indifferenceif npv

npv rule consistent

shareholder wealththe

reject project

project buy

new project

net present value npvwrite

cost of capital