Question

Eureka Mining is considering buying a new machine. There are two choices available for the company. It may buy either machine P or machine Q. Cash flows for these two-mutually exclusive machines are given below:

Year	Machine P	Machine Q
0	-25,000	-25,000
1	13,000	5,500
2	12,315	7,500
3	6,200	12,000
4	4,200	13,000

The IRR of Project P is given as 20% and the IRR of Project Q is given as 16%.

Based on the IRRs given, which project do you choose?

When the discount rate is 6%, NPV of Project P is $6,757. Compute the NPV of the project Q if the discount rate is 6%. Which project would you choose?

Discuss if there is any inconsistency in the choice (using IRR and NPV) and what might be the reason for any such inconsistency.  

Notes: You may solve this question by trial and error method, using a financial calculator, using a spreadsheet. You may provide your answer as text information in the response box below (or attach a word or an excel file).

Answer 1

a) Machine P has an IRR of 205, whereas Machine Q has an IRR of 16%. Based on the IRR values, Machine P should be chosen as it has higher internal rate of return and the company would get higher return by investing in this machine.

b) Given

discount rate r = 6%

NPV of project P = 6757

with the same discount rate of 6%, NPV of Project Q would be

NPV = - CF0 + CF1 / ( 1+r) + CF2 / ( 1+r)^2 + CF3 / ( 1+r)^3 + CF4 / ( 1+r)^4

NPV = -25000 + 5500 / ( 1 + 0.06) + 7500 / ( 1+0.06)^2 + 12000/ ( 1+0.06)^3 + 13000/(1+0.06)^4

NPV = -25000 + 5188.68 + 6674.97 + 1the 0075.43 + 10297.22

NPV = $7236.30

NPV of the project Q is $7236.

Based on the NPV of the project we would chose Project Q as the NPV of Project Q is higher than project P. This means that Project Q will create greater value and would generate more cash in today terms.

c) Yes according to IRR , Project P seems to be ore attractive whereas based on the NPV method of capital budgeting, Project Q is more attractive. The difference between the two methods is because of the difference in the nature of cash flow from each project. NPV is a better measure than IRR as it is an absolute measure of the project's profitability whereas, IRR is a relative measure and the process assumes that all the cash flows are re-invested at the same reinvestment rate. This might not be possible at different timings of the cash flow ans hence IRR calculated may not be very appropriate. We should thus, choose NPV over IRR, thus Project Q is considered to be a better investment than Project P.