Question

Professor Wendy Smith has been offered the following? opportunity: A law firm would like to retain her for an upfront payment of $ 50000. 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. a)What does the IRR rule advise regarding the payment arrangement? (Hint: Find the monthly rate that will yield an effective annual rate of 15 %?.)b) What about the NPV? rule? The IRR is _?% & explain how ? ?(Round to two decimal places.) for ans a )6.72 is a wrong ans plz give me the right ans ?

Answer 1

a) Monthly cash flows are as follows:

Day 0	M1	M2	M3	M4	M5	M6	M7	M8	M9	M10	M11	M12
-50000	540*8=4320	4320	4320	4320	4320	4320	4320	4320	4320	4320	4320	4320

Monthly IRR for the calculation is 0.56%, annualized IRR is (1+0.56%)^12 - 1 which equals 6.94%.

Opportunity cost of capital is 15%, so it is not advisable to pay upfront payment of USD 50000 for saving USD 4320 per month.

b) NPV of above cash flows assuming effective annual rate of 15% is mentioned below:

Monthly hurdle rate = (1+ 0.15)^(1/12) - 1 = 1.17%

NPV of the following cash flows

= - 50000 + 4320/(1 + 1.17/100) + 4320/(1+ 1.17/100)^2 + 4320/ (1 + 1.17/100)^3 + 4320/ (1 + 1.17/100)^4 + 4320/ (1 + 1.17/100)^5 + 4320/ (1 + 1.17/100)^6 + 4320/ (1 + 1.17/100)^7 + 4320/ (1 + 1.17/100)^8 + 4320/ (1 + 1.17/100)^9 + 4320/ (1 + 1.17/100)^10 + 4320/ (1 + 1.17/100)^11 + 4320/ (1 + 1.17/100)^12

=- 1900.79

So, it is not advisable to invest USD 50000 upfront as the overall NPV is negative.