Professor Wendy Smith has been offered the following opportunity: A law firm wou

Question

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 the eight hours each month. Smith's rate is

$ 535

per hour and her opportunity cost of capital is

15 %

per year. What does the IRR rule advise regarding the paymentarrangement? (Hint: Find the monthly rate that will yield an effective annual rate of

15 %.)

What about the NPV rule?

Explanation / Answer

NPV of Incremental cash flows of 1st -2nd

=50000-535*8/(1+15%/12)^1-535*8/(1+15%/12)^2...-535*8/(1+15%/12)^12

=50000-535*8/(1+15%/12)*(1-(1+15%/12)^12)/(1-(1+15%/12))

=-4362.81

IRR of incremental cash flows of 1st - 2nd is where NPV is 0

=>0=50000-535*8/(1+IRR/12)^1-535*8/(1+IRR/12)^2...-535*8/(1+IRR/12)^12

=>0=50000-535*8/(1+IRR/12)*(1-(1+IRR/12)^12)/(1-(1+IRR/12))

IRR=-7.192%

hence, with IRR rule we say that 2nd is preferrable over 1st given incremental (1st-2nd) is giving an IRR lower than opportunity cost of capital

With NPV rule, we say that 2nd is preferrable over 1st given incremental (1st -2nd) is giving negative NPV

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