Question

Using a Calculator and Present Value Table to Impute Interest Rate and Determine Present Value of Operating Leases

AutoZone reports the following in its 2015 Form 10-K.

The Company leases some of its retail stores, distribution centers, facilities, land and equipment, including vehicles. Other than vehicle leases, most of the leases are operating leases...
The Company has a fleet of vehicles used for delivery to its commercial customers and stores and travel for members of field management. The majority of these vehicles are held under capital lease.

Future minimum annual rental commitments under non-cancelable operating leases and capital leases were as follows at the end of fiscal 2015:

	Operating	Capital
$ thousands	Leases	Leases
2016	$259,175	$40,528
2017	250,787	40,562
2018	234,640	28,558
2019	215,692	16,845
2020	192,882	5,077
Thereafter	905,629	-
Total minimum payments required	$2,058,805	131,570
Less: interest		(3,403)
Present value of minimum capital lease payments		$128,167

a. Use a finacial calculator to impute the implicit rate of return (to three decimal places) on the capital leases.
Round answer to three decimal places (ex: 0.023456 = 2.346%).
Answer

%

b. Assume that the appropriate discount rate for the operating leases is 1.16%. Use a financial calculator to determine the present value of the future minimum operating lease payments.
Round answer to the nearest dollar.
$Answer

c. Assume that the appropriate discount rate for the operating leases is 1%. Use presnt value tables to determine the present value of the future minimum operating lease payments.
Round answer to the nearest dollar.
$Answer

Answer 1

Answers:-

a) 1.159%

b) $ 1,970,855

c) $ 1,982,666

Workings:-

A) Since all lease rentals are different we have to use average method to get implicit rate of return:-

First of all we will compute present value of lease rental by taking two different rates, here i take 1% and 1.25%.

Year	Lease Rental	Present value Factor @ 1%	Present value	Present value Factor @ 1.25%	Present Value
2016	40528	0.9901	40,127	0.9877	40028
2017	40562	0.9803	39,763	0.9755	39567
2018	28558	0.9706	27,718	0.9634	27513
2019	16845	0.9610	16,188	0.9515	16028
2020	5077	0.9515	4,831	0.9398	4771
Total of Present value			128,627		127907

Now lets use this formula 1% + [{(128627-128167)/(128627-127907)}*(1.25-1.00)] = 1.159%

That formula means that how much more value needs to extract to get a value equal to present value of capital lease payments.

B) Calculate present value factor and multiply it with amount of minimum annual lease rental commitments.

Year	Lease Rental	Present value Factor	Present value
2016	259175	0.9885	256,203
2017	250787	0.9772	245,068
2018	234640	0.9660	226,660
2019	215692	0.9549	205,968
2020	192882	0.9440	182,074
2020	905629	0.9440	854,882
Total of Present value			1,970,855

C) Calculate present value factor and multiply it with amount of minimum annual lease rental commitments.

Year	Lease Rental	Present value Factor	Present value
2016	259175	0.9901	256,609
2017	250787	0.9803	245,846
2018	234640	0.9706	227,739
2019	215692	0.9610	207,276
2020	192882	0.9515	183,521
2020	905629	0.9515	861,675
Total of Present value			1,982,666