## Question

###### Professor Wendy Smith has been offered the following deal: A law firm would like to retain...

Professor Wendy Smith has been offered the following deal: A law firm would like to retain her for an upfront payment of $ 60,000. In return, for the next year, the firm would have access to eight hours of her time every month. Smith's rate is $ 630 per hour, and her opportunity cost of capital is 14 % (equivalent annual rate, EAR).

What is the IRR (annual)? What does the IRR rule advice regarding this opportunity?

What is the NPV? What does the NPV rule say about this opportunity?

What is the IRR (annual)? The IRR (annual) is ________________%. What does the IRR rule advice regarding this opportunity?

Smith's cost of capital is 14 %, so according to the IRR rule, she should turn down this opportunity. What is the NPV?

The NPV is $_______________ What does the NPV rule say about this opportunity? The NPV is _______________,

## Answers

Calculating NPV:

Present value at Time 0 = cashflow/(1+rate)^{time }

r_{a}= 14% annually. We should convert it to monthly interest rate.

r_{m}=14%/12 =1.17%cash outflow of each month = -630*8 = -5040

Time(months)Cash flowPV of Cash flows0 60000 60000 1 -5040 -4982 2 -5040 -4924 3 -5040 -4868 4 -5040 -4812 5 -5040 -4756 6 -5040 -4701 7 -5040 -4647 8 -5040 -4593 9 -5040 -4540 10 -5040 -4488 11 -5040 -4436 12 -5040 -4385 Sum3867Given, the sum of present value of cash flows is positive, the professor should accept the offer.

IRR calculation:

The rate at which the NPV becomes 0.By hit and trial method, at IRR=0.12% monthly, the NPV is 0. As IRR< r

_{m; the professor should reject the offer.}60000 = (5040/(1 + 1RR)! ) + (5040/(1-IRR)2 ) + (5040/ (1+ IRM" ) + (5040/(1IRR))(5040/(1IRR)) (5040 IRR))(5040/1+ IRR))(5040/(1 IRR(5040/(1IRR))(5040/(1+IRR)10)+ (5040/(1IRR)1) + (5040/(1IRR)12)