Chapter 5

# Chapter 5 - #6 Your company will generate \$49,000 in cash...

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#6 Your company will generate \$49,000 in cash flow each year for the next nine years from a new information database. The computer system needed to set up the database costs \$276,000. Assume you can borrow the money to buy the computer system at 10.25 percent annual interest. Calculate the present value of the generated cash flows. \$279,409.64 To find the PVA, we use the equation: PVA = C ({1 – [1/(1 + r ) t ]} / r ) PVA = \$49,000{[1 – (1/1.1025) 9 ] / 0.1025} PVA = \$279,409.64 Can you afford the new system? Yes The present value of the revenue is greater than the cost, so your company can afford the equipment. Calculator Solution: Enter 9 10.25% ±\$49,000 N I/Y PV PMT FV Solve for \$279,409.64 #18 An investment will pay you \$84,000 in six years. Assume the appropriate discount rate is 7.00 percent compounded daily. What is the present value? \$55,194.16 For this problem, we simply need to find the PV of a lump sum using the equation: PV = FV / (1 + r ) t It is important to note that compounding occurs on a daily basis. To account for this, we will divide the interest rate by 365 (the number of days in a year, ignoring leap year), and multiply the number of periods by 365. Doing so, we get: PV = \$84,000 / [(1 + 0.0700/365) 6(365) ] PV = \$55,194.16 Calculator Solution: Enter 6 × 365 7.00% / 365 ±\$84,000 N I/Y PV PMT FV Solve for \$55,194.16 #22 Friendly’s Quick Loans, Inc., offers you \$8.50 today but you must repay \$15.00 when you get your paycheck in one week (or else). What’s the effective annual return Friendly’s earns on this lending business? 671,369,076,714,525.00% If you were brave enough to ask, what APR would Friendly’s say you were paying? 3,976.47% Here we are trying to find the interest rate when we know the PV and FV. Using the FV

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equation: FV = PV(1 + r ) \$15.00 = \$8.50(1 + r ) r = \$15.00/\$8.50 – 1 r = 0.7647 or 76.47% per week The interest rate is 76.47% per week. To find the APR, we multiply this rate by the number of weeks in a year, so: APR = (52)76.47% = 3,976.47% And using the equation to find the EAR, we find: EAR = [1 + (APR / m )] m – 1 EAR = [1 + 0.7647] 52 – 1 EAR = 6,713,690,767,145.2500 or 671,369,076,714,525.00% Calculator Solution: Enter 1 ±\$8.50 \$15.00 N I/Y PV PMT FV Solve for 76.47% APR = 52(76.47%) = 3,976.47% Enter 3,976.47 52 NOM EFF C/Y Solve for 671,369,076,714,525.00% #25 You make \$7,200 annual deposits into a retirement account that pays 11.3 percent interest compounded monthly. How large will your account balance be in 33 years? 2,414,348.37% The compounding period in this problem is monthly. Since the cash flows are annual, we need to use the EAR to calculate the future value of annual cash flows. It is important to remember that you have to make sure the compounding periods of the interest rate matches with the cash flows. In this case, we have annual cash flows, so we need the EAR since it is the true annual
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## This note was uploaded on 10/31/2011 for the course ECFI 305 taught by Professor Johansen,t during the Fall '08 term at Fort Hays.

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Chapter 5 - #6 Your company will generate \$49,000 in cash...

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