Unformatted text preview: Business Management 301 Day 4: Part 4
Chapter 5: Part 2—TVM
June 30, 2011 WarmUp Question #1
Your company has received a $50,000 loan from an industrial finance company. The annual payments are $6,202.70. If the company is paying 9% interest per year, how many loan payments must the company make?
a) 15
b) 13
c) 12
d) 19
e) None of the above WarmUp Question #1
Your company has received a $50,000 loan from an industrial finance company. The annual payments are $6,202.70. If the company is paying 9% interest per year, how many loan payments must the company make?
a) 15 (setup: 50,ooo PV, 6202.70 PMT, 9 I/Y, 0 FV N)
b) 13
c) 12
d) 19
e) None of the above WarmUp Question #2
Your grandmother invested one lump sum 17 years ago at 4.25 percent interest. Today, she gave you the proceeds of that investment which totaled $5,539.92. How much did your grandmother originally invest?
a) $2,700.00
b) $2,730.30
c) $2,750.00
d) $2,768.40
e) None of the above WarmUp Question #2
Your grandmother invested one lump sum 17 years ago at 4.25 percent interest. Today, she gave you the proceeds of that investment which totaled $5,539.92. How much did your grandmother originally invest?
a) $2,700.00
b) $2,730.30 (5539.92 FV, 4.25 I/Y, 17 N, o PMT PV)
c) $2,750.00
d) $2,768.40
e) None of the above WarmUp Question #3
Keller Krafts is saving money to build a new airplane factory. Six years ago they set aside $250,000 for this purpose. Today, that account is worth $306,958. What rate of interest is Keller Krafts earning on this money?
a) 3.43%
b) 3.45%
c) 3.48%
d) 3.52%
e) None of the above WarmUp Question #3
Keller Krafts is saving money to build a new airplane factory. Six years ago they set aside $250,000 for this purpose. Today, that account is worth $306,958. What rate of interest is Keller Krafts earning on this money?
a) 3.43%
b) 3.45%
c) 3.48% (250,000 PV, 306,958 FV, o PMT, 6 N, I/Yr)
d) 3.52%
e) None of the above Other Cash Flow Other Cash Flow Patterns 0 1 2 3 Perpetuities
Suppose you will receive a fixed payment at a fixed interval every period (month, year, etc.) forever. This is an example of a perpetuity.
You can think of a perpetuity as an annuity that goes on forever. Present Value of a Perpetuity
When we find the PV of an annuity, we think of the following relationship: PV = PMT (PVIFA i, n )
PV = PMT (PVIFA Perpetuities
Mathematically: (PVIFA i, n ) = Note: We said that a perpetuity is an annuity where n = infinity. What happens to this formula when n gets very, very large? Perpetuities
When n gets very large,
When n gets very large,
this becomes zero. So we’re left with PVIFAp = 1
i Present Value of a Perpetuity
The PV of a perpetuity is very simple to find: PMT PV =
i Perpetuity Question #1
What should you be willing to pay in order to receive $10,000 annually forever, if you require 8% per year on the investment? Perpetuity Question #1
What should you be willing to pay in order to receive $10,000 annually forever, if you require 8% per year on the investment? PMT $10,000 PV =
= 0.08
i
= $125,000 Note: When calculating a perpetuity,
the interest rate is written as a decimal. Perpetuity Question #2
What should you be willing to pay in order to receive $6,000 semiannually forever, if you require 8.5% per year (4.25% semiannually) on the investment? Perpetuity Question #2
What should you be willing to pay in order to receive $6,000 semiannually forever, if you require 8.5% per year (4.25% semiannually) on the investment? PMT $6,000 PV =
= 0.0425
i
= $141,176.47 Note: When calculating a perpetuity,
the interest rate is written as a decimal. Perpetuity Question #3
What should you be willing to pay in order to receive $2,750 quarterly forever, if you require 10% per year (2.5% quarterly) on the investment? Perpetuity Question #3
What should you be willing to pay in order to receive $2,750 quarterly forever, if you require 10% per year (2.5% quarterly) on the investment? PMT $2,750 PV =
= 0.025
i
= $11o,ooo Note: When calculating a perpetuity,
the interest rate is written as a decimal. Perpetuity Question #4
The Everlasting Gift Insurance Company is offering you a policy that will pay you and your heirs $11,250 each year forever. The cost of the policy is $385,000. What is the rate of return that will be realized on this policy? Perpetuity Question #4
The Everlasting Gift Insurance Company is offering you a policy that will pay you and your heirs $11,250 each year forever. The cost of the policy is $385,000. What is the rate of return that will be realized on this policy? i = PMT PV 11,250 = 385,000
= 2.92% Note: The formula for the perpetuity has been rearranged to solve for the interest rate rather than the PV. 0 0 0 0 40 40 40 40 40 0 1 2 3 4 5 6 7 8 This type of cash flow sequence is often called a “deferred annuity.” 0 0 0 0 40 40 40 40 40 0 1 2 3 4 5 6 7 8 Three Ways to Solve Uneven Cash Flow Problems:
First Method: Discount each cash flow back to time ZERO separately.
OR… 0 0 0 0 40 40 40 40 40 0 1 2 3 4 5 6 7 Second Method: Find the PV of the 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 cash flow stream today (Time ZERO) is $69,226. 0 0 0 0 40 40 40 40 40 0 1 2 3 Uneven Cash Flow
Third Method: Use the CFj 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. However, the time 0 cash flow always has to be considered separately. 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. ...
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 Summer '11
 JimBrau
 Management, Interest, CFj –Flash

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