Professor Wendy Smith has been offered the following opportunity: A law firm would like to retain her for an upfront payment of $ 50,000. In return, for the next year, the firm would have access to eight hours of her time every month. As an alternative payment arrangement, the firm would pay Professor Smith's hourly rate for eight hours each month. Smith's rate is $ 555 per hour and her opportunity cost of capital is 15 % per year. What does the IRR rule advise regarding the payment arrangement? (Hint: Find the monthly rate that will yield an effective annual rate of 15 %.) What about the NPV rule?
The IRR is ____%.
Monthly payments = 8 hours * 555 per hour = 4440
IRR is the rate where NPV = 0
Monthly IRR = 0.991%
We need to find Effective annual rate
EAR = (1 + r)^n
r = monthly rate
n = number of compoundings
Effective IRR = (1 + 0.991%)^12 - 1 = 12.57%
Since IRR(12.57%) is less than required return (15%) offer is not acceptable.
first we have to find monthly rate for EAR of 15%
=(1+r)^12 - 1 = 15%
(1+r)^12 = 1.15
r = (1.15)^(1/12) - 1
monthly rate = 1.171%
NPV = 50,000 - [4400*PVIFA( n = 12 ; r = 1.171%)]
NPV = 50,000 - [4400*11.134]
NPV = $1010.06
Since NPV is positive accept the offer
(Formula for PVIFA = [1 - (1+r)^-n / r ]
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