Question

Homework #3 Capital Budgeting 2. You are comparing two pieces of equipment with different life expectancies. Their cashflow streams are as below. In order to compare them on an equal basis, we assume that we will run both pieces of equipment forever by replacing them every 4 and 5 years, respectively. A. (10) What is the net PV of equipment A's cashflow, if run just once? B. (10) What is the net PV of equipment B's cashflow, if run just once? C. (20) What is the net PV of equipment A's cashflow, if run forever? D. (20) What is the net PV of equipment B's cashflow, if run forever? Discount rate at 10% Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Equipment A (4-Yr Life) -$35 $20 $12 $14 $8 Equipment B (5-Yr Life) -$45 $21 $12 $15 $10 $16

Answer 1

B Answer A and B 35 Year Discount Rate @10% 1.0000 0.9091 0.8264 0.7513 0.6830 0.6209 NINIAIO Cashflow of A Cashflow of BPV of A @10% ($) PV of B @10% ($) -35.00 -45.00 18.18 19.09 9.92 9.92 10.52 11.27 5.46 6.83 9.93 NPV 9.08 12.04 Both the projects have different lives and hence we cannot make decision based on above results. For comparing projects with unequal lives, we have to calculate Equal Annual Annuity Approach. Equivalent Annual Annuity (EAA) Approach EAA = NPV/ sum of discounting factors Project B Particulars NPV Sum of disconting factors EAA ($) Project A 9.08 3.1699 2.87 12.04 3.7908 3.18 As EAA of Project B is greater than Project A, we shall go ahead with Project B.

Answer C and D As the projects will go on forever, it will be a case of Annuity and will be calculated as follows: Net PV of Equipment A if run forever: PV = EAA/cost of capital Project B EAA COC Net PV ($) Project A 2.87 10% 28.65 3.18 10% 31.77 As the PV of Project B is better than A, we shall go ahead with Project B.

Answer A and B Discount Rate @10% Cashflow of a Cashflow of B -35 20 12 =1/POWER(1.1,B5) =1/POWER(1.1, B6) =1/POWER(1.1,B7) =1/POWER(1.1, B8) =1/POWER(1.1,B9) PV of A @10% ($) =D4*$C4 =D5*$C5 =D6*$C6 =D7*$C7 =D8*$C8 =D9*$C9 =SUM(F4:F9) PV of B @10% ($) =E4*$C4 =E5*$C5 =E6*$C6 =E7*$C7 =E8*$C8 =E9*$C9 ESUM(G4:G9) NPV Both the projects have different lives and hence we cannnot make decision based on above results. For comparing projects with unequal lives, we have to calculate Equal Annual Annuity Approach. Equivalent EAA = NPV/ sum of discounting factors Particulars NPV Sum of disconting factors EAA ($) Project A =+F10 =SUM(C5:08) =+E21/E22 Project B =+G10 =SUM(C5:09) =+F21/F22 As EAA of Project B is greater than Project A, we shall go ahead with Project B.

Answer C and D As the projects will go on forever, it will be a case of Annuity and will be calculated as follows: Net PV of Equipment A if run forever: PV = EAA/cost of capital EAA coc Net PV ($) Project A =+E23 0.1 =+E36/E37 Project B =+F23 0.1 =+F36/F37 As the PV of Project B is better than A, we shall go ahead with Project B.