Draw a cash flow diagram for a tractor a farm bought for $7,000 but generates profit of $3,000 for 5 years. Then find the present worth of the equipment given a discount rate of 5%.
PW= -7,000 + 3,000 (P/F, .05, 5) = $-4,649.42
Imagine you are running a non-profit organization and a wealthy philanthropist gives you two options for a donation - you can receive $80,000 now or $150,000 5 years from now. You have a discount rate of 10%. Which option represents a better present value for the donation? What is the difference in present value?
PWA = $80,000
PWB = 150,000 (P/F, .10, 5) = $93,138.20
The second option ($150,000 5 years from now) has a better present value at $93,138.20.
Difference = PWB - PWA = 93,138.20 – 80,000 = $13,138.20
What is the present value of an investment if it will be worth $500,000 in 5 years with an annual interest rate of 4%?
PW = 500,000 (P/F, .04, 5) = $410,963.55
Draw a cash flow diagram for a new piece of equipment that has an initial cost of $6,000 but generates a profit of $7,000 the first year, $8,000 the second and $9,000 the third, then breaks and is discarded.
Calculate the present worth of the equipment described in question 4 given a 10% discount rate.
PW = -6,000 + 7,000 (P/F, 0.10, 1) + 8,000 (P/F, .10, 2) + 9,000 (P/F, .10, 3) = $13,737.04
An entrepreneur has found a way to turn straw into gold, but he needs $5 million to create the necessary machinery. He wants to earn a 25% rate of return per year and recover the investment in 5 years. How much profit must the machines make every year to accomplish his goal?
5,000,000 = AW (P/A, .25, 5) = AW (1.25^5-1)/.25/1.25^5
Solve for AW. AW= $1,859,233.70
A designer decides to add an additional generation facility to an existing power plant, which costs $4 million. Given an internal rate of return of 7% over a time span of 20 years, how much extra revenue does the new system provide the power plant each year based on annual compounding?
4,000,000 = AW (P/A, .07, 20) = AW (1.07^20-1)/.07/1.07^20
Solve for AW. AW= $377,571.70
What is the present value of an investment that will be worth $1,000,000 in 7 years with an annual interest rate of 8%?
PW = 1,000,000 (P/F, .08, 7) = $583,490.39
You've won a lottery with two options for receiving your prize. One option is to receive $5 million per year for 40 years with an interest rate of 3%. The other option is to receive $222 million upfront. Ignoring taxes, what will result in you receiving the most money?
PWA = 5,000,000 (P/A, .03, 40) = $115,573,859.87
PWB = $222,000,000
The second option ($222 million upfront) will result in receiving more money.
PW = -5,000 + 1,500 (P/F, .02, 1) + 1,500 (P/F, .02, 2) + 2,500 (P/F, .02, 3) = $268.15
The venture will gain $268.15 dollars.
