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

n = 12 months

EAR = 15%

r = monthly interest rate

EAR = (1+r)^n - 1

15% = (1+r)^12 - 1

(1+r)^12 = 1.15

1+r = 1.011714917

r = 0.011714917

r = 1.17%

Calculation of NPV of the project
Month	Cash Flow	Discount Rate @1.17%	Discounted Cash Flows
A	B	C = 1/(1+1.17%)^n	D = B*C
0	-50000	1	-50000
1	4360	0.988435307	4309.577938
2	4360	0.977004356	4259.738992
3	4360	0.9657056	4210.476418
4	4360	0.954537512	4161.78355
5	4360	0.943498578	4113.653801
6	4360	0.932587307	4066.080657
7	4360	0.921802221	4019.057682
8	4360	0.911141861	3972.578514
9	4360	0.900604785	3926.636862
10	4360	0.890189567	3881.226512
11	4360	0.879894798	3836.341319
12	4360	0.869719085	3791.975209
NPV			-1450.872546

IRR (0.705%) < Monthly interest rate (1.17%)

NPV <0 hence it ia better to accept lumpsum payment today