Question

Roberts Fabrication and Automation, Inc. (RFA) just completed its Capital Budgeting analysis for a new metallic 3D printing machine that will aid in the design and production of new “classic” and custom automotive components. The NPV is positive and significant, the IRR is well above the 12% project hurdle rate (required return), and RFA has decided to move forward with the project.

The next part of their analysis involves the financing of the machine, that is, whether to purchase, or to lease the machine.

If the printer is purchased:

The initial investment (printer cost, shipping, & installation) is $327,500. RFA expects to borrow this amount from the 4th Tennessee Bank of the Southeast with a term of 4 years and an interest rate of 7.25%. The loan would be fully amortized and call for annual payments at the end of each year. Maintenance costs are predicted to be $20,000 per year. Base on Internal Revenue Service guidelines, the printer will be depreciated using MACRS (half-year convention) and a 5 year class-life. RFA’s tax rate is 31%

The Leasing option:

The printer will be made by Custom Tools of Middle Tennessee. It has offered to lease the printer to RFA as an alternative to the purchase option. Their proposed lease terms are:

•  Lease payments of $85,000 per year beginning on the installation of the printer with a total of 5 payments. (This means payments at t = 0, 1, 2, 3, and 4).

•  The Lease payments above include all maintenance.

  RFA expects to operate this project for 4 years (and no more), regardless of whether is purchases or leases the printer. The printer is expected to have a market value of $42,500 (“salvage value”) at the end of the 4 year project.

  Using a blank worksheet (or page of paper) conduct the Lease vs Buy analysis.

a. Using Custom Tools’ proposed lease terms, what is the NAL, and should the 3d printer be leased or

purchased?

b. Using your first analysis (part a.), at what lease payment would the firm be indifferent to either leasing or buying? That is, what annual lease payment results in a NAL=0?

c. The salvage value is the most uncertain cash flow in the analysis. With the additional risk of that cash flow (assume a pre-tax discount rate of 15 percent for this item), what would be the effect of a salvage value risk adjustment on the decision? That is, what is the revised NAL, and decision in this scenario? Note: The salvage value is the only cash flow affected in this scenario.

Answer 1

I.Purchase decision

First, we find the annual equal payment on the bank loan

Using the PV of ordinary annuity formula

327500= Pmt.*(1-1.0725^-4)/0.0725

so, the annual payment on the loan=

97234

Drawing up the loan amortisation table, to know the annual payments towards interest & principal,
Year	Annuity	Tow. Int.	Tow.Princ.	Prin. Bal.
0				327500
1	97234	23744	73490	254010
2	97234	18416	78818	175192
3	97234	12701	84532	90660
4	97234	6573	90661	0

MACRS annual depn. rates
Year					Book value(327500*(11.52+5.76)%=	56592
1	20				Salvage	42500
2	32				Loss on salvage	14092
3	19.2				Tax saved on loss(14092*31%)	4369
4	11.52	270908			So, Cash flow on salvage(42500+4369)	46869
5	11.52	56592	Book value
6	5.76	327500
	100

NPV of purchase
Year	Annuity cash outflow	Interest	Depn.	Maintenance costs	Tax savings	Net Cash out flow	PV F at 12%	PV
A	B	C	D	E	F=(C+D+E)*31%	G=B+E-F	H	G*H
0						0	1	0
1	97234	23744	65500	20000	33866	83368	0.89286	74436
2	97234	18416	104800	20000	44397	72837	0.79719	58065
3	97234	12701	62880	20000	29630	87603	0.71178	62354
4	97234	6573	37728	20000	19933	97300	0.63552	61836
4	-42500				4369	-46869	0.63552	-29786
	NPV of the Purchase decision							226905

Lease option
Given the beginning of the year lease payments of $ 85000
there is an annual tax savings of (85000*31%)=26350 ,from end of Yr.1
Working out the NPV :
Year	Lease payment	Tax savings at 31%	Net cash ouflow	PV F at 12%	PV
A	B	C=B*31%	D=B-C	E	D*E
0	85000		85000	1	85000
1	85000	26350	58650	0.89286	52366
2	85000	26350	58650	0.79719	46755
3	85000	26350	58650	0.71178	41746
4	85000	26350	58650	0.63552	37273
5		26350	-26350	0.56743	-14952
	NPV of the Lease decision				248189

NPV of the Purchase decision	226905
NPV of the Lease decision	248189
NAL= (negative)	-21284
Purchase option is cheaper

b. The NPV of Purchase is   226905
So, the if the NPV of the lease should be the same to be indifferent
ie.
Forming an equation with this NPV &PV Factor   figures from the lease NPV workings-Table
Supposing the lease payment as x
x+(3.03735*(1-0.31)*x)-(0.31*x*0.56743)=226905
x+(0.69*x*3.03735)-(0.31*x*0.56743)=226905
Solving for x, the lease payment for NAL to be =0 will be
77710.7
ie. 77710
ie. Annual lease payment that results in a NAL=0 is
$77,710
NAL=0
Year	Lease payment	Tax savings at 31%	Net cash ouflow	PV F at 12%	PV
A	B	C=B*31%	D=B-C	E	D*E
0	77710.7		77710.7	1	77710.7
1	77710.7	24090.32	53620.38	0.89286	47875
2	77710.7	24090.32	53620.38	0.79719	42746
3	77710.7	24090.32	53620.38	0.71178	38166
4	77710.7	24090.32	53620.38	0.63552	34077
5		24090.32	-24090.3	0.56743	-13669
	NPV of the Lease decision				226905

c. Assuming Pretax discount rate = 15% for the salvage cash flow

NPV of purchase as per a. 226905 (Refer NPV-Purchase table)

Discounting the pretax salvage cash flow at the given pretax discount rate of 15%

226905+29786-(42500*0.57175)=                       ( P/F 15%,4)

232392

Even now, NPV of Purchase(2323920 is < NPV of Lease (248189)

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