This preview shows page 1. Sign up to view the full content.
Unformatted text preview: (FVIFA7%,3)(1.07)
= $1,000 (3.215)(1.07) = $3,440
Period
6%
7%
8%
1
1.000
1.000
1.000
2
2.060
2.070
2.080
3
3.184
3.215
3.246
4
4.375
4.440
4.506
5
5.637
5.751
5.867 FVADn
FVAD3 39 Certified Financial Controller CFC Overview of an
Ordinary Annuity  PVA
Cash flows occur at the end of the period 0 1 2 i% n n+1
n+ ...
R R R
R = Periodic
Cash Flow PVAn PVAn = R/(1+i)1 + R/(1+i)2
+ ... + R/(1+i)n 40 Certified Financial Controller CFC 20 Example of an
Ordinary Annuity  PVA
Cash flows occur at the end of the period 0 1 2 3 $1,000 4 $1,000 7%
$1,000
$934.58
$873.44
$816.30
$2,624.32 = PVA3
624. 41 PVA3 = $1,000/(1.07)1 +
$1,000/(1.07)2 +
$1,000/(1.07)3 = $934.58 + $873.44 + $816.30
= $2,624.32
624.
Certified Financial Controller CFC Hint on Annuity Valuation
The present value of an ordinary
present value
an ordinary
annuity can be viewed as
beginning
occurring at the beginning of the
first cash flow period, whereas
the future value of an annuity
due can be viewed as occurring
end
at the end of the first cash flow
period.
42 Certified Financial Controller CFC 21 Valuation Using Table IV
= R (PVIFAi%,n)
= $1,000 (PVIFA7%,3)
= $1,000 (2.624) = $2,624
Period
6%
7%
8%
1
0.943
0.935
0.926
2
1.833
1.808
1.783
3
2.673
2.624
2.577
4
3.465
3.387
3.312
5
4.212
4.100
3.993 PVAn
PVA3 43 Certified Financial Controller CFC Overview of an
Annuity Due  PVAD
Cash flows occur at the beginning of the period 0 1 2 i%
R n1 n ...
R R R R: Periodic
Cash Flow PVADn PVADn = R/(1+i)0 + R/(1+i)1 + ... + R/(1+i)n1
= PVAn (1+i)
44 Certified Financial Controller CFC 22 Example of an
Annuity Due  PVAD
Cash flows occur at the beginning of the period 0 1 2 $1,000 3 4 $1,000 7%
$1,000.00
$ 934.58
$ 873.44 $2,808.02 = PVADn
808. PVADn = $1,000/(1.07)0 + $1,000/(1.07)1 +
$1,000/(1.07)2 = $2,808.02
808.
45 Certified Financial Controller CFC Valuation Using Table IV
PVADn = R (PVIFAi%,n)(1+i)
PVAD3 = $1,000 (PVIFA7%,3)(1.07)
= $1,000 (2.624)(1.07) = $2,808
Period
6%
7%
8%
1
0.943
0.935
0.926
2
1.833
1.808
1.783
3
2.673
2.624
2.577
4
3.465
3.387
3.312
5
4.212
4.100
3.993
46 Certified Financial Controller CFC 23 Steps to Solve Time Value
of Money Problems
1. Read problem thoroughly
2. Create a time line
3. Put cash flows and arrows on time line
4. Determine if it is a PV or FV problem
5. Determine if solution involves a single
CF, annuity stream(s), or mixed flow
6. Solve the problem
7. Check with financial calculator (optional)
47 Certified Financial Controller CFC Mixed
Mixed Flows Example
Julie Miller will receive the set of cash
flows below. What is the Present Value
at a discount rate of 10%.
10% 0 1
10%
$600 2 3 5 $600 $400 $400 $100 PV0
48 4 Certified Financial Controller CFC 24 How to Solve?
1. Solve a “pieceatatime” by
pieceatdiscounting each piece back to t=0.
piece
2. Solve a “groupatatime” by first
groupatbreaking problem into groups of
annuity streams and any single
cash flow groups. Then discount
each group back to t=0.
group
49 Certified Financial Controller CFC “PieceAt“PieceAtATime”
0 1
10%
$600 2 3 4 $600 $400 $400 $100 $545.45
545.
$495.87
495.
$300.53
300.
$273.21
273.
$ 62.09
62. $1677.15 = PV0 of the Mixed Flow
1677.
50 5 Certified Financial Controller CFC 25 “GroupAt“GroupAtATime” (#1)
(#1
0 1 2 3 4 5 10%
$600 $600 $400 $400 $100 $1,041.60
041.
$ 573.57
573.
$ 62...
View
Full
Document
This note was uploaded on 05/28/2013 for the course FINANCE economy taught by Professor Nill during the Fall '12 term at Bronx School Of Law And Finance.
 Fall '12
 nill
 Time Value Of Money

Click to edit the document details