Chapter 2.Time Value of Money ppt
-
Upload
zahramirzayeva -
Category
Economy & Finance
-
view
259 -
download
5
Transcript of Chapter 2.Time Value of Money ppt
![Page 1: Chapter 2.Time Value of Money ppt](https://reader034.fdocuments.net/reader034/viewer/2022051318/58ed7b761a28abf64e8b4695/html5/thumbnails/1.jpg)
Time Value of Money
![Page 2: Chapter 2.Time Value of Money ppt](https://reader034.fdocuments.net/reader034/viewer/2022051318/58ed7b761a28abf64e8b4695/html5/thumbnails/2.jpg)
Section 1 Basic Ideas of Time Value of
Money Concept
2
![Page 3: Chapter 2.Time Value of Money ppt](https://reader034.fdocuments.net/reader034/viewer/2022051318/58ed7b761a28abf64e8b4695/html5/thumbnails/3.jpg)
The Core Question of Finance
Congratulations!!! You have won a cash prize! There are two optional payment schedules: A - receive $100,000 now B - receive $100,000 in five years. Which option would you choose?
3
![Page 4: Chapter 2.Time Value of Money ppt](https://reader034.fdocuments.net/reader034/viewer/2022051318/58ed7b761a28abf64e8b4695/html5/thumbnails/4.jpg)
Time Value of Money Concept
In simple termsthe concept implies that money today is always better than money tomorrow.
4
![Page 5: Chapter 2.Time Value of Money ppt](https://reader034.fdocuments.net/reader034/viewer/2022051318/58ed7b761a28abf64e8b4695/html5/thumbnails/5.jpg)
Why Time Value of Money Exists?
Risk and Uncertainty-future always involves some risk, especially in respect to cash inflows of company as they are highly uncontrollable;
Inflation-in an inflationary economy a dollar today has always more purchasing power in compared to a dollar some point in future;
Consumption Preference- individuals generally prefer current consumption to a future one;
Investment Opportunities-an investor can profitably use money received today by investing it immediately;
5
![Page 6: Chapter 2.Time Value of Money ppt](https://reader034.fdocuments.net/reader034/viewer/2022051318/58ed7b761a28abf64e8b4695/html5/thumbnails/6.jpg)
Allows investors to adjust cash flows for the passage of time;
It’s an integral part of Capital Budgeting Processes;
Applied in present and future value calculations;
6
![Page 7: Chapter 2.Time Value of Money ppt](https://reader034.fdocuments.net/reader034/viewer/2022051318/58ed7b761a28abf64e8b4695/html5/thumbnails/7.jpg)
Section 2Interest Rates
7
![Page 8: Chapter 2.Time Value of Money ppt](https://reader034.fdocuments.net/reader034/viewer/2022051318/58ed7b761a28abf64e8b4695/html5/thumbnails/8.jpg)
8
![Page 9: Chapter 2.Time Value of Money ppt](https://reader034.fdocuments.net/reader034/viewer/2022051318/58ed7b761a28abf64e8b4695/html5/thumbnails/9.jpg)
FormulaFormula SI = P0(i)(n)
SI: Simple InterestP0: Deposit today (t=0)
i: Interest Rate per Periodn: Number of Time Periods
9
![Page 10: Chapter 2.Time Value of Money ppt](https://reader034.fdocuments.net/reader034/viewer/2022051318/58ed7b761a28abf64e8b4695/html5/thumbnails/10.jpg)
SI = P0(i)(n)= $1,000(.07)(2)= $140$140
Simple Interest Example
Assume that you deposit $1,000 in an account earning 7% simple interest for 2 years. What is the accumulated interest at the end of the 2nd year?
10
![Page 11: Chapter 2.Time Value of Money ppt](https://reader034.fdocuments.net/reader034/viewer/2022051318/58ed7b761a28abf64e8b4695/html5/thumbnails/11.jpg)
Compound Interest Yields higher return forinvestors or deposit holders; Cumbersome for borrowers; Makes borrowers to be more adhere to their payment schedule,for example.credit cards;
11
![Page 12: Chapter 2.Time Value of Money ppt](https://reader034.fdocuments.net/reader034/viewer/2022051318/58ed7b761a28abf64e8b4695/html5/thumbnails/12.jpg)
Assume that you deposit $1,000$1,000 at a compound interest rate of 7% for 2 2
yearsyears.
Compound Interest Example
0 1 22
$1,000$1,000FVFV22
7%
12
![Page 13: Chapter 2.Time Value of Money ppt](https://reader034.fdocuments.net/reader034/viewer/2022051318/58ed7b761a28abf64e8b4695/html5/thumbnails/13.jpg)
At the end of first yearPP00 (1+i)1 = $1,000x$1,000x (1.07)
= $1,070$1,070Compound Interest
You earned $70 interest on your $1,000 deposit over the first year.
This is the same amount of interest you would earn under simple interest.
Compound Interest Example
13
![Page 14: Chapter 2.Time Value of Money ppt](https://reader034.fdocuments.net/reader034/viewer/2022051318/58ed7b761a28abf64e8b4695/html5/thumbnails/14.jpg)
At the end of first yearAt the end of first year = $1,000$1,000 (1.07) = $1,070$1,070
At the end of second yearAt the end of second year = 1070 (1+i)1 1070x(1.07)
$1,144.90$1,144.90You earned an EXTRA $4.90$4.90 in Year 2 with
compound over simple interest.
Compound Interest Example(cont.)
14
![Page 15: Chapter 2.Time Value of Money ppt](https://reader034.fdocuments.net/reader034/viewer/2022051318/58ed7b761a28abf64e8b4695/html5/thumbnails/15.jpg)
Section 3Present Value vs Future
Value
15
![Page 16: Chapter 2.Time Value of Money ppt](https://reader034.fdocuments.net/reader034/viewer/2022051318/58ed7b761a28abf64e8b4695/html5/thumbnails/16.jpg)
Valuation Concepts
16
![Page 17: Chapter 2.Time Value of Money ppt](https://reader034.fdocuments.net/reader034/viewer/2022051318/58ed7b761a28abf64e8b4695/html5/thumbnails/17.jpg)
Future Value
The value at some future time of a present amount of money, or a series of payments evaluated at a given interest rate;
The interest earned on the initial principal amount becomes a part of the principal at the end of the compounding period;
17
![Page 18: Chapter 2.Time Value of Money ppt](https://reader034.fdocuments.net/reader034/viewer/2022051318/58ed7b761a28abf64e8b4695/html5/thumbnails/18.jpg)
Future Value Example Problem
Suppose you invest $1000 for three years in a saving account that pays 10 % interest per year. If you let your interest income be reinvested, your investment will grow as follows:First year : Principal at the beginning $1000 Interest for the year ($1,000 × 0.10) $100 Principal at the end $1,100 Second year : Principal at the beginning $1,100 Interest for the year ($1,100 × 0.10) $110 Principal at the end $1,210Third year : Principal at the beginning $1,210 Interest for the year ($1210 × 0.10) $121 Principal at the end $1,331
18
![Page 19: Chapter 2.Time Value of Money ppt](https://reader034.fdocuments.net/reader034/viewer/2022051318/58ed7b761a28abf64e8b4695/html5/thumbnails/19.jpg)
FormulaFormula FV = P0(1+i)n
FV: Future ValueP0: Deposit today (t=0)
i: Interest Rate per Periodn: Number of Time Periods
In the previous example FV=1000(1+0.1)3=1,331
19
![Page 20: Chapter 2.Time Value of Money ppt](https://reader034.fdocuments.net/reader034/viewer/2022051318/58ed7b761a28abf64e8b4695/html5/thumbnails/20.jpg)
Double Your Money!We will use
the““Rule-of-72Rule-of-72””
Quick! How long does it take to
double $5,000 at a compound rate of
12% per year (approx.)?
20
![Page 21: Chapter 2.Time Value of Money ppt](https://reader034.fdocuments.net/reader034/viewer/2022051318/58ed7b761a28abf64e8b4695/html5/thumbnails/21.jpg)
Approx. Years to Double = 7272 / i%
7272 / 12% = 6 Years6 Years[Actual Time is 6.12 Years]
The “Rule-of-72”
Quick! How long does it take to double $5,000 at a compound rate of
12% per year (approx.)?
21
![Page 22: Chapter 2.Time Value of Money ppt](https://reader034.fdocuments.net/reader034/viewer/2022051318/58ed7b761a28abf64e8b4695/html5/thumbnails/22.jpg)
Present ValueWhich one would you prefer assuming that the rate is 8%?a)$1000 today or,b)$2000 10 years later?
22
To answer this question we have to express $2000 in today’s money. PV=FV/(1+i)n
$926=2000/(1+0.8)10
![Page 23: Chapter 2.Time Value of Money ppt](https://reader034.fdocuments.net/reader034/viewer/2022051318/58ed7b761a28abf64e8b4695/html5/thumbnails/23.jpg)
Types of Annuities
• Ordinary AnnuityOrdinary Annuity: Payments or receipts occur at the end of each period(coupon);
• Annuity DueAnnuity Due: Payments or receipts occur at the beginning of each period(rent);
An AnnuityAn Annuity represents a series of equal payments (or receipts) occurring over a specified number of equidistant periods.
23
![Page 24: Chapter 2.Time Value of Money ppt](https://reader034.fdocuments.net/reader034/viewer/2022051318/58ed7b761a28abf64e8b4695/html5/thumbnails/24.jpg)
Parts of an Annuity
0 1 2 3
$100 $100 $100
(Ordinary Annuity)EndEnd ofPeriod 1
EndEnd ofPeriod 2
Today EqualEqual Cash Flows Each 1 Period Apart
EndEnd ofPeriod 3
24
![Page 25: Chapter 2.Time Value of Money ppt](https://reader034.fdocuments.net/reader034/viewer/2022051318/58ed7b761a28abf64e8b4695/html5/thumbnails/25.jpg)
Parts of an Annuity
0 1 2 3
$100 $100 $100
(Annuity Due)BeginningBeginning ofPeriod 1
BeginningBeginning ofPeriod 2
Today EqualEqual Cash Flows Each 1 Period Apart
BeginningBeginning ofPeriod 3
25
![Page 26: Chapter 2.Time Value of Money ppt](https://reader034.fdocuments.net/reader034/viewer/2022051318/58ed7b761a28abf64e8b4695/html5/thumbnails/26.jpg)
FVAFVA33 = $1,000(1.07)2 + $1,000(1.07)1 + $1,000(1.07)0
= $1,145 + $1,070 + $1,000 = $3,215 or R(FVIFA$3,215 or R(FVIFAi,ni,n))
Example of anOrdinary Annuity -- FVA
$1,000 $1,000 $1,000
0 1 2 3 3 4
$3,215 = FVA$3,215 = FVA33
7%
$1,070
$1,145
Cash flows occur at the end of the period
26
![Page 27: Chapter 2.Time Value of Money ppt](https://reader034.fdocuments.net/reader034/viewer/2022051318/58ed7b761a28abf64e8b4695/html5/thumbnails/27.jpg)
PVAPVA33 = $1,000/(1.07)1 + $1,000/(1.07)2 + $1,000/(1.07)3
= $934.58 + $873.44 + $816.30 = $2,624.32 or R(PVIFA$2,624.32 or R(PVIFAi,ni,n))
Example of anOrdinary Annuity -- PVA
$1,000 $1,000 $1,000
0 1 2 3 3 4
$2,624.32 = PVA$2,624.32 = PVA33
7%
$934.58$873.44 $816.30
Cash flows occur at the end of the period
27
![Page 28: Chapter 2.Time Value of Money ppt](https://reader034.fdocuments.net/reader034/viewer/2022051318/58ed7b761a28abf64e8b4695/html5/thumbnails/28.jpg)
FVADFVAD33 = $1,000(1.07)3 + $1,000(1.07)2 + $1,000(1.07)1
= $1,225 + $1,145 + $1,070 = $3,440 or R(FVIFA$3,440 or R(FVIFA i,ni,n)(1+i))(1+i)
Example of anAnnuity Due -- FVAD
$1,000 $1,000 $1,000 $1,070
0 1 2 3 3 4
$3,440 = FVAD$3,440 = FVAD33
7%
$1,225$1,145
Cash flows occur at the beginning of the period
28
![Page 29: Chapter 2.Time Value of Money ppt](https://reader034.fdocuments.net/reader034/viewer/2022051318/58ed7b761a28abf64e8b4695/html5/thumbnails/29.jpg)
PVADPVADnn = $1,000/(1.07)0 + $1,000/(1.07)1 + $1,000/(1.07)2 = $2,808.02 $2,808.02
or or R(PVIFAR(PVIFA’,n-1’,n-1+1)+1)
Example of anAnnuity Due -- PVAD
$1,000.00 $1,000 $1,000
0 1 2 3 3 4
$2,808.02 $2,808.02 = PVADPVADnn
7%
$ 934.58$ 873.44
Cash flows occur at the beginning of the period
29
![Page 30: Chapter 2.Time Value of Money ppt](https://reader034.fdocuments.net/reader034/viewer/2022051318/58ed7b761a28abf64e8b4695/html5/thumbnails/30.jpg)
Julie Miller will receive the set of cash flows below. What is the Present Value Present Value at a discount rate of 10%10%.
Mixed Flows Example
0 1 2 3 4 55
$600 $600 $400 $400 $100$600 $600 $400 $400 $100
PVPV00
10%10%
30
![Page 31: Chapter 2.Time Value of Money ppt](https://reader034.fdocuments.net/reader034/viewer/2022051318/58ed7b761a28abf64e8b4695/html5/thumbnails/31.jpg)
How To Solve 1 2 3 4 55
$600 $600 $400 $400 $100$600 $600 $400 $400 $10010%
$545.45$545.45$495.87$495.87$300.53$300.53$273.21$273.21$ 62.09$ 62.09
$1677.15 $1677.15 = = PVPV00 of the Mixed Flowof the Mixed Flow31
![Page 32: Chapter 2.Time Value of Money ppt](https://reader034.fdocuments.net/reader034/viewer/2022051318/58ed7b761a28abf64e8b4695/html5/thumbnails/32.jpg)
The actual rate of interest earned (paid) after adjusting the nominal rate for
factors such as the number of compounding periods per year.
(1 + [ i / m ] )m - 1
Effective Annual Interest Rate
32
![Page 33: Chapter 2.Time Value of Money ppt](https://reader034.fdocuments.net/reader034/viewer/2022051318/58ed7b761a28abf64e8b4695/html5/thumbnails/33.jpg)
Basket Wonders (BW) has a $1,000 CD at the bank. The interest rate is 6%
compounded quarterly for 1 year. What is the Effective Annual Interest Rate
(EAREAR)?EAREAR = ( 1 + 6% / 4 )4 - 1
= 1.0614 - 1 = .0614 or 6.14%!6.14%!
BW’s Effective Annual Interest Rate
33
![Page 34: Chapter 2.Time Value of Money ppt](https://reader034.fdocuments.net/reader034/viewer/2022051318/58ed7b761a28abf64e8b4695/html5/thumbnails/34.jpg)
Julie Miller is borrowing $10,000 $10,000 at a compound annual interest rate of 12%.
Amortize the loan if annual payments are made for 5 years.
Step 1: Payment PVPV00 = R (PVIFA i%,n)
$10,000 $10,000 = R (PVIFA 12%,5)
$10,000$10,000 = R (3.605)RR = $10,000$10,000 / 3.605 = $2,774$2,774
Amortizing a Loan Example
34
![Page 35: Chapter 2.Time Value of Money ppt](https://reader034.fdocuments.net/reader034/viewer/2022051318/58ed7b761a28abf64e8b4695/html5/thumbnails/35.jpg)
Amortizing a Loan ExampleEnd ofYear
Payment Interest Principal EndingBalance
0 --- --- --- $10,0001 $2,774 $1,200 $1,574 8,4262 2,774 1,011 1,763 6,6633 2,774 800 1,974 4,6894 2,774 563 2,211 2,4785 2,775 297 2,478 0
$13,871 $3,871 $10,000
![Page 36: Chapter 2.Time Value of Money ppt](https://reader034.fdocuments.net/reader034/viewer/2022051318/58ed7b761a28abf64e8b4695/html5/thumbnails/36.jpg)
Thank You