Ganges Express, a package delivery company, operates a fleet of Volvo trucks at
ID: 2737865 • Letter: G
Question
Ganges Express, a package delivery company, operates a fleet of Volvo trucks at one terminal where the lease of 175,000 euros per year is expiring. They had planned to set up another lease with Volvo for next three years at a cost of 200,000 euros per year in operating expenses. This is the total cost for the entire fleet. A Scania sales rep just called to offer a discounted price of 700,000 euros for Ganges to purchase a new fleet (instead of leasing). If the new fleet is purchased, then Ganges expects to sell the Scania trucks at book value at the end of three years. They use straight-line depreciation over 5 years for new vehicles. Assume the tax rate is 30% and the discount rate for Ganges Express is 10%. Ignore inflation.
What is the highest discount rate under which Ganges Express would choose to purchase the Scania trucks?
Please do not copy/paste the other answer on Chegg. It is incorrect and unhelpful.
Explanation / Answer
Cost of leasing:
Cost of lease per year=200,000.
After tax cost of leasing =200,000*(1-.30)
=140000
Discount rate=10%.
Present value annuity factor for 3 years at 10% =(1-(1+i)-n)/i where i is the dicount rate.
=1-(1+.10)-3/.10
=2.4868.
Therefore present value of leasing =2.4868*140000
= 348,159 Euros.
Present value of purchasing the fleet:
cost of fleet - Present value of tax savings on account of depreciation - Present value of resale value
Cost of fleet=$700,000.----------(1)
Life of the fleet = 5years.
Depreciation under straight line basis = (Cost of the fleet- Salvage value)/5
=$700,000-0/5
=$140,000.
Tax savings on account of depreciation =$140,000 *(1-.30)
=140,000* (.70)
=98,000.
Present value of tax savings on account of depreciation =98,000* present value annuity factor for three years
=98000*2.4868
=243,711.-------(2)
Present value of resale price=700,000 -140,000*3 *(1/(1+.10)3)
=280,000.*0.751
=210368.144------(3)
NPV=(1)-(2)+(3)
=700000-243,711-210368.144
=-245,920.
At 10% discount rate it is good option to purchase than to lease. By trail and error method and replacing the annuity factor and discount factor for both cases, it is observed that at 17%.
Particulars Amount 10% 11% 12% 13% 14% 15% 16% 17% 18% Savings per year on account of depreciation 98000 2.486851991 2.443714715 2.40183127 2.361152598 2.32163203 2.283225117 2.24588954 2.209584962 2.17427293 Resale proceeds 280000 0.751314801 0.731191381 0.71178025 0.693050162 0.67497152 0.657516232 0.640657674 0.624370556 0.60863087 Present value of savings on account of depreciation 243711.4951 239484.0421 235379.464 231392.9546 227519.939 223756.0615 220097.175 216539.3263 213078.747 Present value of sale proceeds of the fleet 210368.1443 204733.5868 199298.469 194054.0454 188992.025 184104.5451 179384.1486 174823.7558 170416.644 Total cash inflows/Savings 454079.6394 444217.6289 434677.934 425447 416511.963 407860.6066 399481.3235 391363.0821 383495.391 Cash outflow on account of purchase 700000 700000 700000 700000 700000 700000 700000 700000 700000 NPV -245920.361 -255782.3711 -265322.07 -274553 -283488.04 -292139.393 -300518.6765 -308636.9179 -316504.61 Cost of lease net off savings on account of depreciation -140000 Present value of lease -348159.279 -342120.0602 -336256.38 -330561.364 -325028.48 -319651.516 -314424.5357 -309341.8947 -304398.21Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.