Money time value definition p1

TIME
VALUE
www.antonioalcocer.com
@antonioalcocer


4. Company valuation methods

3. Investment appraisal for economic feasibility

PRESENTS

2. Compound interest & CAGR

1. Time value of money definition

Why ($100, today) are not equivalent to
($100, when I was younger)?


TIME VALUE
OF
MONEY


*!$%?


TIME VALUE OF MONEY
TIME VALUE
OF
MONEY TIME VALUE OF MONEY
OPPORTUNITY COST


Opportunity cost

“Money can be invested
today in different options
with a different return
ovetime”


OPTION 1
($398 in t21=2011)

OPTION 2

($100 in t21=2011)

($100 in t0=1990) OPTION 3
($0 in t21=2011)

CAGR= Compound Annual Growing Rate
Apple share price: 01/08/1990: $9.96 – 01/08/2011: $396.75 – CAGR: 19.17%
Money at home below my pillow: 01/08/1990: $100 – 01/08/2011: $100 – CAGR: 0%
Money placed at a default subprime product: 01/08/1990: $100 – 01/08/2011: $0 – CAGR: -100%

TIME VALUE OF MONEY
MEANS OPPORTUNITY COST
MEANING
THAT IN FINANCE
WE TALK
ABOUT
THE
PAIR:

($,time)

That is why different cash-flows at different moments in time
cannot be operated unless moved to the same point in time


How can be
cash-flows
moved
in time?

Compound interest formula
VF=V0 x (1+i)^t

Two cash-flows are equal in time at a given interest rate
VF: Future value of the cash-flow
V0: Present or actual value of the cash-flow
i: Compound annual interest or growing rate
t: Time between both cash-flows

CAGR = ((V /V )^(1/t))-1
F O

R”
“CAG
n as
know
Also

CAGR=Compound Annual Growing Rate
t in years so CAGR on a yearly basis

…and moving cash-flows to the future
is called:

N
T IO
SA
LI
TA
PI
C A
VF=V0 x (1+i)^t

…and moving cash-flows from the future
is called:

Ic%
VO Vf
DISCOUNTING
Vo=VF / (1+i)^t


And what about simple interest?

Simple interest - Is
VF=V0 x (1+i*t)
“Interests earnt are not re-invested”

Compound interest - Ic TIME VALUE OF MONEY

VF=V0 x (1+i)^t
“Interests earnt are re-invested”

Yield =12%
[annual]

I12=1% I6=2% I4=3% I2=6%
MONTHLY BI-MONTHLY QUARTERLY SEMI-ANNUALLY

NO REINVESTMENT REINVESTMENT

Is Ic
By convention yields are provided in a yearly basis IF NOT SPECIFIED www.antonioalcocer.com

EXAMPLE 1

Banking deposit
3-years time
10% annual interest rate (*)
Initial investment: €1.000

(*) The 10% interest rate is an annual yield. It depends if there are reinvestment of interests, using compound interest.
In the case there are not re-investment of interests we use simple interest formula

+€1000+€100+€100+€100

Is (+€100) (+€100) (+€100)

1 2 3

VF = 1000*(1+10%*3) = €1300
-€1000

+€1000+€100+€110+€121

Ic (+€100) (+€110) (+€121)

1 2 3

VF = 1000*(1+10%)^3 = €1331
-€1000

Calculations made for a 3-years bank deposit with a 10% annual interest rate and €1000 initial investment
As you can see due to “time value of money”, and if interests are reinvested or not reinvested; €1000 at t0 are equal to €1331 at a10% compound interest rate or €1300 at a 10% simple interest
Simple interest is used if the interests earnt are not reinvested. Compound interest is used if interests are reinvested
As general rule, investments lasting less than 1 year use simple interest and investments lasting>=1 year use compound interest but which one to use if determined by the existance or not of the re-investment of the interests

EXAMPLE 2

Banking deposit
2-years time
10% annual interest rate
Bi-monthly re-investment of interests
4 semesters
Initial investment: €1.000

Ic
12% ANNUAL YIELD = 12% / 2 = 6% BI-MONTHLY YIELD

CAGR = ((V /V )^(1/t))-1=((1263/1000)^(1/2))-1
F O +€1000+€60+€63.6+€67.4+€71.4

12.38%
(+€60) (+€63.6) (+€67.4) (+€71.4)

1s 2s 3s 4s

VF = 1000*(1+6%)^4 = €1263
-€1000

Annual yield is used to obtain the bi-monthly yield, and then apply compound interest formula for calculations in order to obtain €1263
But this investment has not a compound annual growing rate (CAGR)=12% due to the bi-monthly reinvestment. www.antonioalcocer.com

but as a general rule in finance we assume…



…reinvestment of interests
& use compound interest!


Compound interest’s power it’s one
of the strongest powers on Earth
Albert Einstein

Example 1: Investment in the S&P500 – CAGR: 7.16%

Vf
$337.494

Vo
$30.000

t0=30 t35=65

S&P500 CAGR = 7.16% in the period 01/02/1950-01/02/2010
VF=30.000*(1+7.16%)^35=Vf*(1+i)^t www.antonioalcocer.com

You better would
have invested in
Berkshire Hathway
- Oracle of Omaha’s word -


Example 2: Investment in Berkshire Hat. – CAGR: 20.3%

Vf
$19.338.296

Vo
$30.000

t0=30 t35=65

Warren Buffet’s Berkshire Hathway Investment Fund CAGR = 20.3% in the period 1965-2009 year ending

I rather go for Apples

www.antonioalcocer.com - Get back soon Steve! -

Example 3: Investment in Apple shares – CAGR: 23.06%

Vf
$42.812.697

Vo
$30.000

t0=30 t35=65

Apple shares’ CAGR = 23.06% in the period 27 August 1985 – 27 August 2011

$42.812.697?

*!$%?

www.antonioalcocer.com REDBUBBLE.COM

Yes, $42.8 million

But in 35-years time

& we know about time value of money

& the pair ($,t)

& moving cash-flows in time

& discounting cash-flows

Using Vo=Vf / (1+i)^t

So you are telling me that today I would not be
worthy $42.8 million?


Yes, because of INFLATION!

CPI CAGR=2.7%

CAGR Consumer Price Index (inflation) in the period 1920-2005 = 2.7%


$42.8 millions
in t=35 years
would be
$16.85 millions
today at a 2,7%

Vo=Vf/(1+i)^35=42.8/(1+2.7%)^35=$16.85 millions

So you better assume

your purchasing
power today
would be

$16.85 million
rather than

$42.8 million


Yes, if you would have invested in Apples
HAVE YOU?

Thank you very much for you time!
Any comment, suggestion is more than welcome:
@antonioalcocer

Money time value definition p1

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