Transcript C H A P T E R 13

FINC3240
International Finance
Capital Budgeting (1)
1
The value of financial assets
0
Value
r%
1
2
N
...
CF1
CF2
CFN
CF2
CF1
CFN
Value 

 ...
1
2
(1  r)
(1  r)
(1  r)N
Question
You are asked to choose from the
following:
 Receive $100 today
 Receive $100 one year from now
Would you choose 1 or 2?
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Important observations 1

Money has time value--People prefer
to receive (and spend) it sooner
rather than later.
You prefer receiving $100 today to receiving
$100 one year from now because you place a
LOWER value on cash flow received at a later
date.
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Important observations 2
You cannot simply add sums of money
received at different points in time
because the same face amount of money
at different points of time have different
value. Money received (or paid) at
different times must first be converted to
a common basis, the same point in time,
for comparison.
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Time Value Basics
Deposit problem: If you put $100 in a bank deposit
account earning 10% annually, how much will be in
the account after one year?
100
+
10
=
110
Principal + Interest = Future Value
100
+ 100(.10) =
110
100
x (1+.10)
110
=
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Time Value Basics
What would it be worth after two years?
110
x
1.1
=
121
But, since 110 = 100(1+.10)…
100 x (1+.10) x (1+.10)
=
121
=
121
or
100 x (1+.10)2
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The Formula for Future Value
Future Value
Number of
periods
FV  PV  (1  r )
Present
Value
n
Rate of return or
discount rate or
interest rate or
growth per
period
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The Formula for Future Value


The formula lets you convert a
current cash flow into its future
value.
This process is called compounding.
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The Formula for Present Value
From before, we know that
FV  PV  1  r 
n
Solving for PV, we get
FV
PV 
n
(1  r )
Unless otherwise
stated, r stated
on an annual
basis.
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The Formula for Present Value


The formula lets you convert future
cash flows into their present values.
This process is called discounting.
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Discount rate and PV
If FV is fixed, then as the discount
rate increases, PV decreases.
110
100
Present value

90
80
70
60
0
10
20
30
Disco unt ra te (% )
40
50
60
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FV and PV formulas
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
These are the basic building blocks which we will
use to construct bigger and more complex ideas
& concepts.
Not surprisingly, we will use these basic building
blocks to solve complicated capital budgeting
problems.
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1-period, find FV
You require $1,700 to buy a
computer and the bank is offering a
loan at an interest rate of 14
percent. If you plan to repay the
loan after one year, how much will
you have to pay the bank?
Use FV = PV(1 + r)
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1-period, find PV
What is the present value of $16,000
to be received at the end of one year
if the discount rate is 10 percent?
Use PV = FV/(1 + r)
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2-period, find FV
You plan to loan $11,000 to your
friend at an interest rate of 8 percent
per year compounded annually. The
loan is to be repaid in two years.
How much will your friend pay you at
t = 2?
Use FV = PV(1+r)2
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2-period, find PV
You are offered the chance to buy into an
investment that promises to pay you
$28,650 at the end of two years. If your
required rate of return is 12 percent, what
is the maximum amount that you would
pay for this investment?
Use PV = FV/(1+r)2
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Time line: visualizing cash flows


For a problem with 2 or more periods, a time line
helps you to understand the problem better.
A time line is a graphical representation of a
problem. For the previous problem, the time line
would look like this:
-$ 5,000
t=0
-$ 4,000
t=1
t=2
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Capital Budgeting Decision 1


Capital budgeting: the process of
analyzing projects and decide which ones
to invest in.
Project: any investment that involves cash
outflows (costs) made in order to receive
cash inflows (benefits).
E.g.,: new product, new plant &
machinery, cost saving technologies, new
accounting software.
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Capital Budgeting Decision 2




Let’s be more specific about the decision
to be made:
Given the cash inflows and outflows of a
project, should the firm accept or reject
the project.
If the firm accepts, it will invest in the
project. If the firm rejects, it will not
invest in the project.
This type of decision is known as a capital
budgeting decision.
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Capital Budgeting Decision 3

If the firm makes a wrong capital
budgeting decision, e.g., invest in the
wrong project, then scarce resources are
wasted. It also means that firm value and
shareholder wealth will be reduced.
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The Value of a Project

Determined by the present value of
its expected investment cost and
future cash flows.
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Net present value (NPV) rule
Accept project if
Net present value > 0
What is Net present value?
Net present value
= Benefits minus Costs
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How do we measure
benefits & costs?
Benefits, B
= Present value of all cash inflows from the
project
Cash inflow at
N
=
Number of
years in the
project’s life
CIFt

t
t  0 1  r 
the end of
period t
Discount rate
for the
project’s cash
flows
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How do we measure
benefits & costs?
Costs, C
= Present value of all cash outflows from the
project
N
=
Number of
years in the
project’s life
COFt

t
t  0 1  r 
Cash outflow at the
end of period t
Discount rate for
the project’s
cash flows
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NPV
N
N
CIFt
COFt
NPV = B – C = 

t
t
t 0 1  r 
t 0 1  r 
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NPV Profile
NPV profile is a graph showing the
NPV values for different discount
rates.
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NPV Profile
5000
Net Present Value ($)
4000
3000
2000
I RR
1000
0
-1000
0
10
20
30
40
50
60
Discount Rate (%)
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Example 1
A firm is considering investment in a
project that costs $1,200 and yields
cash flows of $500 in the first year,
$600 in the second year and $700 in
the third year. The appropriate
discount rate for this project is 10%.
Compute the NPV of this project.
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By Math
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Computing NPV using BA II Plus

Press CF, press -1200 and then press ENTER for CF0.
Next press “” and enter 500 for C01.
Press “” and enter 1 for F01.
Similarly enter C02 = 600, F02 = 1, C03 = 700, and F03 = 1.
Make sure that all the cash flows later than C03 are zero.
Press NPV. Enter the discount rate of 10 percent by pressing
10 and then ENTER.
The display will show that I = 10.
Next press the “” and press CPT.
The calculator will display the NPV of 276.33.
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Decision: Accept project
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Example 2
Project K costs $52,125, its expected
net cash inflows are $12,000 per
year for 8 years, and its cost of
capital is 12%. Shall we reject the
project or not?
NPV = $7,486.68.
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Homework
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
1. Your division is considering a projects with the following
net cash flows (in millions). The initial investment cost is
25, the cash flows at the end of year 1, 2, 3 are 5,10,17,
respectively. What are the projects’ NPV assuming the cost
of capital is 5%? 10%? 15%?
2. Your division is considering a projects with the following
net cash flows (in millions). The initial investment cost is 20, the cash flows at the end of year 1, 2, 3 are 10,9,6,
respectively. What are the projects’ NPV assuming the cost
of capital is 5%? 10%? 15%?
3. A firm with a 14% capital cost is evaluating a project.
The project needs 6000 as the initial investment and has
2,000 cash inflows for the following 5 years. Calculate NPV.
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