Question

Boeheim County is considering two lease options for new garbage trucks. Option A is a five-year lease that requires a $20,000 down-payment at the beginning and monthly lease payments of $3,000. The trucks are expected to use $1,000 per month in gas. Option B is a three-year lease on hybrid trucks, with a $50,000 down-payment and $2,500 per month lease payments. The hybrids use only $500 per month in gas. Assume the cost of capital is 9% per year and that all payments come at the end of each month. Based on the finances, which lease is better?

Answer 1

Let us calculate the present va;ue of the cashflows for both options in order to find out option is better.

Cashflows given are:

Option A:

Down Payment = $ 20,000

Monthly lease- payments = 3000

Gas expenses per month = 1000

cost of capital = 9%

Let us now find out the present value of the lease and gas payments considering the 5-year lease tenure

Total Expenses per month= 3000 + 1000 = 4000

PV of Lease payments can be calculated using Present Value of Annuity formula. Annuity refers to recurring payment that are made periodically, similar to lease payments and gas expenses in this case.

Here PMT is the periodic payment = 4000

r is the discount rate per period = 9%/12 = 0.0075

n is the number of periods = 5*12 months = 60 months

Hence present value of Lease payments and cost of gas for Option A is 192,693.50

Hence, Total Expenses for Option A = Down pament + PV of lease & Gas payments

Total Expenses for Option A = 20000 + 192,693.50 = 212,693.5

For Option B:

Down payment = 50,000

Lease payments per month = 2500

Tenure = 3 years

Gas expenses per month = 500

Cost of capital = 9% per year

Total expenses per month = 2500 + 500 = 3000

PV of these expenses is given by:

Here PMT is the periodic payment = 3000

r is the discount rate per period = 9%/12 = 0.0075

n is the number of periods = 3*12 months = 36 months

Hence present value of Lease payments and cost of gas for Option B is 94340.42

Hence, Total Expenses for Option B = Down pament + PV of lease & Gas payments

Total Expenses for Option B = 50000 + 94340.42= 14434040.42

Since the life-time of both the options is different, let us calculate the equivalent annuity Value in both the cases to compare them on common grounds.

Equivalent annual annuity formula is given by:

where P is the Present Value of the total expenses

r is the discount rate = 9%

n is the number of time periods

Equivalent annual annuity for Option A is

Equivalent annual annuity of Option A = 54,681.89

Similarly, Equivalent annual annuity for Option B is:

Equivalent annual annuity of Option B = 57,022.37

Equivalent annual annuity of expenses in case of Option A is less than that of Option B, hence Option A should be considered in this case.