Professor Wendy Smith has been offered the following opportunity: A law firm would like to retain her for an upfront payment of
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 the eight hours each month. Smith's rate is
per hour and her opportunity cost of capital is
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
What about the NPV rule?
Solving in excel,
|Pmt||4360||(545 * 8)|
|Annual IRR||8.79%||(=(1+0.00704773)^12 -1)|
According to the IRR rule,
Since IRR is less than cost of capital (15%), smith should turn down this opportunity.
EAR = 15%
EAR = (1 + r/m)^m - 1
0.15 = (1 + r/12)^12 -1
1.15 = (1 + r/12)^12
1.15^1/12 = (1 + r/12)
1.011715 = (1 + r/12)
r/12 = 0.011715
Monthly rate is 1.1715%
NPV = Payment received - PV of work done
NPV = 50000 - 4360 * ( PVIFA @ 1.1715% for 12 months)
PVIFA = A/r*(1-(1/1+r)^n))
NPV = 50000 - 4360/(0.011715) * (1-(1/1+0.011715)^12))
As NPV is positive, he should accept the deal.
An upvote would be appreciated. If you have any doubts, let me know in the comments.
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