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 ]