Question

3. The Capitalpoor Company is considering purchasing a business machine for $100,000. An alternative is to rent it for $35,000 at the beginning of each year. The rental would include all repairs and service. If the machine is purchased, a comparable repair and service contract can be obtained for $1,100 per year. The salesperson of the business machine firm has indicated that the expected useful service life of this machine is five years, with zero market value at the end of any year, but the company is not sure how long the machine will actually be needed. If the machine is rented, the company can cancel the lease at the end of any year. Assuming an income tax rate of 30%, a straight-line depreciation charge of $20,000 for each year the machine is kept, and an after-tax MARR of 12%, prepare an appropriate analysis to help the firm decide whether it is more desirable to purchase or rent. Assume that the machine will be used for 4 years. 2 Click the icon to view the interest and annuity table for discrete compounding when i = 12% per year. The AW of leasing is $ thousand. (Round to one decimal place.) The AW of buying is $ thousand. (Round to one decimal place.) What is more desirable? Choose the correct answer below. O O Purchase Lease 2: More Info Discrete Compounding; i = 12% Single Payment Uniform Series Compound Compound Sinking Amount Present Amount Present Fund Factor Worth Factor Factor Worth Factor Factor To Find F To Find P To Find F To Find P To Find A Given P Given F Given A Given A Given F FIP P/F FIA PIA AIF 1.1200 0.8929 1.0000 0.8929 1.0000 1.2544 0.7972 2.1200 1.6901 0.4717 1.4049 0.7118 3.3744 2.4018 0.2963 1.5735 0.6355 4.7793 3.0373 0.2092 1.7623 0.5674 6.3528 3.6048 0.1574 1.9738 0.5066 8.1152 4.1114 0.1232 2.2107 0.4523 10.0890 4.5638 0.0991 2.4760 0.4039 12.2997 4.9676 0.0813 2.7731 0.3606 14.7757 5.3282 0.0677 3.1058 03220 17.5487 56502 00570 60 V AWN Capital Recovery Factor To Find A Given P A/P 1.1200 0.5917 0.4163 0.3292 0.2774 0.2432 0.2191 0.2013 0.1877 1770

Answer 1

Refer to the below Excel analysis & following explanation :

Inputs
New Machine Cost	100000
Annual maintenance costs	1100
Annual Depriciation (Deprn)	20000
Annual Lease payments	35000
Tax rate (T)	30%
Planned life for machine (years)	4
MARR	12%
Cost of Owning	year= 0	1	2	3	4
Cost of machine	-100000
Annual maintenance costs		-1100	-1100	-1100	-1100
Maintenance tax savings (=Maint.x T)		330	330	330	330
depriciation tax savings (=Depr. x T)		6000	6000	6000	6000
After tax salvage value (=Salvage Value x(1- T)					14000
Net effect on cash flow	-100000	5230	5230	5230	19230
	NPV of buying	$                      -75,217.4
	AW of buying	₹ 24,764.2
Cost of Leasing	year= 0	1	2	3	4
Annual lease payment		-35000	-35000	-35000	-35000
Tax Savings on lease (=Lease*Tax rate)		10500	10500	10500	10500
Cash flow		-24500	-24500	-24500	-24500
	NPV of leasing	$                      -74,415.1
	AW of Leasing	₹ 24,500.0

The relevant cash flows in case of owning are - cost of machine, the annual maintenance costs as given, the tax savings on Maintenance costs as these costs will get subtracted from income while calculating tax, similarly the tax savings due to depcricition (Only tax savings on depriciation are relevant since it is a non cash charge) and lastly the after tax salvage value- which would be 100000-80000(cumulative depriciation till year 4) = 20000 and tax on it at 30% will be 6000 so After tax salvage value will be 14000 as shown above. Adding all these we get the Net cash flow effect of owning the machine.

Similarly we find cash flows for leasing by using the relevant cash flow which are only the leasing expense & tax savings on it

Next, using these cash flows in the Excel NPV function we find the NPV of these cash flow streams. Once we get the NPV, we use Excel's (or any financial calculator's) PMT function with rate =12%, NPER= 4 & PV = NPV for each case as found above to find the AW as shown.

Now, to answer what is more desirable, we see that the AW of leasing is less than that of Buying so Leasing is more desirable in this case.