Lec Sept 18 Ch3 Lec Cash Flow Analysis II
-
Upload
matheus-danella -
Category
Documents
-
view
235 -
download
0
Transcript of Lec Sept 18 Ch3 Lec Cash Flow Analysis II
-
8/10/2019 Lec Sept 18 Ch3 Lec Cash Flow Analysis II
1/23
Engineering Economics
Chapter 3
Cash Flow Analysis - II
3 - 1
Sept. 18, 2014
-
8/10/2019 Lec Sept 18 Ch3 Lec Cash Flow Analysis II
2/23
Example: Uneven Multiple Cash Flows, but we separate(decompose) these into single cash f lows!
How much do you need to deposit today (P) to withdraw $25,000at n=1, $3,000 at n= 2, and $5,000 at n=4, if your account earns10% annual interest?
0
1 2 3 4
$25,000
$3,000 $5,000
P
-
8/10/2019 Lec Sept 18 Ch3 Lec Cash Flow Analysis II
3/23
3 - 3
Decomposit ion of uneven multiple cash flows
Notice that in this example, using the factor seems to beeasier than using the equation!
-
8/10/2019 Lec Sept 18 Ch3 Lec Cash Flow Analysis II
4/23
Example: Future Value of an Uneven CashFlows with Varying Interest Rates
Given: Deposit series as given over 5 years
Find: Balance at the end of year 5=?
Complicated
-
8/10/2019 Lec Sept 18 Ch3 Lec Cash Flow Analysis II
5/23
Example: Future Value of an Uneven Serieswith Varying Interest Rates
Given: Deposit series as given
over 5 years
Find: Balance at the end of year 5
-
8/10/2019 Lec Sept 18 Ch3 Lec Cash Flow Analysis II
6/23
So far, for single cash flow problems, we can
use one of the following approaches:1. Use the equations
2. Use the Compound Interest Factors (the tables)
3. In addition, we can use the Excel Spreadsheet
Functions3 - 6
F = P(1+ i)N
P = F/(1+ i)N
Compound Amount Factor : (F/P,i,N)
Present Worth Factor: (P/F, i, N)
-
8/10/2019 Lec Sept 18 Ch3 Lec Cash Flow Analysis II
7/23
3 - 7
Compound Interest Factors and Excel Function(Textbook p.50)
-
8/10/2019 Lec Sept 18 Ch3 Lec Cash Flow Analysis II
8/23
3 - 8
Single Cash Flow - Finding the Future Value F=?
-
8/10/2019 Lec Sept 18 Ch3 Lec Cash Flow Analysis II
9/23
In Excel: FVfunction (Future Value function).
Syntax FV rate, nper, [pmt], -pv, [type])
Rate Required. The interest rate per period. (e.g. 10%/12, or 0.83%, or 0.0083)Nper Required. The number of periods.Pmt Optional. The payment made each period (annuity).
Pv Required. The present value (required if Pmt is omitted).Type Optional. The number 0 or 1 and indicates when payments are due. If type isomitted, it is assumed to be 0.
-
8/10/2019 Lec Sept 18 Ch3 Lec Cash Flow Analysis II
10/23
In Excel: PVfunction (Present Value function).
SyntaxPV rate, nper, 0, - fv, [type])
Rate Required. The interest rate per period. (e.g. 10%/12, or 0.83%, or 0.0083)Nper Required. The total number of periods.Pmt Optional. The payment made each period (annuity).Fv Required. The future value, (required if Pmt is omitted)
Type Optional. The number 0 or 1 and indicates when payments are due.
-
8/10/2019 Lec Sept 18 Ch3 Lec Cash Flow Analysis II
11/23
Single Cash Flow - Finding the interest rate i=?
-
8/10/2019 Lec Sept 18 Ch3 Lec Cash Flow Analysis II
12/23
Excel: RATEfunction
RATE(nper, pmt, -pv, [fv], [type], [guess])Syntax
The RATE function syntax has the following arguments:
Nper Required. The total number of periods.Pmt Required. The payment made each period (annuity). If pmt is omitted, you must
include the fv argument.Pv Required. The present value.Fv Optional. The future value. If fv is omitted, it is assumed to be 0.
Type Optional. The number 0 or 1 and indicates when payments are due.
-
8/10/2019 Lec Sept 18 Ch3 Lec Cash Flow Analysis II
13/23
Single Cash Flow - Finding the compoundingperiods N=?
-
8/10/2019 Lec Sept 18 Ch3 Lec Cash Flow Analysis II
14/23
Excel: NPERfunction
NPER(rate, pmt, -pv, [fv], [type])Syntax
The NPER function syntax has the following arguments:
Rate Required. The interest rate per period.Pmt Required if no Fv value specified. If no annuity, Pmt=0.Pv Required. The present value.Fv Optional. The future value. If fv is omitted, it is assumed to be 0.Type Optional. The number 0 or 1 and indicates when payments are due.
-
8/10/2019 Lec Sept 18 Ch3 Lec Cash Flow Analysis II
15/23
3 - 15
Annuity:series of Nreceipts or disbursements that beginat end of period 1and continue to end of period N.Notice that if there is any cash flow occurred at period0, it can not be considered as part of the series cashflows, even though the amount is the same as A!
loan payments are classical examples of annuities.
3.5 Compound Interest Factors forAnnuities
0 1 2 3 4 5 6
A
.. NN-1
..
A A A AA A A
-
8/10/2019 Lec Sept 18 Ch3 Lec Cash Flow Analysis II
16/23
3 - 16
TheSinking Fund Factor: (A/F, I, N)
To find a series of Nreceipts/disbursements(A) thatshould be set aside each period in order to meet a major
financial need in the future (F)
3.5 Compound Interest Factors forAnnuities
1)1(),,,(
+
=N
i
iNiFA
-
8/10/2019 Lec Sept 18 Ch3 Lec Cash Flow Analysis II
17/23
3 - 17
TheCapital Recovery Factor: (A/P, i, N)
Is used to compute how much to be set aside eachperiod to repay a present use of money.
easily derived from the sinking fund factor and theuniform series compound amount factor:
3.5 Compound Interest Factors for Annuities(contd)
1)1(
)1(
),,/)(,,/(),,/(
+
+=
=
N
N
i
ii
NiPFNiFANiPA
-
8/10/2019 Lec Sept 18 Ch3 Lec Cash Flow Analysis II
18/23
How did we get these equations?Example: Find the Equation for F, given A, i, N
0 1 2 N 0 1 2 N
A A A
F
A(1+i)N-1
A(1+i)N-2
A
1 2 (1 ) 1(1 ) (1 )
N
N N iF A i A i A A
i
+ = + + + + + =
-
8/10/2019 Lec Sept 18 Ch3 Lec Cash Flow Analysis II
19/23
How did we get these equations?Example: Find the Equation for F, given A, i, N
1 2 (1 ) 1(1 ) (1 )N
N N iF A i A i A Ai
+ = + + + + + =
Based on the above equation, we can also derive theEquation for finding P,givenA, i, N as
1 2 (1 ) 1(1 ) (1 )
N
N N iF A i A i A A
i
+ = + + + + + =
+
+=
N
N
ii
iAP
)1(
1)1(
To see how the formula derivation, check appendix 3A (p.82)
-
8/10/2019 Lec Sept 18 Ch3 Lec Cash Flow Analysis II
20/23
Equations- Find P given F
- Find F given P
- Find A given F
- Find A given P
- Find F given A
- Find P given A
ni
FP
)1( +=
niPF )1( +=
+=
i
iAF
n 1)1(
+=
1)1( ni
iFA
+
+=
n
n
ii
iAP
)1(
1)1(
+
+=
1)1(
)1(n
n
i
iiPA
-
8/10/2019 Lec Sept 18 Ch3 Lec Cash Flow Analysis II
21/23
3 - 21
Practice Problem 3.5a
A Ford Mustang costs $17 000. It can be financed at5.9% for 48 months, with monthly compounding. Howmuch will the monthly payments be?
Answeri= 0.059/12 = 0.00492 per month
A = P(A/P, i, N)= $17 000(A/P, 0.00492, 48) =$398.50
Cannot find values from the Tables!
+
+=
1)1(
)1(n
n
i
iiPA
-
8/10/2019 Lec Sept 18 Ch3 Lec Cash Flow Analysis II
22/23
-
8/10/2019 Lec Sept 18 Ch3 Lec Cash Flow Analysis II
23/23
3 - 23
Practice Problem 3.5b
What is the present worth of a series of 15 annualpayments of $1000 each, when the first payment isnowand the interest rate is 5%, compoundedmonthly?
AnswerAn effective annual interest rate must be calculated first:
P = 1000 + 1000(P/A, 5.116%, 14)= 1000 + 1000 (9.82563) = $10 826
0.05116=1)12/05.01( 12
+=ei