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

$545

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

Solving in excel,

PV	50000	upfront payment
Pmt	4360	(545 * 8)
months	12
IRR(monthly)	0.704773%	(=Rate(12,-4360,5000,0,0)

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))

NPV

1455.45

(=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.