Question

Professor Wendy Smith has been offered the following​ opportunity: A law firm would like to retain her for an upfront payment of $48,000.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 $535 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. The IRR and NPV is? (two decimal places)

Answer 1

Answer :

Calculation of IRR

IRR is the rate at which present value of cash Inflow is equal to Present value of Cash Outflow which means that NPV is 0 at IRR

Therefore

Monthly Amount = 535 * 8 = 4280

NPV = 48000 - {[4280 / r] * (1 - [1/(1 + r)^n])}

where r is the rate of interest or IRR

n is the number of periods i.e 12

0 = 48000 - {[4280 / r] * (1 - [1/(1 + r)^12])}

48000 = {[4280 / r] * (1 - [1/(1 + r)^12])}

To simplify the calculation we can use rate function of excel to calculate Rate or IRR

=RATE(nper,pmt,pv,fv)

where nper is the number of periods i.e 12

pmt is the periodic amount i.e 4280 (535 * 8)

pv is the upfront payment i.e 48000

fv is 0

=RATE(12,-4280,48000,0)

therefore Monthly IRR is 1.0566%

Yearly IRR = (1 + 0.010566)^12 - 1

= 1.134426 - 1

= 13.44%

Smith’s cost of capital is 15%,  she should not accept as IRR is less than cost of capital.

Calculation of NPV when cost of capital is 15%

NPV = 48000 - {[4280 / r] * (1 - [1/(1 + r)^n])}

where r is the cost of capital compounded monthly or (1.15)^(1/12) = 1.011715 or 1.1715% (i.e  monthly rate that will yield an effective annual rate of 15%)

NPV = 48000 - {[4280 / 0.011715] * (1 - [1 / (1 + 0.011715)^12])}

= 48000 - {365346.168 * (1 - 0.869565)}

= 48000 - {365346.168 * 0.130435}

= 48000 - 47653.85

= 346.15

Since Net Present value is positive accept the project.