Question

Bates Company has entered into two lease agreements. In each case the cash equivalent purchase price of the asset acquired is known and you wish to find the interest rate which is applicable to the lease payments.
Calculate the implied interest rate for the lease payments.

Lease A — Lease A covers office equipment which could be purchased for $36,048. Bates Company has, however, chosen to lease the equipment for $10,000 per year, payable at the end of each of the next 5 years.

Lease B — Lease B applies to a machine which can be purchased for $57,489. Bates Company has chosen to lease the machine for $12,000 per year on a 6-year lease. Payments are due at the start of each year.

Answer 1

Answer:

A) rate of 12%

B) rate of 10%

Explanation:

$PV \div \frac{1-(1+r)^{-time} }{rate} = C$

C   =  10000

n    = 5

PV = 36048

We solve for rate using a financial calculator or try an error or by looking at the PV tables of an annuitiues for the factor at n = 5 which equals PV/C

36048 / 10000 = 3.6048

this give us 12%

we do the same for b:

57,000 / 12,000 = 4.7500

we look for n= 7 for that facotr as; this is annuity-due (payment at the beginning)

which give us 10.000%

we could also use the rte function in excel:

=RATE(5;-12000;57000;;1)The first argument is the time period, then the installemtn and last the present value finally we add to excel that this is an annuity due.