Question

You are considering the following two projects and can only take one. Your cost of capital is 11.4 %. The cash flows for the two projects are as follows​ ($ million):

Project	Year 0	Year 1	Year 2	Year 3	Year 4
A	−$102	$27	$31	$39	$49
B	−$102	$49	$39	$31	$20

a. What is the IRR of each​ project? b. What is the NPV of each project at your cost of​ capital? c. At what cost of capital are you indifferent between the two​ projects? d. What should you​ do?

a. The IRR for project A is nothing​%. ​ (Round to one decimal​ place.) The IRR for project B is nothing​%. ​(Round to one decimal​ place.)

b. The NPV for project A is ​$ nothing million. ​(Round to two decimal​ places.) The NPV for project B is ​$ nothing million. ​(Round to two decimal​ places.)

c. You will be indifferent if the cost of capital is nothing​%. ​(Round to one decimal​ place.)

d. Given your cost of​ capital, which project would you​ choose? ​(Select the best choice​ below.)

A. You should invest in project Upper A​, as it has the higher NPV.

B. You should invest in project Upper B​, as it has the higher IRR.

C. You should invest in project Upper A​, as it has the higher IRR.

D. You should invest in project Upper B​, as it has the higher NPV.

Answer 1

Cost of Capital (r) Discount Factor 11.40% 1/(1+r)An Ans (c Indifference Differences in Cash Flow of Project A & B Project A Project B Present Value Present Value Cash Flowfactor (B) PV (A B) Cash Flow factor PV (A B) 4 102 27 31 39 49 102.00 1.00 (102.00) 1.00 0.90 0.81 0.72 0.65 102 49 39 31 20 24.24 24.98 28.21 31.82 7.24 14.38% 0.9043.99 0.81 31.43 0.72 22.42 12.99 8.82 (22.00) (8.00) 8.00 29.00 7.00 8.69% 0.65 10 Ans (b) 11 Ans (a) NPV IRR NPV IRR 16.07% Ans (c) Indifference Point (Cost of Capital) steps 1. Calculate difference in the the cashflows of 2 projects 2. Calculate the IRR of the difference, Using Excel or the formula in left applying Algebra 3. The IRR of differences is the indifference point of two projects 4. In our case it is 8.69% 13 IRR IRR) + 16 18 19 CFo-Initial Investment/Outlay CF,CF.CPCF Cash fows N Holding Period Net Present Value 23 Ans (d) 24 25 26 27 28 29 D. You should invest in project Upper B, as it has the higher NPV With the same outflow, we are getting more return in same time frame using NPV method The IRR projects the will give the rate of retun at which the NPV is "O". Projects with IRR Expected return are preferred Sheet28Sheet29 Sheet30 Sheet31 Sheet32 Sheet33 Sheet34 Sheet35 Sheet36

0.114 1/1+r)An Cost of Capital Ir) Discount Factor Ans (c) Indifference Project A Project B Differences in Cash Flow of Project A & B -C5-G5 Present Value factor (B) Present Value Cash Flow (A) PV (A *B) Cash Flow PV (A*B) Yr 1/(1+SD$1) B5-CS DS 102 49 39 31 20 0 102 27 31 39 49 -G6 H6 -C8-G8 -C9-G9 SUM(K5:K9) IRR(K5:K9,0.1) 10 Ans (b) NPV IRR -SUM(E5:E9) NPV IRR -SUM(I5:19) IRR(G5:G9,0.1) 11 Ans (a) 12 13 14 15 16 17 18 19 CFo -Initial investment /Outla IRR(C5:C9,0.1) IRR Ans (c) Indifference Point (C 1. Calculate difference in the the cashflows of 2 projects 2. Calculate IRR of difference, using formula in left applying Algebra or excel 3. The IRR of differences is the indifference point of two projects 4. In our case it is 8.69% NP CF.C-Cash flows 2 -Internal kRate of Rurn 23 Ans (d) D. You should invest in t Upper B, as it has the higher NPV With the same outflow, we are getting more return in same time frame using NPV method. The IRR projects the will give the rate of retun at which the NPV is "O". Projects with IRR>Expected return are preferred 24 25 Sheet28 Sheet29 Sheet30 Sheet31 Sheet32 Sheet33 Sheet34 Sheet35 Shet36