Question

Luang Company is considering the purchase of a new machine. Its invoice price is $122,000, freight
charges are estimated to be $3,000, and installation costs are expected to be $5,000. Salvage value of the new
machine is expected to be zero after a useful life of 4 years. Existing equipment could be retained and used for an
additional 4 years if the new machine is not purchased. At that time, the salvage value of the equipment would be
zero. If the new machine is purchased now, the existing machine would be scrapped. Luang’s accountant, Lisa
Hsung, has accumulated the following data regarding annual sales and expenses with and without the new
machine.
1. Without the new machine, Luang can sell 10,000 units of product annually at a per unit selling price of
$100. If the new unit is purchased, the number of units produced and sold would increase by 25%, and the selling
price would remain the same.
2. The new machine is faster than the old machine, and it is more efficient in its usage of materials.
With the old machine the gross profit rate will be 28.5% of sales, whereas the rate will be 30% of sales with the new machine.
(Note: These gross profit rates do not include depreciation on the machines. For purposes of determining net income,
treat depreciation expense as a separate line item.)
3. Annual selling expenses are $160,000 with the current equipment. Because the new equipment would produce a greater
number of units to be sold, annual selling expenses are expected to increase by 10% if it is purchased.
4. Annual administrative expenses are expected to be $100,000 with the old machine, and $112,000 with the new machine.
5. The current book value of the existing machine is $40,000. Luang uses straight-line depreciation.
6. Luang’s management has a required rate of return of 15% on its investment and a cash payback period of no more than 3 years.
Instructions: (Ignore income tax effects.)
(a) Calculate the annual rate of return for the new machine. (Round to two decimals.)
(b) Compute the cash payback period for the new machine. (Round to two decimals.)
(c) Compute the net present value of the new machine. (Round to the nearest dollar.)
(d) On the basis of the foregoing data, would you recommend that Luang buy the machine? Why?

Answer 1

a
Annual rate of return	Operating income/Investment
Annual rate of return	54500/90000
Annual rate of return	61%

Please note that in absence of information regarding sale price of Old assets, it is assumed that the Scrap price is equal to the book value of old assets.

b
Payback period	Investment/Cash Flow
Payback period	90000/87000
Payback period	1.03 Years

c
PV of Inflows	87000*2.85498	248,383
Investment		90,000
Net Present value		158,383

d.

Yes, as it will earn us incremental Cash flow of 62,000 per Year with Net present value of 158,383 and the payback period of Initial investment is 1. 03 years.  

Workings:

	New Machine	Old Machine
Sale Units	12,500	10,000
Sales	1,250,000	1,000,000
Gross Profit(30% and 28.5%)	375,000	285,000
Selling Expenses	176,000	160,000
Admin Expesnes	112,000	100,000
Annual cash Flow	87,000	25,000
Depreciation	32,500	10,000.00
Net Operating Income	54,500	15,000

Purchase of a new machine	122,000
Freight	3,000
installation costs	5,000
Initial Investment	130,000
Scrap value of Old Machine	40,000
Relevant Investment	90,000
Depreciation	32,500

Year	PV Factor
1	0.86957
2	0.75614
3	0.65752
4	0.57175
Annuity Factor	2.85498

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