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 $540 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? (Pls work out prob)

Answer 1

Option 1 = $50,000 upfront payment for 8 hours per month for 12 months

so $50,000 for 96 hours

Option 2 = $ 540 per hours for 8 hours per month for 12 months

Cost of Capital = 15% per year

Monthly Cost of Capital = 1.25% which is (15/12)

Ans ) What does the IRR rule advise regarding the payment​ arrangement,

IRR is a point where inflows equals to outflows. As this is monthly flows some months have 30 days and some have 31 days so due to inconsistency of months, we will be using XIRR function which consider number of days into inflows.

IRR gives rate of 7% where 50,000 taken today will be equals to fee collecting into monthly basis. As this is less than opportunity cost of 15% so she should go for $50,000 upfront payment.

Months	Date	Money Flows
0	01-01-2011	-50000
1	31-01-2011	4320
2	28-02-2011	4320
3	31-03-2011	4320
4	30-04-2011	4320
5	31-05-2011	4320
6	30-06-2011	4320
7	31-07-2011	4320
8	31-08-2011	4320
9	30-09-2011	4320
10	31-10-2011	4320
11	30-11-2011	4320
12	31-12-2011	4320
	XIRR	0.070

Ans ) What about the NPV​ rule?

NPV is -2137.37 offer of monthly payment should be rejected and she should accept upfront payment of $50,000

	0	1	2	3	4	5	6	7	8	9	10	11	12
Upfront Payment 50000	50000
Monthly Payment 540 Per Hours		4320	4320	4320	4320	4320	4320	4320	4320	4320	4320	4320	4320
Discounting at 1.25	-50000	4266.67	4213.99	4161.97	4110.58	4059.84	4009.72	3960.21	3911.32	3863.03	3815.34	3768.24	3721.72
NPV	-2137

To Conclude according to both IRR and NPV she should accept upfront payment of $50,000.

Hope this helps. Thanks and have a good day.