Transcript ch_5_fin_200.pptx

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Introduction to valuation:
The time value of money
CH 5
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Introduction
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One of the basic problems faced by the financial manager is
how to determine the value today of cash flow expected in
the future.
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Time value of money: is refer to the fact that a dollar in hand
today is worth more than a dollar promised at some time in
the future. The reason for this is that you could earn interest
while you waited; so a dollar today would grow to more than
a dollar later.
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5.1 future value and compounding
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future value: refer to the amount of money an investment will
grow to over some period of time (one or more period) at
some given interest rate.
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Investing for a single period
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Suppose you invest $100 in a saving account that pay 10%
interest per year, how much will you have in one year?
You will have $110, this $110 is equal to yours original principal
plus $10 in interest that you earn 100+(100*10%)=$110. this is
the future value of $100.
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In general if you invest for one period at an interest rate of ,
your investment will grow to (1+r) per dollar invested.
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in our example: r is 10%, so yours investment grows tp
(1+0.10)=1.1 dollar per dollar invested. You invest $100 so
you ended up with $100*(1.1)=$110.
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Investing for more tan one period
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Going back to our $100 investment, what will you have
after two years, assuming the interest rate doesn’t
change?
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If you leave the entire $110 in the bank, you will earn
$110*0.10= $11in interest during the second years.
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So you will have a total of $110+11=$121.
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This $121 is the future value of $100 in two years.
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You will end up with $1.10 for every dollar invested, or
$110*1.1=$121
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Investing for more tan one period
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This process of leaving your money and any accumulated
interest in an investment for more than one period, thereby
reinvesting the interest is called compounding.
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Compounding the interest means earning interest on
interest.
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So we called the result compound interest.
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With simple interest, the interest is not reinvested, so interest
is earned each period only on the original principal.
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Investing for more tan one period
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Future value = $1 * (1+r)t
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The growth of your $100 for 5 years
year
Beginning
amount
Simple
interest
Compoun
d interest
Total
interest
earned
Ending
amount
1
$100
$10
$0
$10
$110
2
$110
$10
$1
$11
$121
3
$121
$10
$2.1
$12.1
$133.1
4
$133.1
$10
$3.31
$13.31
$146.41
5
$146.41
$10
4.64
$14.64
$161.05
$50
$11.05
61.05
total
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Or $100*(1+0.10)5= $161.05
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Future value, simple interest, and compound interest
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rates
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example
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The TICO corporation currently pays a cash dividends of
$5 per share. You believe the dividends will be increased
by 4% each year indefinitely. How big will the dividends
be in eight years?
Future vale = $5 * 1.048 =
= $5 * 1.3686= $6.84
The dividends will grow by $1.84 over the period.
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Present value and discounted
 Suppose
you need to have $10,000 in 10 years, and
you can earn 6.5% on your money. How much do
you have to invest today to reach your goal?
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The single period
Present value: is the current value of future cash flow
discounted at the appropriate discount rate.
Present value * (1+r) t = future value
Present value = future value/ (1+r) t
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Instead of compounding the money forward into the future,
we discount it back to the present.
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Discount: calculate the present value of some future amount
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example
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Suppose you need $400 to buy textbook next year. You can
earn 7% on your money. Hoe much do you have to put up
today?
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Present value = $400 * (1/1.07) = $373.83
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Present value for multiple period
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Suppose you need to have $1,000 in two year. If you can earn
7%, how much do you have to invest to make sure you have
the $1,000 when you need it? In other words, what is the
percentage value of $1,000 in two year if the relevant rate
7%?
$1,000 = PV * 1.07 * 1.07
$1,000 = PV * 1.072
$1,000 = PV * 1.1449
PV = $1,000/ 1.1449 = $873.44
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Calculating present value is quite similar to calculating future
value.
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PV = $1 * [ 1/ (1+r) t]
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The quantity [1/(1+r) t], goes by several different names.
Because it’s used to discount a future cash flow, it is often
called a discount factor. This quantity also called present
value interest factor or just present value factor.
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The rate used in the calculation is often called discount rate.
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Calculating the present value of a future cash flow determine
its worth today is commonly called discounted cash flow
(DCF) valuation.
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Present value of $1 for different
periods and rates
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Present Value – Important
Relationship
 For
a given interest rate – the longer the
time period, the lower the present value
 For
a given time period – the higher the
interest rate, the smaller the present value
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5.3 more about present and future
value
There is a simple relationship between
present and future cash flow.
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Present versus future value
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What we called the present value factor is just the reciprocal of
(that is, 1 dividends by) the future value factors
Future value factor = (1+r) t
Present value factor = 1/(1+r) t
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It is easy to calculate future value first.
PV * (1+r) t = FV
PV = FV / (1+r) t = FV / [1/(1+r) t]
equation
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PV: present value
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FV: future value
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T: period of time.
basic present value
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example
Your company proposes to buy an assets for $335. this
investment is very safe. You would sell off the assets in
three years for $400. you know you could invest the $335
elsewhere a1 10% with very little risk.
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What do you think of the proposed investment?
if you invest this $335 in elsewhere at 10%, you will get
FV = $335 * (1+0.10)3
FV= $445.89
$445 in elsewhere is higher than $400 in your company
proposed. So your company proposed is not a good
investment.
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Determine the discount rate
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We need to determine what discount rate is implicit in an
investment. We can do this by looking to the basic present
value equation:
PV = FV / (1+r) t
FV = PV(1 + r)t
r = (FV / PV)1/t – 1
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You are considering a one-year investment. If you put up
$1,250, you will get back $1,350. what rate is this investment
paying?
You are getting $100 in addition to your $1,250. this implicit
rate on thus investment is $100/1,250 = 8%
PV = FV / (1+r)1
1+r = $1,350 / 1,250 = 1.08
r = 0.08
r = 8%
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We need to calculate r. there are three ways we could
use:
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Use a financial calculators.
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Solve the equation for 1+r.
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Use a future value table.
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Finding a number of period
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Suppose we are interested in purchase an assets that cost
$50,000. we currently have $25.000. if you can earn 12% on
this $25,000, how long until we have the $50,000?
PV = FV / (1+r) t
$25,000 = $50,000 / (1+0.12)t
$50,000/$25,000= 1.12t=2
t= 2
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You’ve been saving up to buy the Godot company. The total cost
will be $10 million. You currently have about $2.3 million. If you
can earn 5% on your money, how long will you have to wait? At
16% how long you have to wait?
$2.3 million = $10 million / (1+0.05)t
1.05t = 4.35
t= 30 years
Or use this formula to find t= ln (fv/pv) / ln 1+r
At 5% you will have to wait a long time.
At 16% things are little better.
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Review Questions
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Luis is going to receive $20,000 six years from now. Soo Lee is going to receive $20,000
nine years from now. Which one of the following statements is correct if both Luis and
Soo Lee apply a 7 percent discount rate to these amounts?
A. The present values of Luis and Soo Lee's monies are equal.
B. In future dollars, Soo Lee's money is worth more than Luis' money.
C. In today's dollars, Luis' money is worth more than Soo Lee's.
D. Twenty years from now, the value of Luis' money will be equal to the value of Soo
Lee's money.
E. Soo Lee's money is worth more than Luis' money given the 7 percent discount rate.
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Gerold invested $6,200 in an account that pays 5 percent simple interest. How much
money will he have at the end of ten years?
A. $8,710
B. $9,000
C. $9,300
D. $9,678
E. $10,099
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Review Questions
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You invested $1,650 in an account that pays 5 percent simple
interest. How much more could you have earned over a 20-year
period if the interest had compounded annually?
A. $849.22
B. $930.11
C. $982.19
D. $1,021.15
E. $1,077.94
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Today, you earn a salary of $36,000. What will be your annual
salary twelve years from now if you earn annual raises of 3.6
percent?
A. $55,032.54
B. $57,414.06
C. $58,235.24
D. $59,122.08
E. $59,360.45
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Review Questions
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. One year ago, you invested $1,800. Today it is worth $1,924.62.
What rate of interest did you earn?
A. 6.59 percent
B. 6.67 percent
C. 6.88 percent
D. 6.92 percent
E. 7.01 percent
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. Some time ago, Julie purchased eleven acres of land costing
$36,900. Today, that land is valued at $214,800. How long has she
owned this land if the price of the land has been increasing at
10.5 percent per year?
A. 13.33 years
B. 16.98 years
C. 17.64 years
D. 19.29 years
E. 21.08 years