PLEASE HELP!!!!

Question

I am having a lot of trouble in a managerial finance class. If you could help, I would greatly appreciate it.

A bicycle manufacturer currently produces 300,000 units a year and expects output levels to remain steady in the future. It buys chains from an outside supplier at a price of $2 a chain. The plant manager believes that it would be cheaper to make these chains rather than buy them. Direct in-house production costs are estimated to be only $1.50 per chain. The necessary machinery would cost $250,000 and would be obsolete after 10 years. This investment could be depreciated to zero for tax purposes using a 10-year straight-line depreciation schedule. The plant manager estimates that the operation would require $50,000 of inventory and other working capital upfront (year 0), but argues that this sum can be ignored because it is recoverable at the end of the 10 years. Expected proceeds from scrapping the machinery after 10 years are $20,000.

If the company pays tax at a rate of 35% and the opportunity cost of capital is 15%, what is the net present value of the decision to produce the chains in-house instead of purchasing them from the supplier?



I got the formula, but I can't apply it at all.

Free Cash Flow = EBIT (1 – t) + depreciation + depreciation & Amortization – capital expenditures – the change in net working capital

Answer 1

To determine whether the bicycle manufacturer should make its own chains or continue buying them from the supplier, we need to calculate the Net Present Value (NPV) of producing the chains in-house.

The important idea is that making the chains saves money every year, but the company must spend money upfront on machinery and working capital. We need to determine whether the savings are worth more than the initial investment.

Step 1: Calculate the annual cost savings.

The company currently purchases 300,000 chains per year at $2.00 each.

Annual purchasing cost:

300,000 × $2.00 = $600,000

If the company makes the chains itself, each chain will cost only $1.50.

Annual production cost:

300,000 × $1.50 = $450,000

Therefore, the annual savings are:

$600,000 - $450,000 = $150,000

Annual savings = $150,000

This means the company would save $150,000 each year by manufacturing its own chains.

Step 2: Calculate annual depreciation.

The machinery costs $250,000 and will be depreciated to zero over 10 years using straight-line depreciation.

Annual depreciation = Machinery Cost / Useful Life

= $250,000 / 10

Annual depreciation = $25,000

Depreciation is not an actual cash payment each year. However, it reduces taxable income, which saves the company money on taxes.

Step 3: Calculate the annual after-tax operating cash flow.

First, subtract depreciation from the annual savings to find the additional taxable income:

$150,000 - $25,000 = $125,000

Next, calculate the taxes at 35%:

$125,000 × 0.35 = $43,750

Now subtract taxes from the annual savings:

$150,000 - $43,750 = $106,250

Annual after-tax operating cash flow = $106,250

We can also check this using the standard operating cash flow formula:

Operating Cash Flow = (Savings - Depreciation) × (1 - Tax Rate) + Depreciation

= ($150,000 - $25,000) × 0.65 + $25,000

= $81,250 + $25,000

= $106,250

The company generates an additional $106,250 in cash each year for 10 years.

Step 4: Calculate the initial investment.

The company needs to purchase machinery costing $250,000 and invest $50,000 in working capital.

Initial Investment = Machinery + Working Capital

= $250,000 + $50,000

Initial Investment = $300,000

The plant manager is incorrect to suggest ignoring working capital simply because it will eventually be recovered.

The company must spend the $50,000 today but will not receive it back until year 10. Because of the time value of money, receiving $50,000 in 10 years is worth less than having $50,000 today.

Therefore, we must include both the initial working capital investment and its eventual recovery.

Step 5: Calculate the after-tax salvage value.

At the end of 10 years, the machinery can be sold for $20,000.

Since the machinery will be fully depreciated, its book value will be zero.

This means the entire $20,000 salvage value is taxable.

Tax on salvage value:

$20,000 × 0.35 = $7,000

After-tax salvage value:

$20,000 - $7,000 = $13,000

After-tax salvage value = $13,000

Step 6: Calculate the total cash flow in year 10.

At the end of year 10, the company receives:

1. Annual operating cash flow = $106,250
2. After-tax salvage value = $13,000
3. Recovery of working capital = $50,000

Total year 10 cash flow:

$106,250 + $13,000 + $50,000 = $169,250

However, when calculating NPV, we will value the $106,250 annual operating cash flows as a 10-year annuity and add the $63,000 of additional year 10 proceeds separately. This prevents double-counting.

Step 7: Calculate the Net Present Value (NPV).

The NPV formula is:

NPV = Present Value of Annual Cash Flows + Present Value of Terminal Cash Flows - Initial Investment

The annual cash flow is $106,250 for 10 years, and the discount rate is 15%.

Present value of annual cash flows:

PV = $106,250 × [1 - (1.15)^(-10)] / 0.15

The annuity factor is approximately 5.01877.

PV = $106,250 × 5.01877

PV ≈ $533,244.50

Next, calculate the present value of the additional cash received in year 10.

Terminal cash flow = $13,000 + $50,000 = $63,000

PV = $63,000 / (1.15)^10

PV ≈ $15,573.59

Finally, subtract the initial investment:

NPV ≈ $533,244.50 + $15,573.59 - $300,000

NPV ≈ $248,818.09

Final Answer: The NPV is approximately positive $248,818.

Should the company manufacture the chains in-house?

Yes. Since the NPV is positive, producing the chains in-house is financially preferable to purchasing them from the outside supplier, assuming the estimates are accurate.

The company must invest $300,000 initially, but it will save enough money over the next 10 years to recover that investment, cover its 15% required return, and create approximately $248,818 in additional value.

The key lesson is that we must account for all relevant cash flows, including taxes, depreciation tax savings, working capital, and the after-tax salvage value of the machinery.