Chapter Seven
Discount cash Flow
Valuation
Copyright  2007 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
7-1
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
2
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.
Copyright  2007 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
7-3
NPV
Steps 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.
Copyright  2007 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
7-4
NPV Illustrated
0
1
Initial outlay
($1100)
Revenues
Expenses
$1000
500
Cash flow
– $1100.00
$500 x
$500
2
Revenues
Expenses
$2000
1000
Cash flow $1000
1
1.10
+454.55
$1000 x
1
1.102
+826.45
+$181.0
0
NPV
Copyright  2007 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
7-5
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.
Copyright  2007 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
7-6
Example:
• New product development costs and
returns are shown in the table below
• If cost of capital is 16%, is this project
viable?
Year
0
1
2
3
4
5
Development
Cost ($000)
420
320
154
Returns
($000)
215
225
420
240
160
7
Example: Continue
• Before we proceed we must find the net
cash flows for each year
Year
0
1
2
3
4
5
Development
Cost ($000)
420
320
154
Returns Net Cash
($000)
Flows
-420
215
-105
225
71
420
420
240
240
160
160
8
Example: Continue
• 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
9
Example: Continue
• 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.
10
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
11
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.
Copyright  2007 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
7-12
Example 1—IRR
Initial investment = –$200
Year
Cash flow
1
2
3
$ 50
100
150
n Find the IRR such that NPV = 0
0 = –200 +
50
100
(1+IRR)1
50
200 =
(1+IRR)1
+
(1+IRR)2
100
+
150
(1+IRR)2
+
(1+IRR)3
150
+
(1+IRR)3
Copyright  2007 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
7-13
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%
Copyright  2007 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
7-14
Example: Continue
• 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
15
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.
16
Illustration:
– 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
17
Illustration:
• 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
18
Illustration:
Net
Year
Cash
Depreciation Taxation
Cash
Flow
Flow
0 (100,000)
(100,000)
(1)
(2)
(3)
1
68,000
15,000
21,200
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
19
Illustration:
•
•
•
•
•
•
•
•
•
+/- 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%
20
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.
Copyright  2007 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
7-21
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.
Copyright  2007 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
7-22
Multiple Rates of Return
Assume you are considering a project for
which the cash flows are as follows:
Year
Cash flows
0
–$60
1
155
2
–100
Copyright  2007 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
7-23
Multiple Rates of Return
n To find the IRR on this project
NPV is calculated at various rates:
n
at 10%:
NPV =
-$1.74
at 20%:
NPV =
- 0.28
at 30%:
NPV =
0.06
at 40%:
NPV =
- 0.31
NPV crosses
zero
Two questions:
u
u
1. What is going on here?
2. How many IRRs can there be?
Copyright  2007 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
7-24
NPV Profile
Copyright  2007 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
7-25