Question

Doane Company has entered into two rental 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 rental payments.

Instructions:

Calculate the implied interest rate for the rental payments in each situation below:

Agreement A — Covers office equipment which could be purchased for $37,907.90. Doane Company has, however, chosen to rent the equipment for $10,000 per year, payable at the end of each of the next 5 years.

Agreement B — Applies to a machine which can be purchased for $48,448.20. Doane Company has chosen to rent the machine for $12,000 per year on a 5-year rental agreement. Payments are due at the beginning of each year.

Answer 1

The lease liability is the present value of minimum lease payments discounted at implicit rate of interest,

Since the rate of interest is required, we need to use trail and error method.

Lets assume 10% rate of interest.

Present value of lease payments = 37907.9, lease payments= 10000, no.of years =5

Year	PVF(10%,n)	lease payments	present value
1	0.90909	10000	9090.9
2	0.82645	10000	8264.5
3	0.75131	10000	7513.1
4	0.68301	10000	6830.1
5	0.62092	10000	6209.2
		Total	37907.8

Since present value of lease payments is approximately equal to 37907.9, rate of interest = 10%

2.

Present value of lease payments = 48448.20

Lease payments = 12000, No.of Lease payments = 5years at the beginning of the year.

Since the Payment is made at the beginning of the year, Only Four lease payments need to be discounted.

--> 48448.20 = 12000*1+ PVAF(r%,4)*12000

---> 48448.20 - 12000 = PVAF(r%,4). ----> 36448.20 = PVAF(r%,4)

We need to use trail and error method to find the actual rate of interest:

Assume 10% is rate of interest .

Year	PVF(10%,n)	leasepayments	present value
1	0.90909	12000	10909.08
2	0.82645	12000	9917.4
3	0.75131	12000	9015.72
4	0.68301	12000	8196.12
		Total	38038.32

Since The present value at 10% = 38038.32 exceeds the required amount we need to increase the interest rate.

Lets assume 12 % rate of interest

Year	PVF(12%,n)	leasepayments	present value
1	0.89286	12000	10714.32
2	0.79719	12000	9566.28
3	0.71178	12000	8541.36
4	0.63552	12000	7626.24
		Total	36448.2

The present value at 12% equals 36448.2 , rate of interest is 12%.