Question

Kiddy Toy Corporation needs to acquire the use of a machine to be used in its manufacturing process. The machine needed is manufactured by Lollie Corp. The machine can be used for 8 years and then sold for $23,000 at the end of its useful life. Lollie has presented Kiddy with the following options: (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.) 1. Buy machine. The machine could be purchased for $173,000 in cash. All insurance costs, which approximate $18,000 per year, would be paid by Kiddy. 2. Lease machine. The machine could be leased for a 8-year period for an annual lease payment of $38,000 with the first payment due immediately. All insurance costs will be paid for by the Lollie Corp. and the machine will revert back to Lollie at the end of the 8- year period. Required: Assuming that a 9% interest rate properly reflects the time value of money in this situation and that all maintenance and insurance costs are paid at the end of each year, determine which option Kiddy should choose. Ignore income tax considerations. (Negative amounts should be indicated by a minus sign. Round your final answers to nearest whole dollar amount.) PV Buy option Lease option Kiddy should choose

Answer 1

Buying	$261080
Lease	$229252
Kiddy should choose	Lease

Solution :

Present value of Buy option :

Present value = Purchase amount + PV of insurance payments - PV of residual value.

Where,

Purchase amount = $173000

PV of insurance payments = $18000 × present value annuity factor at 9% for 8 years.

= $18000 × 5.5348

= $99626.4

= $99626

PV of residual value = $23000 × PV factor at 9% for 8th year.

= $23000×0.502

= $11546

Therefore,

PV of buying option = $173000 + $99626 - $11546

= $261080

This is present of cash outflows, it means the cost of the machine for today is $261080.

PV of lease option :

PV = first lease payment + (annual lease payment × present value annuity factor at 9% for 7 years)

= $38000 + ($38000×5.03295)

= $38000 + $191252

= $229252

This is present value of cash outflows, it means that today's cost of machine is $229252

Note1 : "PV" is present value of cash outflows. If it is taken as present value of cash inflows then the same figures entered in the answer will be taken as negative figures.

Note 2 : calculations of present value annuity factor

PV annuity factor = [1-(1+r)^-n  /r]

r = rate of interest and n = number of years

So PV annuity factor at 9% for 8 years = [1-(1+0.09)^-8 ]/0.09

= [1-1/(1.09)⁸ ]/0.09

= 5.5348

PV of annuity at 9% for 7 years = [1-(1+0.9)⁷  ]/0.09

= [1-(1.09)^-7]/0.09

= [1-1/(1.09)⁷ ]/0.09

= 5.03295

Note3 : calculations of PV factor

PV factor = 1/(1+r)ⁿ

r = rate of interest and n is number of years

PV factor at 9% for 8th = 1/(1+0.09)⁸

= 1/(1.09)⁸

= 0.502