Money time value definition p1
-
Upload
antonio-alcocer -
Category
Business
-
view
1.988 -
download
2
description
Transcript of Money time value definition p1
![Page 1: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/1.jpg)
TIME VALUE
www.antonioalcocer.com@antonioalcocer
![Page 2: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/2.jpg)
www.antonioalcocer.com
PRESENTS
4. Company valuation methods
1. Time value of money definition
2. Compound interest & CAGR
3. Investment appraisal for economic feasibility
![Page 3: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/3.jpg)
Why ($100, today) are not equivalent to($100, when I was younger)?
www.antonioalcocer.com
![Page 4: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/4.jpg)
TIME VALUE OF
MONEY
www.antonioalcocer.com
![Page 5: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/5.jpg)
*!$%?
www.antonioalcocer.com
![Page 6: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/6.jpg)
TIME VALUE OF
MONEY
TIME VALUE OF MONEY
TIME VALUE OF MONEY
OPPORTUNITY COST
www.antonioalcocer.com
![Page 7: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/7.jpg)
“Money can be investedtoday in different options
with a different returnovetime”
Opportunity cost
www.antonioalcocer.com
![Page 8: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/8.jpg)
($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)
($0 in t21=2011)
OPTION 1
OPTION 2
OPTION 3
www.antonioalcocer.com
![Page 9: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/9.jpg)
TIME VALUE OF MONEYMEANS OPPORTUNITY COSTMEANINGTHAT IN FINANCE WE TALKABOUT THEPAIR:
($,time)
That is why different cash-flows at different moments in time cannot be operated unless moved to the same point in time
www.antonioalcocer.com
![Page 10: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/10.jpg)
How can be cash-flows
moved in time?
www.antonioalcocer.com
![Page 11: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/11.jpg)
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
![Page 12: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/12.jpg)
Also known as “CAGR”
CAGR=Compound Annual Growing Ratet in years so CAGR on a yearly basis
CAGR = ((VF/VO)^(1/t))-1
www.antonioalcocer.com
![Page 13: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/13.jpg)
…and moving cash-flows to the futureis called:
CAPITALISATIO
N
VF=V0 x (1+i)^twww.antonioalcocer.com
![Page 14: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/14.jpg)
VOIc%
Vo=VF / (1+i)^t
Vf
DISCOUNTING
…and moving cash-flows from the futureis called:
www.antonioalcocer.com
![Page 15: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/15.jpg)
And what about simple interest?
www.antonioalcocer.com
![Page 16: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/16.jpg)
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”
www.antonioalcocer.com
![Page 17: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/17.jpg)
www.antonioalcocer.com
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
![Page 18: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/18.jpg)
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
![Page 19: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/19.jpg)
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
www.antonioalcocer.com
€1331
€1300
(+€121)
(+€100) (+€100) (+€100)
![Page 20: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/20.jpg)
EXAMPLE 2
Banking deposit2-years time10% annual interest rateBi-monthly re-investment of interests4 semestersInitial investment: €1.000
![Page 21: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/21.jpg)
Ic
1s 2s 3s
-€1000
(+€63.6) (+€67.4)
+€1000+€60+€63.6+€67.4+€71.4
VF = 1000*(1+6%)^4 =
www.antonioalcocer.com
€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%
![Page 22: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/22.jpg)
but as a general rule in finance we assume…
www.antonioalcocer.com
![Page 23: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/23.jpg)
…reinvestment of interests& use compound interest!
www.antonioalcocer.com
![Page 24: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/24.jpg)
www.antonioalcocer.com
![Page 25: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/25.jpg)
Compound interest’s power it’s oneof the strongest powers on EarthAlbert Einstein
www.antonioalcocer.com
![Page 26: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/26.jpg)
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
![Page 27: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/27.jpg)
You better wouldhave invested in Berkshire Hathway- Oracle of Omaha’s word -
www.antonioalcocer.com
![Page 28: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/28.jpg)
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
![Page 29: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/29.jpg)
I rather go for Apples
- Get back soon Steve! -www.antonioalcocer.com
![Page 30: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/30.jpg)
t0=30
Vf$42.812.697
Example 3 : Investment in Apple shares – CAGR: 23.06%
Vo $30.000
t35=65
Apple shares’ CAGR = 23.06% in the period 27 August 19 85 – 27 August 2011VF=30.000*(1+23.06%)^35=Vf*(1+i)^t www.antonioalcocer.com
![Page 31: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/31.jpg)
*!$%?
REDBUBBLE.COM
$42.812.697?
www.antonioalcocer.com
![Page 32: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/32.jpg)
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
![Page 33: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/33.jpg)
So you are telling me that today I would not beworthy $42.8 million?
www.antonioalcocer.com
![Page 34: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/34.jpg)
Yes, because of INFLATION!
CAGR Consumer Price Index (inflation) in the period 192 0-2005 = 2.7%
CPI CAGR=2.7%
www.antonioalcocer.com
![Page 35: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/35.jpg)
$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
www.antonioalcocer.com
![Page 36: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/36.jpg)
So you better assume
your purchasingpower todaywould be
$16.85 millionrather than
$42.8 million
www.antonioalcocer.com
![Page 37: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/37.jpg)
Yes, if you would have invested in Apples
HAVE YOU?www.antonioalcocer.com
![Page 38: Money time value definition p1](https://reader034.fdocuments.us/reader034/viewer/2022051514/549263acb47959474d8b45d4/html5/thumbnails/38.jpg)
Thank you very much for you time!Any comment, suggestion is more than welcome:
www.antonioalcocer.com@antonioalcocer