Question

The management of The Alexandrov Company decided to acquire the use of a machine to be used in its manufacturing process. The machine is manufactured only by Chang, Incorporated. The machine would have a useful life of ten years and would then be sold for $10,000 at the end of its useful life. Chang’s management has presented Alexandrov with the following acquisition options: Lease: The machine could be leased for an eight-year period for an annual lease payment of $25,000, with the first payment due on the date that the agreement is signed. Related annual executory costs (maintenance and insurance expenses for the machine), which are expected to be about $5,000 per year, would be paid by Alexandrov. Purchase: The machine could be purchased for $130,000 in cash. The related maintenance and insurance costs would also become the additional responsibility of Alexandrov. Assume that (1) Alexandrov and Chang will agree on a transaction on November 30, 2020; and (2) the current interest rate for Alexandrov’s lease arrangements is 12%, but the rate applicable to annual maintenance and insurance expenses is only 8%. Prepare a schedule showing the alternatives available to The Alexandrov Company for the acquisition of the equipment.

Answer 1

STEP 1 - PRESENT VALUE OF CASH OUTFLOW - LEASE

	Year	Lease payment	Annual maintenance and insurance	PVF12%	PVF 8%	Present value of cash outflow
	(1)	(2)	(3)	(4)	(5)	(2)x(4) + (3)x(5)
	1	$           25,000.00	$                  5,000.00	1.0000	1.0000	$            30,000.0000
	2	$           25,000.00	$                  5,000.00	0.8929	0.9259	$            26,951.0582
	3	$           25,000.00	$                  5,000.00	0.7972	0.8573	$            24,216.5410
	4	$           25,000.00	$                  5,000.00	0.7118	0.7938	$            21,763.6674
	5	$           25,000.00	$                  5,000.00	0.6355	0.7350	$            19,563.1012
	6	$           25,000.00	$                  5,000.00	0.5674	0.6806	$            17,588.5874
	7	$           25,000.00	$                  5,000.00	0.5066	0.6302	$            15,816.6262
	8	$           25,000.00	$                  5,000.00	0.4523	0.5835	$            14,226.1824
					TOTAL	$          170,125.7638

	STEP 1 - PRESENT VALUE OF CASH OUTFLOW - PURCHASE
	Year	Initial investment and salvage vale	Annual maintenance and insurance	PVF8%	PVF 8%	Present value of cash outflow
	(1)	(2)	(3)	(4)	(5)	(2)x(4) + (3)x(5)
	1	$        130,000.00	$                  5,000.00	1.0000	1.0000	$          135,000.0000
	2	$                          -	$                  5,000.00	0.9259	0.9259	$               4,629.6296
	3	$                          -	$                  5,000.00	0.8573	0.8573	$               4,286.6941
	4	$                          -	$                  5,000.00	0.7938	0.7938	$               3,969.1612
	5	$                          -	$                  5,000.00	0.7350	0.7350	$               3,675.1493
	6	$                          -	$                  5,000.00	0.6806	0.6806	$               3,402.9160
	7	$                          -	$                  5,000.00	0.6302	0.6302	$               3,150.8481
	8	$                          -	$                  5,000.00	0.5835	0.5835	$               2,917.4520
	9	$                          -	$                  5,000.00	0.5403	0.5403	$               2,701.3444
	10	$        (10,000.00)	$                  5,000.00	0.5002	0.5002	$            (2,501.2448)
					TOTAL	$          161,231.9499

If machine is purchased, there are two benefits. Firstly, it has the lower cash outflow. Secondly, it can be used for 10years while lease term is jut 8 years. And hence, Purchase of machinery is recommended.

Notes :

1. Since two discounting rates are given, For lease, 12% will be considered and for others 8% will be taken.

2. Due to lack of information, it is assumed that annual maintenance and insurance expense are paid at the beginning of the year. Student can also assume that such payments are made at the end of the year, in such case, in below tables, 'PVF 8%' column have to modified. That is, for year 1, the value would be 0.9259 instead of 1.0000, for year to value would be 0.8573 and so on.