+
Net Present Value
RWJ-Chapter 9
+
Overview



In late 2010, Foxconn, electronics contract manufacturing
company (which manufactures many of the Apple products and
Kindle), announced its plans to open a factory in China at a
cost of $10 billion.
Foxconn’s new plant is an example of capital budgeting
decision. Decisions such as these, with a price tag of $10
billion, are major undertakings, and risks and rewards must be
carefully weighed.
In this chapter, we discuss the basic tools used in making such
decisions.
+ Mutually Exclusive vs. Independent Projects
 Mutually
Exclusive Projects: only ONE of
several potential projects can be chosen, e.g.
acquiring an accounting system.

RANK all alternatives and select the best one.
 Independent
Projects: accepting or rejecting one
project does not affect the decision of the other
projects.

Must exceed a MINIMUM acceptance criteria.
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The Net Present Value (NPV)

Net Present Value (NPV) =
Total PV of future CF’s + Initial Investment

Estimating NPV:
1. Estimate future cash flows: how much? and when?
2. Estimate discount rate
3. Estimate initial costs

Minimum Acceptance Criteria: Accept if NPV > 0

Ranking Criteria: Choose the highest NPV
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NPV Example


Alpha Corp. is considering investing in a riskless project costing
$100. The project receives $107 in one year and has no other
cash flows. The risk-free interest rate is 6%.
NPV of the project is:
$0.94= -100 + (107/1.06)

NPV is positive, accept the project.

NPV leads to good decisions. Why?
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NPV Example (Contd.)

Consider these two strategies:
1.
2.


Use $100 of corporate cash to invest in the project. The
$107 will be paid as a dividend in one year.
Forgo the project and pay the $100 of corporate cash as
a dividend today.
If strategy 2 is employed, the shareholders might
deposit the dividend in the bank for one year.
With the interest rate of 6 percent, strategy 2 will
produce cash of $100 x 1.06 =$106 at the end of
year 1.
Which strategy would the shareholders prefer?
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How do We Interpret NPV?


In the previous example, NPV of the project was $0.94.
Let’s say the firm today has productive assets worth $V
and has $100 of cash. If the firm foregoes the project, the
value of the firm today would be:
$V +100

If the firm accepts the project, the firm will receive $107 in
one year but will have no cash today.
V + 107/1.06

The difference between the two equations is $0.94, i.e.
NPV
The value of the firm rises by the NPV of the project.
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Discount Rate in NPV Calculations


In the previous example, we assumed that the project was
riskless. In real life, the future cash flows from a project are
estimated rather than known.
Let’s say, Alpha Corp. estimates that with 50% chance the
cash flow will be $117, or it will be $97. The expected cash
flow will be (0.5) (117) +(0.5) (97)= $107

Suppose the project is as risky as the market and expected
return on the market is 10%.

NPV= -100 + 107/1.10 = -$2.73

Expected return on the project is 7%. If the investors gets the
cash in dividends and invest it at the market, the expected
return is 10%.
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Why Use Net Present Value?

Accepting positive NPV projects benefits shareholders.

NPV uses cash flows

NPV uses all the cash flows of the project

NPV discounts the cash flows properly
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9.2 The Payback Period

How long does it take the project to “pay back” its initial
investment?

Payback Period = number of years to recover initial costs

Minimum Acceptance Criteria:


set by management
Ranking Criteria:

set by management
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Example-Payback Period

Here are the projected cash flows from a proposed investment:
Year
Cash Flows
1
10
2
60
3
80

This project costs $100.

What is the payback periods?
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Example – Calculating Payback
Period
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The Payback Period Rule
(continued)

Disadvantages:







Ignores the time value of money
Fails to consider risk
Ignores cash flows after the payback period
Biased against long-term projects
Requires an arbitrary acceptance criteria
A project accepted based on the payback criteria may not have a
positive NPV
Advantages:


Easy to understand
Biased toward liquidity
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The Payback Period - Uses



In relatively small decisions since it is simple.
Firms with good investment opportunities but no available cash.
Quick cash recovery enhances the reinvestment possibilities
for such firms.
Firms prefer NPV when they look at bigger projects.
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The Discounted Payback



How long does it take the project to “pay back” its initial
investment taking the time value of money into account?
Still has some of the major flaws as payback.
By the time you have discounted the cash flows, you might as
well calculate the NPV.
+
Example – Discounted Payback
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The Average Accounting Return
Average Net Income
AAR 
Average Book Value of Investment

Another attractive but fatally flawed approach.

Ranking Criteria and Minimum Acceptance Criteria set by
management

Disadvantages:




Ignores the time value of money
Uses an arbitrary benchmark cutoff rate
Based on book values, not cash flows and market values
Advantages:


The accounting information is usually available
Easy to calculate
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Example-AAR

You are deciding whether to open a store in a new shopping mall. The
required investment is $500,000.

The required investment would be 100% depreciated (straight-line) over
the five years.

The following table provides yearly revenue and costs for average
accounting return:
Year 1
Year 2
Year 3
Year 4
Year 5
Revenue
433,333
450,000
266,667
200,000
133,333
Expenses
200,000
150,000
100,000
100,000
100,000
EBITDA
233,333
300,000
166,667
100,000
33,333
Depreciation
100,000
100,000
100,000
100,000
100,000
EBIT
133,333
200,000
66,667
0
-66,667
Taxes
33,333
50,000
16,667
0
-16,667
NI
100,000
150,000
50,000
0
-50,000
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Example-AAR
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒 =
$100,000 + 150,000 + 50000 + 0 − 50,000
= $50,000
5
$500,000 − 0
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐵𝑜𝑜𝑘 𝑉𝑎𝑙𝑢𝑒 =
= 250,000
2
or
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐵𝑜𝑜𝑘 𝑉𝑎𝑙𝑢𝑒 =
= 250,000
$500,000 + 400,000 + 300,000 + 200,000 + 100,000 + 0
6
𝐴𝐴𝑅 =
$50,000
= 20%
$250,000
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The Internal Rate of Return (IRR)
 IRR:
the discount rate that sets NPV to zero
 Minimum Acceptance Criteria:

Accept if the IRR exceeds the required return.

Select alternative with the highest IRR

All future cash flows assumed reinvested at the IRR.
 Ranking
Criteria:
 Reinvestment
assumption:
 Disadvantages:
Does not distinguish between investing and borrowing.
 IRR may not exist or there may be multiple IRRs.
 Problems with mutually exclusive investments.

 Advantages:

Easy to understand and communicate
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The Internal Rate of Return: Example

Consider the following project:
$50
0
1
$100
2
$150
3
-$200

The internal rate of return for this project is 19.44%
$50
$100
$150
NPV  0  200 


2
(1  IRR) (1  IRR) (1  IRR) 3
+ The NPV Payoff Profile for This Example
If we graph NPV versus discount rate, we can see the IRR as
the x-axis intercept.
Discount Rate
0%
4%
8%
12%
16%
20%
24%
28%
32%
36%
40%
NPV
$100.00
$71.04
$47.32
$27.79
$11.65
($1.74)
($12.88)
($22.17)
($29.93)
($36.43)
($41.86)
$120.00
$100.00
$80.00
$60.00
NPV

$40.00
$20.00
$0.00
($20.00)
-1%
9%
19%
($40.00)
($60.00)
Discount rate
29%
39%
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Problems with the IRR Approach
•
•
General problems affecting both independent
and mutually exclusive projects:
• Investing or Financing
• Multiple IRRs
Problems specific to mutually exclusive
projects:
• The Scale Problem
• The Timing Problem
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Investing or Financing?

Two different projects


Project A (Investing type)
 CF0 = -100
 CF1 = 130
 NPV @10% = $18.2
 IRR = 30%
Project B (Financing type)
 CF0 = 100
 CF1 = -130
 NPV @10% = -$18.2
 IRR = 30%
IRR is greater than discount rate in both cases. But Project B’s
NPV is negative.
IRR rule is reversed for financing type projects.
+ Multiple IRRs
There are two IRRs for this project:
Which one should
we use?
NPV

$100.00
100% = IRR2
$50.00
$0.00
-50%
0%
($50.00)
($100.00)
($150.00)
50%
100%
0% = IRR1
150%
200%
Discount rate
+ How Do We Solve Multiple IRR Problem?

Rely on NPV when cash flows are non-normal.

OR calculate Modified Internal Rate of Return (MIRR)

Three steps to calculate MIRR (Combination approach):



Find the PV of cash outflows
Find the FV of cash inflows
Find the rate of return which makes the FV of cash inflows equal to
PV of cash outflows (MIRR)
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Example - MIRR
$200
0
1
-$200
$800
2
3
- $800

Let’s assume the discount rate is 10%

PV of cash outflows = -200 + [-800/(1.10)3] = $ -801.06

FV of cash inflows = 200 * (1.1)2 + 800 *(1.1) = $1,122

801.06 = 1,122/(1+MIRR)3

MIRR= 11.886%
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Problems with MIRR




“Meaningless internal rate of return”?
There are three methods of calculating MIRR (we have seen
only one).
MIRR requires compounding and discounting. If we have the
discount rate, why not calculate NPV?
MIRR depends on the discount and compound rate, so it is not
truly an internal rate of return, which should depend on only the
project’s cash flows.
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The Scale Problem (of IRR)
•
Suppose that a friend promises to pay you $2 tomorrow if you
lend him $1 today. This deal promises a return of 100% (IRR).
•
Another friend asks you to lend him $100 today in exchange of
$150 tomorrow. IRR on this deal is 50%.
•
Which one would you choose?
•
The first deal increases your wealth by $1 (NPV), the second
deal increases your wealth by $50.
+ How Do We Solve the Scale Problem?

Compare NPVs
Project
CF 0
NPV @
CF 1
25%
IRR
Small Budget
-10
40
22
300%
Large Budget
-25
65
27
160%
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The Timing Problem

The preferred project in this case depends on the discount rate.
NPV of project B is higher with low discount rates and the NPV
of project A is higher with high discount rates.
The Timing Problem
$5,000.00
$4,000.00
Project A
$3,000.00
Project B
$2,000.00
NPV
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$1,000.00
$0.00
($1,000.00) 0%
10%
20%
30%
($2,000.00)
($3,000.00)
($4,000.00)
Discount rate
40%
Calculating the Crossover Rate

Compute the IRR for either project “A-B” or “B-A”
Year Project A Project B Project A-B Project B-A
0 ($10,000) ($10,000)
$0
$0
1 $10,000
$1,000
$9,000
($9,000)
2 $1,000
$1,000
$0
$0
3 $1,000 $12,000
($11,000)
$11,000
$3,000.00
$2,000.00
NPV
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$1,000.00
$0.00
($1,000.00) 0%
5%
10%
($2,000.00)
($3,000.00)
Discount rate
15%
20%
A-B
B-A
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IRR vs. NPV


Either due to differences in timing or in size, the project with the
highest IRR need not have the highest NPV.
When working with mutually exclusive projects, it is very
common that you will face scale or timing problem. Then you
should simply use NPV.
+
IRR vs. NPV
Consider these two statements:


1.
You must know the discount rate to compute NPV of a project
but you can compute the IRR without referring to the discount
rate.
2.
Hence, the IRR rule is easier to apply than the NPV rule
because you don’t use the discount rate when applying IRR.
First statement is true, while the second statement is not.