Question

One year ago, your company purchased a machine used in manufacturing for $90,000. You have learned that a new machine is available that offers many advantages and you can purchased it for $130,000 today. It will be depreciated on a straight line basis over 10 years and has no salvage value. You expect that the new machine will produce a gross margin (revenue minus operating expense other than depreciation) of $40,000 per year for the next ten years. The current machine is expected to produce a gross margin of $20,000 per year. The current machine is being depreciated on a straight line basis over a useful life of 11 years, and has no salvage value, so depreciated expense for the current machine is $9,000 per year. The market value today for the current machine is $50,000. Your company's tax rate is 45%, and the discount rate is 10%. show your steps

1) What is the after tax salvage value if selling the current machine today? (hint: first find out  what is the total depreciation of the current machine and what is the book value of the current machine)

2) What is the incremental depreciation if your company purchasing the new machine and at the same time selling the old machine? (hint:  First find out what is the new depreciation per year for the new machine?And what is the depreciation of the current machine? The incremental depreciation is the difference between new depreciation and old depreciation)

3) What is the cash flow for year 0 if your company decide to sell the current machine and purchase the new machine today? (hint: thinking about what are possible cash flows for year 0)

4) What is the NPV if your company decide to purchase the new machine? (hint: to find NPV you need to know the cash flow for year 0 and cash flow for year 1-10, and discount rate.  What is the incremental cash flow for the year 1 to 10 if your company decide to sell the current machine and purchase the new machine today?  the formula you can use to find the cash flow from year 1 to 10 is {(sales-cost)*(1-tax rate)+Depreciation *tax rate} .

Answer 1

Solution 1) Old machine purchase price = $90,000

Depreciation per year on the old machine = $9,000

Number of years passed since purchase = 1

Current book value of the machine = 90000 - 9000 = $81,000

The current market price of the machine = $50,000

Loss on sale of old machine = Current Book Value - Current Market Price

= 81000 - 50000 = $31,000

Tax Savings on the loss of sale = Tax rate*Loss on sale of machine

= 45%*31000 = $13950

After-tax salvage value = Current Market Price + Tax Savings due to loss on sale of machine

= 50000 + 13950 = $63,950

Solution 2) Purchase Price for new machine = $130,000

The useful life of the new machine = 10 years

Salvage Value = 0

Depreciation = (Purchase price - Salvage value)/Useful life

Depreciation = (130000 - 0)/10

Depreciation = 130000/10 = $13,000

Depreciation on old machine = $9,000

Incremental depreciation = Depreciation on new machine - Depreciation on old machine

= 13000 - 9000 = $4000

Solution 3) Initial investment for a replacement project = Purchase price for new machine - After-tax Salvage Value of old machine

= 130,000 - 63,950

= $66,050

Hence, net cash outflow in year t = 0 is: $66,050

Note: Here, it is cash outflow so it is written positive.

Solution 4) The cash flows are shown as follows:

Initial Investment in t = 0 is calculated as = $66,050

Cash Flows from year 1 to year 10 is calculated as:

= (Change in sales - Change in cost)*(1-tax rate) + Change in Depreciation *tax rate

= (Change in gross margin)*(1-tax rate) + Change in Depreciation *tax rate

= (40000 - 20000)*(1 - 45%) + (13000 - 9000)*45%

= 20000*(0.55) + 4000*(0.45)

= 11000 + 1800

= $12,800

Discount rate = 10%

Present value of annuity = Annuity Amount*[1 - 1/(1+r)^n]/i

Net Present Value (NPV) of the project = Present values of annuity of cash flows from t=1 to t=10 - Initial Investment

= 12800*[1 - 1/(1+10%)^10]/10% - 66,050

= 12800*[1 - 1/2.59974]/10% - 66,050

= 12800*[1 - 0.385543]/10% - 66,050

= 12800*0.614457/10% - 66,050

= 78650.46 - 66050

= $12,600.46

Since, the NPV of the project is positive, hence, we should accept the project and replace the machine.

Please comment in case of any doubt or clarifications required. Please Thumbs Up!!