The company you work for needs to rent a bulldozer for a job. The company has ma
ID: 1167741 • Letter: T
Question
The company you work for needs to rent a bulldozer for a job. The company has made a non-refundable deposit of the first month’s rent (equal to $1,000) on a 6-month lease for a bulldozer. The next day, you find a different bulldozer that also meets the requirements for the job, but only costs $900/month for a 6-month lease. Assuming the plan is to use the bulldozer for 6 months, and there are no additional costs associated with a switch in equipment, should you recommend that the company switch to the new bulldozer? What if the bulldozer is needed for 1 year, with both bulldozers having a 1-year lease term? The annual interest rate is 12%.
Explanation / Answer
In a given problem, it is assumed that deposit is done in the beginning of the month on monthly basis, for a given lease term. It makes a case of annuity due.
Annual interest rate = 12%
Thus, Monthly interest rate (r) = 12%/12 = 1%
Lease term is 6 month:
No. of months (n) = 6
P = monthly deposit
For old bulldozer ($1000 / month)
Present value of all payment for old bulldozer = (P*(1-1/(1+r)^n) / R)*(1+r)
Present value of all payment for old bulldozer = (1000*(1-1/1.01^6)/.01)*1.01) = $5853.44
Now
Present value of all payment for new bulldozer = (900*(1-1/1.01^6)/.01)*1.01) = $5268.09
Here, PV. Of payments for new bulldozer is less but company has already deposited $1000 that is nonrefundable. It means that
Total PV payment by the company if we hire new bulldozer = 5268.09 + 1000 = $6268.09
$6268.09 is higher than $5853.44 (of old bulldozer).
Thus, I will recommend the company to go with old bulldozer when lease period is 6 month.
Lease term is 12 months:
Present value of all payment for old bulldozer = (1000*(1-1/1.01^12)/.01)*1.01 = $11367.63
Present value of all payment for New bulldozer = (900*(1-1/1.01^12)/.01)*1.01 = $10230.87
Total PV of payment if new bulldozer is hired = $10230.87 + $1000 = $11230.87
Now, payment of $11230.87 is lesser than $11367.63 (of old bulldozer).
Thus, I will recommend the company to go for new bulldozer for 1 year lease term.