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 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 ____%.

Answer #1

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

where,

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.**

b)

NPV rule:

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 ]**

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
$545
per hour and her opportunity cost of capital is
15%
per year. What does...

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alternative payment arrangement, the firm would pay Professor
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In return, for the next year the firm would have access to eight
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