+

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 ProjectsMutually 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.

+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 rate3. Estimate initial costs

Minimum Acceptance Criteria: Accept if NPV > 0

Ranking Criteria: Choose the highest NPV

+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?

+NPV Example (Contd.)

Consider these two strategies:1. Use $100 of corporate cash to invest in the project.

The $107 will be paid as a dividend in one year.2. 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?

+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.

+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%.

+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

+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

+Example-Payback Period

Here are the projected cash flows from a proposed investment:

This project costs $100.

What is the payback periods?

Year Cash Flows

1 10

2 60

3 80

+Example – Calculating Payback Period

+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

+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.

+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

+The Average Accounting Return

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

Investment of ValueBook Average

IncomeNet AverageAAR

+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 5Revenue 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

+Example-AAR

𝐴𝑣𝑒𝑟𝑎𝑔𝑒𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒=$ 100,000+150,000+50000+0−50,000

5=$50,000

𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐵𝑜𝑜𝑘𝑉𝑎𝑙𝑢𝑒=$500,000−0

2=250,000

or

𝐴𝑣𝑒𝑟𝑎𝑔𝑒𝐵𝑜𝑜𝑘𝑉𝑎𝑙𝑢𝑒=$500,000+400,000+300,000+200,000+100,000+0

6=250,000

𝐴𝐴𝑅=$ 50,000$ 250,000

=20 %

+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.Ranking Criteria:

Select alternative with the highest IRRReinvestment assumption:

All future cash flows assumed reinvested at the IRR.

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

+The Internal Rate of Return: Example

Consider the following project:

0 1 2 3

$50 $100 $150

-$200

The internal rate of return for this project is 19.44%

32 )1(

150$

)1(

100$

)1(

50$2000

IRRIRRIRRNPV

+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 NPV

0% $100.004% $71.048% $47.3212% $27.7916% $11.6520% ($1.74)24% ($12.88)28% ($22.17)32% ($29.93)36% ($36.43)40% ($41.86) ($60.00)

($40.00)

($20.00)

$0.00

$20.00

$40.00

$60.00

$80.00

$100.00

$120.00

-1% 9% 19% 29% 39%

Discount rate

NP

V

+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

+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?

($150.00)

($100.00)

($50.00)

$0.00

$50.00

$100.00

-50% 0% 50% 100% 150% 200%

Discount rate

NP

V

100% = IRR2

0% = IRR1

+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)

+Example - MIRR

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%

0 1 2 3

$200 $800

-$200 - $800

+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.

+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 CF 1NPV @

25% IRR

Small Budget -10 40 22 300%

Large Budget -25 65 27 160%

+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

($4,000.00)

($3,000.00)

($2,000.00)

($1,000.00)

$0.00

$1,000.00

$2,000.00

$3,000.00

$4,000.00

$5,000.00

0% 10% 20% 30% 40%

Discount rate

NP

V

Project A

Project B

+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 $01 $10,000 $1,000 $9,000 ($9,000)2 $1,000 $1,000 $0 $03 $1,000 $12,000 ($11,000) $11,000

($3,000.00)

($2,000.00)

($1,000.00)

$0.00

$1,000.00

$2,000.00

$3,000.00

0% 5% 10% 15% 20%

Discount rate

NP

V A-B

B-A

+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.