Money time value definition p1

TIME VALUE

www.antonioalcocer.com@antonioalcocer

www.antonioalcocer.com

PRESENTS

4. Company valuation methods

1. Time value of money definition

2. Compound interest & CAGR

3. Investment appraisal for economic feasibility

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


“Money can be investedtoday in different options

with a different returnovetime”

Opportunity cost


($100 in t0=1990)

CAGR= Compound Annual Growing RateApple 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%

($398 in t21=2011)

($100 in t21=2011)

($0 in t21=2011)

OPTION 1

OPTION 2

OPTION 3


TIME VALUE OF MONEYMEANS OPPORTUNITY COSTMEANINGTHAT IN FINANCE WE TALKABOUT THEPAIR:

($,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?


VF=V0 x (1+i)^t

Compound interest formula

Two cash-flows are equal in time at a given interest rat eVF: Future value of the cash-flow

V0: Present or actual value of the cash-flowi: Compound annual interest or growing rate

t: Time between both cash-flowswww.antonioalcocer.com

Also known as “CAGR”

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

CAGR = ((VF/VO)^(1/t))-1


…and moving cash-flows to the futureis called:

CAPITALISATIO

N

VF=V0 x (1+i)^twww.antonioalcocer.com

VOIc%

Vo=VF / (1+i)^t

Vf

DISCOUNTING

…and moving cash-flows from the futureis called:


And what about simple interest?


TIME VALUE OF MONEYCompound interest - Ic

VF=V0 x (1+i*t)

Simple interest - Is

VF=V0 x (1+i)^t

“Interests earnt are not re-invested”

“Interests earnt are re-invested”



Yield[annual]=12%

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

IsBy convention yields are provided in a yearly basis IF NOT SPECIFIED

NO REINVESTMENT REINVESTMENT

Ic

EXAMPLE 1

Banking deposit3-years time10% 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

1 2 3

-€1000

+€1000+€100+€100+€100

VF = 1000*(1+10%*3) =

Is

Ic1 2 3

-€1000

(+€100) (+€110)

+€1000+€100+€110+€121

VF = 1000*(1+10%)^3 =

Calculations made for a 3-years bank deposit with a 10% annual interest rate and €1000 initial investmentAs 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 interestSimple interest is used if the interests earnt are not reinvested. Compound interest is used if interests are reinvestedAs 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


€1331

€1300

(+€121)

(+€100) (+€100) (+€100)

EXAMPLE 2

Banking deposit2-years time10% annual interest rateBi-monthly re-investment of interests4 semestersInitial investment: €1.000

Ic

1s 2s 3s

-€1000

(+€63.6) (+€67.4)

+€1000+€60+€63.6+€67.4+€71.4

VF = 1000*(1+6%)^4 =


€1263

(+€71.4)

4s

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

(+€60)

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

CAGR = ((VF/VO)^(1/t))-1=((1263/1000)^(1/2))-1

12.38%

but as a general rule in finance we assume…


…reinvestment of interests& use compound interest!


Compound interest’s power it’s oneof the strongest powers on EarthAlbert Einstein


t0=30

Vf$337.494

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

Vo $30.000

t35=65

S&P500 CAGR = 7.16% in the period 01/02/1950-01/02/201 0VF=30.000*(1+7.16%)^35=Vf*(1+i)^t www.antonioalcocer.com

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


t0=30

Vf$19.338.296

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

Vo $30.000

t35=65

Warren Buffet’s Berkshire Hathway Investment Fund CAGR = 20.3% in the period 1965-2009 year endingVF=30.000*(1+20.3%)^35=Vf*(1+i)^t www.antonioalcocer.com

I rather go for Apples

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

t0=30

Vf$42.812.697

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

Vo $30.000

t35=65

Apple shares’ CAGR = 23.06% in the period 27 August 19 85 – 27 August 2011VF=30.000*(1+23.06%)^35=Vf*(1+i)^t www.antonioalcocer.com

*!$%?

REDBUBBLE.COM

$42.812.697?


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)^twww.antonioalcocer.com

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


Yes, because of INFLATION!

CAGR Consumer Price Index (inflation) in the period 192 0-2005 = 2.7%

CPI CAGR=2.7%


$42.8 millionsin t=35 yearswould be$16.85 millionstoday at a 2,7%

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


So you better assume

your purchasingpower todaywould be

$16.85 millionrather than

$42.8 million


Yes, if you would have invested in Apples

HAVE YOU?www.antonioalcocer.com

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

www.antonioalcocer.com@antonioalcocer

Money time value definition p1

Business

Transcript of Money time value definition p1