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

$550

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?

Answer 1

Showing the working in excel

PV	50000	upfront payment
Pmt	4400	(550 * 8)
months	12
IRR(monthly)	0.8484%	(=Rate(12,-4400,5000,0,0)
Annual IRR	10.67%	(=(1+0.008484)^12 -1)

IRR rule advise regarding the payment​ arrangement

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 = 1.1715%

NPV = Payment received - PV of work done

NPV = 50000 - 4400 * ( PVIFA @ 1.1715% for 12 months)

PVIFA = A/r*(1-(1/1+r)^n))

NPV = 50000 - 4400/(0.011715) * (1-(1/1+0.011715)^12))

NPV

1010.088

(=50000-4400/(0.011715)*(1-(1/(1+0.011715)^12)))

As NPV is positive, he should accept the deal.

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