Cariba Company bought an old repair machine for $200,000 with annual operating cost $150,000 (4-year life, $0 salvage). A new machine costs $240,000 installed with annual operating cost $90,000 (4-year life, $0 salvage). The old machine can be sold for $100,000 but requires a $20,000 removal cost. Annual cash revenue is $1,500,000 and other annual cash costs are $1,100,000 regardless. Ignore income taxes and time value of money: (1a) prepare 4-year cash receipts and disbursements for keep vs replace and find the 4-year cumulative cash flow difference; (1b) prepare 4-year income statements for keep vs replace using straight-line depreciation and find the 4-year cumulative difference in operating income; (1c) identify irrelevant items and explain why; (2) if the old machine originally cost $1,000,000 instead of $200,000, would the net differences in 1a and 1b change; (3) discuss any conflict between the decision model and the incentives of the manager who just bought the old machine.

What this problem is really asking

You are comparing two alternatives, keep the current machine or replace it immediately. Because taxes and time value of money are ignored, you can add up four years of totals directly. The decision logic still uses incremental (difference) cash flows, not the original purchase price that is already paid.

1(a) Cash receipts and disbursements (4 years)

Given (same under both alternatives each year):

• Cash revenue = $1,500,000 per year
• Other cash costs = $1,100,000 per year

Alternative A: Keep the old machine

Old machine annual operating cost = $150,000.

Net annual cash flow: $$1{,}500{,}000 - 1{,}100{,}000 - 150{,}000 = 250{,}000$$

Cash summary (Keep old):

• Year 1: receipts $1,500,000; disbursements $1,250,000; net $250,000
• Year 2: net $250,000
• Year 3: net $250,000
• Year 4: net $250,000

Cumulative (4 years): $$250{,}000 \times 4 = 1{,}000{,}000$$

Alternative B: Replace with the new machine

New machine annual operating cost = $90,000. Immediate replacement cash flows (Year 1):

• Buy new machine: $240,000 outflow
• Sell old machine: $100,000 inflow
• Removal cost: $20,000 outflow

Net disposal proceeds from old machine: $$100{,}000 - 20{,}000 = 80{,}000$$

Net initial cash outflow to replace: $$240{,}000 - 80{,}000 = 160{,}000$$

Operating cash flow each year with the new machine: $$1{,}500{,}000 - 1{,}100{,}000 - 90{,}000 = 310{,}000$$

Cash summary (Replace):

• Year 1: operating net $310,000 minus net initial outflow $160,000 = $150,000
• Year 2: $310,000
• Year 3: $310,000
• Year 4: $310,000

Cumulative (4 years): $$150{,}000 + 310{,}000 \times 3 = 1{,}080{,}000$$

Cumulative difference in cash flow

$$1{,}080{,}000 - 1{,}000{,}000 = 80{,}000$$ Replacement is better by $80,000 over four years.

1(b) Income statements (straight-line depreciation)

Depreciation:

• Old machine: $$200{,}000/4 = 50{,}000 \text{ per year}$$
• New machine: $$240{,}000/4 = 60{,}000 \text{ per year}$$

Alternative A: Keep the old machine (each year)

Operating income per year: $$1{,}500{,}000 - 1{,}100{,}000 - 150{,}000 - 50{,}000 = 200{,}000$$ Cumulative operating income (4 years): $$200{,}000 \times 4 = 800{,}000$$

Alternative B: Replace with the new machine

Operating income from operations (each year): $$1{,}500{,}000 - 1{,}100{,}000 - 90{,}000 - 60{,}000 = 250{,}000$$ Cumulative operating income (4 years): $$250{,}000 \times 4 = 1{,}000{,}000$$

So the cumulative difference in operating income (operations only) is: $$1{,}000{,}000 - 800{,}000 = 200{,}000 \text{ in favor of replacing}$$

If your income statement also includes the disposal loss (common in practice)

Book value of old machine at replacement time (start of Year 1) is $200,000. Net proceeds on sale are $80,000, so loss on disposal is: $$200{,}000 - 80{,}000 = 120{,}000$$

Year 1 net income under Replace would be: $$250{,}000 - 120{,}000 = 130{,}000$$ Years 2 to 4 net income would be $250,000 each. Cumulative net income (4 years): $$130{,}000 + 3 \times 250{,}000 = 880{,}000$$ Difference vs keeping ($800,000) is $80,000.

1(c) Irrelevant items and why

Items that are irrelevant to the decision (and to a differential analysis) include:

• Annual cash revenue ($1,500,000): same under both alternatives, so it cancels in the comparison.
• Other annual cash costs ($1,100,000): also identical under both alternatives.
• The $200,000 original purchase price of the old machine: it is already paid, so it is a sunk cost.
• Accounting depreciation on the old machine (and its book value): it is an allocation of a sunk cost, not a future cash flow; it can distort income comparisons if treated as “real” economics.

The relevant items are the cash you can still change: the $60,000/year operating cost savings, the $240,000 purchase price of the new machine, and the $80,000 net cash you would receive from selling the old machine.

2) If the old machine originally cost $1,000,000 instead of $200,000

• Requirement 1(a) cash flow difference does not change. The old purchase price is still sunk; you still give up (or receive) the same future cash flows: sell for net $80,000, buy new for $240,000, and save $60,000 per year in operating costs.
• Requirement 1(b) accounting operating income can change because straight-line depreciation would become $$1{,}000{,}000/4 = 250{,}000$$ per year for the keep alternative. That lowers reported operating income for keeping even though it does not change cash.
• If you include the disposal loss, that loss also becomes larger when historical cost is larger. This is another way sunk cost can heavily affect reported income even when the underlying cash advantage of replacement is unchanged.

3) Incentives conflict (decision model vs manager behavior)

Economically (ignoring taxes and discounting), replacement is attractive because you pay a net $160,000 now and save $60,000 per year for 4 years, which totals $240,000 of savings and a net gain of $80,000.

But a manager who just approved the old machine may resist replacing it because:

• The replacement often triggers a visible accounting loss on disposal in Year 1.
• Short-term performance measures (operating income, ROI, budget compliance) may look worse even if total cash over four years improves.
• There can be reputational and career costs from admitting the first purchase was a mistake, which leads to “throwing good money after bad” (the sunk cost fallacy).