Day 4-Part 4

Day 4-Part 4 - Business Management 301 Day 4: Part 4...

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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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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.

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