Question

Deutsche Transport can lease a truck for four years at a cost of €49,000 annually. It can instead buy a truck at a cost of €99,000, with annual maintenance expenses of €29,000. The truck will be sold at the end of four years for €30,000. Ignore taxes.

What is the equivalent annual cost of buying and maintaining the truck if the discount rate is 12%?

Which is the better option: leasing or buying?

Answer 1

Solution

Present value of a cashflow=Cashflow/(1+r)^n

where

r=discount rate=12%

n=period of cashflow

Present value of the cost of owneship of truck=Initial cost of buying+Present value of maintainance expenses-Present value of selling price of truck

Present value of the cost of owneship of truck =99000+29000/(1+.12)^1+29000/(1+.12)^2+29000/(1+.12)^3+29000/(1+.12)^4-30000/(1+.12)^4

=168017.589

Present value of the cost of owneship of truck=Annual equivalent cost*((1-(1/(1+i)^m))/i)

i=discount rate=12%

m=number of periods=4

Present value of the cost of owneship of truck=168017.589

Therefore

168017.589=Annual equivalent cost*((1-(1/(1+.12)^4))/.12)

Solving we get Annual equivalent cost=55317.18

Since Annual cost of leasing is less than ownership, therefore leasing is better

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