Transcript FI3300 Corporation Finance

FINC3131
Business Finance
Chapter 5:
Time Value of Money:
The Basic Concepts
1
Time value of money:
Practical relevance
Examples
1. Retirement
2. Mortgage payment
3. Price of a stock
4. Helping your company to decide which
project to undertake
2
Learning objectives
1.
Understand the difference between a nominal
interest rate and a real interest rate
2.
Recall the present value and future value formulas
3.
Solve 1-period time value of money problems
involving one cash flow.
4.
Solve 2-period time value of money problems
involving one cash flow.
5.
Solve 2-period time value of money problems
involving 2 cash flows.
3
Question
1. A bill of $100 today
2. A bill of $100 one year from now
Which bill has a higher value?
4
Important implications
1. Money has time value
2. For the same amount of money, people require
some compensation if receiving it later.
3. For adding or subtracting money received (or
paid) at different times, the amounts must first
be converted to a common basis: the same
point in time
5
Interest rates 1
1. Real rate of interest (rreal) : the return
(compensation) you demand for lending
someone money and thus postponing
consumption.
2. In a world with NO inflation, we only
need to work with the real rate of
interest.
Inflation: general rise in prices. Same commodity
becomes more expensive over time.
6
Interest rates 2
1. In a world with inflation, when you lend
money to people, you want to adjust your
interest rate for inflation.
2. Inflation-adjusted interest rate is known
as Nominal rate of interest (rnominal).
In the real world, all the quoted rates are nominal
rates (e.g., car loan, house loan, student loan)
7
Preparing BAII Plus for use
1.
Press ‘2nd’ and [Format]. The screen will display the
number of decimal places that the calculator will
display. If it is not eight, press ‘8’ and then press
‘Enter’.
2.
Press ‘2nd’ and then press [P/Y]. If the display does
not show one, press ‘1’ and then ‘Enter’.
3.
Press ‘2nd’ and [BGN]. If the display is not END, that
is, if it says BGN, press ‘2nd’ and then [SET], the
display will read END.
8
Time Value Basics
Deposit problem: If you save $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
=
9
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
10
The Formula for Future Value
Future Value
Number of periods
FV  PV  (1  r )
Present Value
n
Right now
we look at
n = 1, n = 2
Rate of return or
discount rate or
interest rate or
growth per period
11
The Formula for Future Value
1. The formula lets you convert a current
cash flow (present value) into its future
value.
2. This process is called compounding.
 What about the reverse process? How
do we convert future cash flows into their
present values?
12
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.
13
The Formula for Present Value
1. The formula lets you convert future cash
flows into their present values.
2. This process is called discounting.
14
More observations
We assume the discount rate, r, is positive.
With that assumption, we can say:
1. PV is always less than FV.
2. 1/(1 + r) is always less than one.
3. (1 + r) is always greater than one.
15
Discount rate and PV
If FV ($100) after 1-year is fixed, then as the discount
rate increases, PV decreases.
110
100
Present value

90
80
70
60
0
10
20
30
40
50
60
16
Disco unt ra te (% )
FV and PV formulas
1.
These are the basic building blocks that we will use to
construct more complex concepts.
2.
Not surprisingly, we will use these basic building
blocks to solve complicated TVM problems.
17
TVM problems
1.
2.
3.
4.
Given PV, n, and r, find FV.
Given FV, n, and r, find PV.
Given PV, n, and FV, find r.
Given PV, r, and FV, find n.
18
1-period, find FV
You need to borrow $1,700 to buy a
computer and a 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)
19
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)
20
1-period, find r
If the bank promises to give you $28,400
after one year if you deposit $27,000
today, what is the annual interest rate
that the bank offers?
Use r = (FV/PV) – 1
21
2-period, find FV
You plan to lend $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 that time?
Use FV = PV(1+r)2
22
2-period, find PV
You are offered a chance to buy into an
investment that promises to pay you $28,650
after two years. If your required rate of return
is 12 percent, what is the maximum price that
you would pay for this investment?
Use PV = FV/(1+r)2
23
2-period, find r
You are offered an investment opportunity
which requires you to pay $31,500 today and
promises to give you $39,700 at the end of the
second year. What is the rate of return on this
investment?
24
Value additivity principle
You will make two investments. The first
investment will give you $5,500 after one year
and the second investment will give you
$12,100 after one year. If your required rate of
return for both investments is 10 percent, what
is the present value of your investments?
25
Value additivity principle
This problem illustrates the
value additivity principle
which says:
You can add values only when they are scaled
at the SAME point in time.
26
2-period, 2 cash flows, find FV
You deposit $5,000 in a bank account today.
You will make another deposit of $4,000 into
the account at the end of the first year. If the
bank pays interest at 6 percent compounded
annually, how much will you have in your
account after two years?
27
Time line: visualizing cash flows
1. For a TVM problem with 2 or more periods, a
time line helps you to understand the problem
better.
2. A time line is a graphical representation of a
TVM problem. For the previous problem, the
time line would look like this:
-$ 5,000
-$ 4,000
?
t=0
t=1
t=2
28
2-period, 2 cash flows, find PV
You want to withdraw $3,200 from your
account at the end of the first year and $7,300
at the end of the second year. How much
should you deposit in your account today so
that you can make these withdrawals? Your
account pays 6 percent p.a.
Draw a time line to help you understand the question.
29
Summary
1.
2.
3.
4.
5.
6.
Time value of money
Real vs. nominal interest rate
1-period problems (find FV, PV, r)
2-period problems (find FV, PV, r)
Value additivity principle
2-period, 2 cash flows problems
(find FV, PV)
30