Question

The Robinson Corporation is considering replacing the wood steamer it currently uses to shape guitar sides. The steamer has 6 years of remaining life. If kept, the steamer will have depreciation expenses of $350 for 6 years. Its current book value is $2,100, and it can be sold on an Internet auction site for $4,500 at this time. Thus, the annual depreciation expense is $2,100/6=$350 per year. If the old steamer is not replaced, it can be sold for $800 at the end of its useful life.

Robinson is considering purchasing the Side Steamer 3000, a higher-end steamer, which costs $8,200, and has an estimated useful life of 6 years with an estimated salvage value of $900. This steamer falls into the MACRS 5-years class, so the applicable depreciation rates are 20.00%, 32.00%, 19.20%, 11.52%, 11.52%, and 5.76%. The new steamer is faster and allows for an output expansion, so sales would rise by $2,000 per year; the new machine's much greater efficiency would reduce operating expenses by $1,400 per year. To support the greater sales, the new machine would require that inventories increase by $2,900, but accounts payable would simultaneously increase by $700. Robinson's marginal federal-plus-state tax rate is 40%, and the project cost of capital is 12%.

What is the NPV of the project? Do not round intermediate calculations. Round your answer to the nearest dollar.

Answer 1

If New machine is purchased and old machine is sold.

NPV= Present Value of cash Inflow- Present Value of Cash outflow

In this case the NPV of this option shall be:-

Present Value of Cash Inflow = $20487.16

Present Value of Cash Outflow = $10360

NPV = PV of Cash inflow- PV of Cash outflow

= $20487.16 -$10360

= $10127.16 or $10127 (rounded off)

Since the NPV is positive, the decision to buy new machine and sell old machine should be taken.

Working for Present Value of Cash inflow

Year	Cash Inflow in $ (a)	Depreciation Added back in $ (b)	Total Cash Inflow In $ (c)=(a)+(b)	Present Value factor @ 12%(according to PVF table) (d)	Amount in $ (c)*(d)
1	3400	1640	5040	.8929	4500.22
2	3400	2624	6024	.7972	4802.33
3	3400	1574.4	4974.4	.7118	3540.78
4	3400	944.64	4344.64	.6355	2761.02
5	3400	944.64	4344.64	.5674	2465.15
6	4300	472.32	4772.32	.5066	2417.66
			Total	20487.16

Cash Inflow = Rise in sales + Saving in expenses = $2000+ $1400 = $3400 per year

At 6th Year the cash inflow shall include the residual value

That is,

Cash Inflow in 6Th Year = $3400 + $ 900= $4300

Depreciation calculation

In MACRS method, the dwepreciation is calculated on the Cost price for each year.

Year	Depreciation Rate in %	Amount in $
1	20	8200*20/100= 1640
2	32	8200*32/100= 2624
3	19.20	8200*19.20/100= 1574.4
4	11.52	8200*11.52/100= 944.64
5	11.52	8200*11.52/100= 944.64
6	5.76	8200*5.76/100= 472.32

Working for Present Value of Cash Outflow

If old machine is sold:-

Current Book Value of old machine= $ 2100

Current Sale Value of old machine= $ 4500

Profit on sale = sale price - book value = 4500-2100 = $2400

Now, Tax paid on profit @ 40% = $2400*40/100 = $960

Net Sale Value of old machine Adjusted after tax = $2400- $960 = $1440

Now,

Total Cash outlow in case of new machine = Cost price + Cost of Inventory Increase + Increase in Accounts Payable

i.e. = $8200+ $2900+ $ 700 = $11800

Now,

Net Cash Outlflow = Total Cash outflow - Net Sale value recieved from old machine

= $11800- $1440 = $10360

Present value of cash outflow = $10360 * Present value factor @12% for 0year

= $10360*1 = $10360