7-1Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

Discount cash Flow Valuation

Chapter Seven

2

Discounted Cash Flow (DCF)

• DCF is used to evaluate an investment to see if it meets profit objectives

• Uses the concept of Time Value of Money

• Two methods

– Net present value

– Internal rate of return

7-3Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

Net Present Value (NPV)

• Net present value (NPV) is the difference between an investment’s market value (in today’s dollars) and its cost (also in today’s dollars).

• An investment is worth undertaking if it creates value for its owners.

• Value is created by identifying an investment that is worth more in the marketplace than it costs to acquire. NPV provides a measure of how much value is created by undertaking an investment.

7-4Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

NPVSteps in calculating NPV:

• The first step is to estimate the expected future cash flows.

• The second step is to estimate the required return for projects of this risk level.

• The third step is to find the present value of the cash flows and subtract the initial investment.

7-5Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

NPV Illustrated

0 1 2

Initial outlay($1100)

Revenues $1000Expenses 500

Cash flow $500

Revenues $2000Expenses 1000

Cash flow $1000

– $1100.00

+454.55

+826.45

+$181.00

1$500 x 1.10

1$1000 x 1.10

2

NPV

7-6Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

NPV

• An investment should be accepted if the NPV is positive and rejected if it is negative.

• NPV is a direct measure of how well the investment meets the goal of financial management—to increase owners’ wealth.

• A positive NPV means that the investment is expected to add value to the firm.

7

Example:

• New product development costs and returns are shown in the table below

• If cost of capital is 16%, is this project viable?

YearDevelopment

Cost ($000)Returns ($000)

0 4201 320 2152 154 2253 4204 2405 160

8

Example: Continue• Before we proceed we must find the net

cash flows for each year

YearDevelopment

Cost ($000)Returns ($000)

Net Cash Flows

0 420 -4201 320 215 -1052 154 225 713 420 4204 240 2405 160 160

9

• The net cash flows can be entered into the calculator

• CFi 2ndF CA{MODE} (clears cash flows.)

• +/- 420 Data• +/- 105 Data• 71 Data • 420 Data• 240 Data• 160 Data• Press On/C

• 2ndF CASH{CFi}• 16 ENT (interest rate)• ▼ COMP

• The NPV = 20.05• The net present

value of the sequence of cash flows is $20,050 when cost of capital is 16%

• Project is viable

Example: Continue

10

• Is the project viable if the cost of capital is 18%?

• To see what happens when the cost of capital is increased to 18%,

• Press ▲ Scrolls up to the interest rate screen.

• 18 ENT Enters the new interest rate. • ▼ COMP Computes the new NPV• NPV = -8.64 The NPV is now (-$8,640). • So at 18% NPV = (-$8,640) which means the

project is going to lose money at this cost of capital. This project is no longer viable as the costs are greater than the returns.

Example: Continue

11

Internal Rate of Return

• The discount rate that equates the PV of cash inflows with the PV of the cash outflows

• The highest rate of capital at which a company could afford to undertake the project

7-12Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

Internal Rate of Return (IRR)

• IRR is the discount rate that equates the present value of the future cash flows with the initial cost.

• A project is accepted if:

IRR > the required rate of return

• The IRR on an investment is the required return that results in a zero NPV when it is used as the discount rate.

7-13Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

Example 1—IRR

Initial investment = –$200

Year Cash flow

1 $ 50 2 100 3 150

Find the IRR such that NPV = 0

50 100 150 0 = –200 + + + (1+IRR)1 (1+IRR)2 (1+IRR)3

50 100 150 200 = + + (1+IRR)1 (1+IRR)2 (1+IRR)3

7-14Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

Example 1—IRR (continued)

Trial and Error

Discount rates NPV

0% $100

5% 68

10% 41

15% 18

20% –2

IRR is just under 20%—about 19.44%

15

• What is the break even point for this project?

• That is, find the IRR• (assuming all the cash flows are still in the

calculator)• Press ▲ Scrolls up to the interest

rate screen.• COMP Computes the IRR• IRR = 17.38%• As long as the cost of capital is below

17.38% this project is viable

Example: Continue

16

Illustration:

• Proposal to purchase new machinery will cost $100,000 with a terminal salvage value of $10,000 after 6 years

– Selling price = $12/unit

– Variable cost = $4/unit

– Selling cost = $1/unit

– Manufacturing overheads - depreciation = $15,000 p.a.

– Maintenance = $2000 p.a.

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– Overheads = $3000 p.a.– Administrative and selling overheads =

$10,000 p.a.– Sales = 10,000 p.a.– Tax rate = 0.4– Weighted cost of capital = 20% after

tax• What is the NPV for this project?• The first step is to find the yearly net

cash flows

Illustration:

18

• Cash flow year 1

• = (12-(4+1))x10,000-2,000 = 68,000

• Depreciation based on straight line depreciation of $100,000 less $10,000 salvage

• Tax based on cash flow, less depreciation, excl. capital items

• Salvage value added to final year cash flow

Illustration:

19

Year

Cash Flow

Depreciation

Taxation

Net Cash Flow

0 (100,000) (100,000) 1 68,000(1) 15,000(2) 21,200(3) 46,800 2 68,000 15,000 21,200 46,800 3 68,000 15,000 21,200 46,800 4 68,000 15,000 21,200 46,800 5 68,000 15,000 21,200 46,800 6 78,000(3) 15,000 21,200 56,800

Illustration:

20

• +/- 100000 Data• 46,800 Data• 46,800 Data• 46,800 Data• 46,800 Data• 46,800 Data• 56,800 Data• 2ndF CASH{CFi}• 20 ENT (interest

rate)• ▼ COMP• NPV = $58,982

• OR• +/- 100000 Data• 46,800 (x,y) 5 Data• 56,800 Data• 2ndF CASH{CFi}• 20 ENT (interest rate)• ▼ COMP• NPV = $58,982• The project is viable!• Press ▲ COMP• IRR = 41.48%

Illustration:

7-21Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

Advantages of IRR

• Popular in practice.

• Does not require a discount rate.

• The IRR appears to provide a simple way of communicating information about a proposal.

7-22Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

Problems with IRR

• Multiple rates of return

– Occurs if more than one discount rate makes the NPV of an investment zero.

– This will happen when there is more than one negative cash flow (non-conventional cash flows).

• Mutually exclusive investment decisions

– Project is not independent mutually exclusive investments. Highest IRR does not indicate the best project.

7-23Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

Multiple Rates of Return

Assume you are considering a project forwhich the cash flows are as follows:

Year Cash flows

0 –$60

1 155

2 –100

7-24Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

Multiple Rates of Return

To find the IRR on this projectNPV is calculated at various rates:

at 10%: NPV = -$1.74

at 20%: NPV = - 0.28

at 30%: NPV = 0.06

at 40%: NPV = - 0.31

Two questions:

1. What is going on here?

2. How many IRRs can there be?

NPV crosseszero

7-25Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

NPV Profile