Question

Your friend Harold is trying to decide whether to buy or lease his next vehicle. He has gathered information about each option but is not sure how to compare the alternatives. Purchasing a new vehicle will cost $28,000, and Harold expects to spend about $650 per year in maintenance costs. He would keep the vehicle for five years and estimates that the salvage value will be $11,100. Alternatively, Harold could lease the same vehicle for five years at a cost of $3,640 per year, including maintenance. Assume a discount rate of 10 percent. Required: 1. Calculate the net present value of Harold's options. (Future Value of $1. Present Value of $1, Future Value Annuity of $1. Present Value Annuity of $1.) (Use appropriate factor(s) from the tables provided. Negative amounts should be indicated by a minus sign. Round your final answers to 2 decimal places. Do not round intermediate calculations.) NPV Purchase Option Lease Option 2. Advise Harold about which option he should choose. Lease Option Purchase Option

Answer 1

Alterative 1: Cost= Maintenance cost= Salvage Value= Purchase Option $28000 $650 $11100 Year Cost (A) PV Factor Present value (AXB) 0-$ 28,000.00 1 -$ 28,000.00 1-$ 650.00 0.909091 -$ 590.91 2 - $ 650.00 0.826446 -$ 537.19 3-$ 650.00 0.751315 -$ 488.35 4-$ 650.00 0.683013 - 443.96 5 $ 10,450.00 0.620921 $ 6,488.63 Total -$ 23,571.78 Cost for year 5 = salvage value - maintenance cost i.e. ($11100-$650) Net present value = -$23571.80 Alternative 2: Lease option Year Cost (A) 1 -$ 3,640.00 2 - $ 3,640.00 3 -$ 3,640.00 4-$ 3,640.00 5 -$ 3,640.00 Total Net present value = -$13798.46 PV Factor Present value (AXB) 0.909091 - $ 3,309.09 0.826446 -$ 3,008.26 0.751315 -$ 2,734.79 0.683013 - 2,486.17 0.620921-$ 2,260.15 $ 13,798.46

Purchase NPV $ 23,571.78 $ 13,798.46 Lease 2) Harold should choose lease option as there is less outflow in lease option compared to purchase option. Choose lease option Working note: PV factor = 1/ (1+r)^n n=no. Of year r=rate of interest i.e. 10% Year (1+0.10)^n PV factor = 1/(1+r)^n 1.1 1.21 1.331 1.4641 1.61051 0.909090909 0.826446281 0.751314801 0.683013455 0.620921323