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Unformatted text preview: Business Management 301 Day 5: Part 1
Chapter 5: Part 3—TVM
July 5, 2011 Day 5: Part 1 Agenda
1) TA Review Session 2:003:00 W308
2) Personal Information Cards
3) Manning Case POW—Questions?
4) Calculator Tips
5) TVM FaceOff POW #4: Manning Case
The Manning Case POW #4 is your first real case; welcome to the business school.
Be aware of your decision framework: you are the credit manager. Should you ship to both clients, neither client, or just one of the clients?
Key Insight: you must look inside the ratios.
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–
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– This case will turn on big issues.
Look for fundamental differences.
Don’t get bogged down in small details.
Most importantly, be thorough and professional! Calculator Tips
1) Match Pmt frequency (PMT), interest rate (I/YR), and compounding period (N). (These three variables must be stated in similar terms and all three move together!)
2) Clear calculator before each problem
HP: 2nd C All; TI: 2nd CLR TVM
3) Watch “begin” vs. “end” mode (Default for TVM is end mode. Clearing calculator will not change the mode!) TVM Problem Tips
Read Question Carefully!
Recognize where you are standing in time.
Inflows: +
Outflows:
CFj : Shortcut for Uneven CF Problems : White keystroke used to backspace
Enter info for ALL 5 variables across top of calculator in order to avoid mistakes. (One variable will always be ZERO.) Ordinary Annuity
Ordinary Annuity vs. Annuity Due
$1000 $1000 $1000
4 5 6 7 8 Begin Mode vs. End Mode
1000 1000 1000
4 year year year 5 6 7 5 6 7 8 Begin Mode vs. End Mode
1000 1000 1000
4 PV
in
END
Mode year year year 5 6 7 5 6 7 FV
in
END
Mode 8 Begin Mode vs. End Mode
1000 1000 1000
4 year 6 year 6 7 5 7 year 8 8 Begin Mode vs. End Mode
1000 1000 1000
4 year 6 year 6 7 5 PV in
BEGIN
Mode 7 year 8 8 FV in
BEGIN
Mode “Ordinary” Annuity Example
1000
1000 0 1 Future Value (at time 3) END Mode
N=3
PMT=1000
I/Yr=8
PV=0 FV=?
FV: $3,246.40 1000 2 1000 3 Present Value (at time 0) END Mode
N=3
PMT=1000 I/Yr=8 FV=0 PV=?
PV: $2,577.10 “Annuity Due” Example
1000 1000 1000 0 1 Same 3year time line.
Same 8% discount rate.
Same 3 $1000 cash flows, but...
The cash flows occur at the beginning of each year, rather than at the end of each year.
Therefore this is an “annuity due.” 1000 2 3 Note: Basically, the cash flow
for the annuity due is identical to the cash flow for the regular annuity, except the receipt of $ has been shifted one period forward. We will look at this problem on a timeline, then solve using TVM functions. Annuity Due Example
1000
1000 1000 0 1 Future Value (at time 3) BEGIN Mode
N=3
PMT=1000
I/Yr=8
PV=0 FV=?
FV: $3,506.11 1000 2 3 Present Value (at time 0) BEGIN Mode
N=3
Regular Annuity:
FV= $3,246.40
PMT=1000 PV= $2,577.10
I/Yr=8 FV=0 PV=?
PV: $2,783.26 Note: The only difference in calculation is BEGIN mode rather than END mode. Uneven Cash Flows
Uneven Cash Flows 0 1 2 3 Uneven Cash Flow Example #1
10,000 10,000 0 2,000 1 4,000 2 6,000 3 7,000 4 If we have a 10% discount rate, how do we calculate the PV of the uneven cash flow stream?
Traditionally, we have to discount each cash flow back separately. (See next slide.) 10,000 0 2,000 4,000 6,000 1 2 3 Period CF PV (CF) 0 10,000 10,000.00 1 2,000 1,818.18 2 4,000 3,305.79 3 6,000 4,507.89 4 7,000 4,781.09
PV of Cash Flow Stream: $ 24,412.95 7,000 4 Uneven Cash Flow Example #1
10,000 10,000 0 2,000 1 4,000 2 6,000 3 7,000 4 With an understanding of the CFj function of our financial calculator there is a shortcut… 10,000 0 2,000 4,000 6,000 1 2 3 Period CF Calculator Keystrokes: 1)10,000 CFj –Flash 0 0 10,000 2)2,000 CFj –Flash 1 1 2,000
3)4,000 CFj –Flash 2 2 4,000 4)6,000 CFj –Flash 3
5)7,000 CFj –Flash 4 3 6,000
6)10 I/YR
7) 2nd Function NPV 4 7,000
8)Answer: $24,412.95
PV of Cash Flow Stream: $ 24,412.95 7,000 4 Uneven Cash Flow Example #2
Cash flows from an investment are expected to be $40,000 per year at the end of years 4, 5, 6, 7, and 8. You require a 20% rate of return.
What is the PV of these cash flows? 0 0 0 0 40 40 40 40 40 0 1 2 3 4 5 6 7 Three Ways to Solve:
First Method: Discount each cash flow back to time ZERO separately.
OR… 8 0 0 0 0 40 40 40 40 40 0 1 2 3 4 5 6 7 Second Method (Two Steps): Find the PV of the Deferred Annuity at end of year 3:
PV3: End Mode P/YR = 1 I = 20 PMT = 40,000 N = 5 FV = 0
PV3 = $119,624 Note: This is the first step, we are not finished yet. 8 0 0 0 0 40 40 40 40 40 0 1 2 3 4 5 6 7 8 ? $119,624 …Discount this single sum of $119,624 back to time 0.
PV0: End Mode P/YR = 1 I = 20 N = 3
PMT = 0 FV = 119,624
Solve: PV0 = $69,226 Note: Now we know the value today (time zero). 0 0 0 0 40 40 40 40 40 0 1 2 3 4 5 6 7 8 $69,226 $119,624
$119,624 The PV of the uneven cash flow stream is $69,226. 0 0 0 0 40 40 40 40 40 0 1 2 3 Uneven Cash Flow
Third Method: Use the CFi function of your calculator.
Clear out Calculator!
(2nd Function ‘C All’)
PV: End Mode P/YR = 1 4 5 6 7 Calculator Keystrokes: 1)0 CFj –Flash 0
2)0 CFj –Flash 1
3)0 CFj –Flash 2
4)0 CFj –Flash 3
5)40,000 CFj –Flash 4
6)40,000 CFj –Flash 5
7)40,000 CFj –Flash 6
8)40,000 CFj –Flash 7
9)40,000 CFj –Flash 8
10) 20 I/YR
11) 2nd Function NPV
12)Answer: $69,227.13 8 0 0 0 0 40 40 40 40 40 0 1 2 3 4 5 6 7 8
This uneven cash flow stream represents a Special Case that can be condensed even further with the CFj and Nj function on your calculator. However, if it confuses you, disregard the next two slides. 0 0 0 0 40 40 40 40 40 0 1 2 3 4 5 6 7 Note: The ‘0’ cash inflow is repeated four times and the ‘40,000’ cash inflow is repeated five times in consecutive years. Uneven Cash Flow: Special Case
When you have an uneven cash flow that REPEATS cash inflow amounts in CONSECUTIVE years, you can condense the CFj even more… 8 0 0 0 0 40 40 40 40 40 0 1 2 3 4 5 6 7 8 Uneven Cash Flow: Special Case
Third Method (Condensed): Use the CFj function of your calculator.
Clear out Calculator!
(2nd Function ‘C All’)
PV: End Mode P/YR = 1 Calculator Keystrokes: 1)0 CFj –Flash 0
2)0 CFj –Flash 1
3)3 2nd Function Nj –Flash 1
4)40,000 CFj –Flash 2
5)5 2nd Function Nj –Flash 2
6)20 I/YR
7) 2nd Function NPV
8)Answer: $69,227.13 Note: The ‘cash inflow at time zero is always entered separately. Thus you use 3 rather than 4 on step three for the repeating ‘0’ cash inflow. TVM FaceOff
TVM FaceOff
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This note was uploaded on 11/17/2011 for the course BUS M 301 taught by Professor Jimbrau during the Summer '11 term at BYU.
 Summer '11
 JimBrau
 Management

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