Machine Replacement Cash Flows and Salvage Value in Present-Value Analysis
Summary
The document examines a present-value comparison of machine replacement plans over a five-year operating need. The question is why buying a new machine at the beginning of the first year produces an initial cash flow equal to its purchase price, even though that year also has an operating cost. The answer explains that the company can sell its existing machine immediately for its current value. That sale offsets the new machine’s purchase price and first-year operating expense, leaving the stated net initial outflow.
The example illustrates why replacement analysis must include disposal proceeds for assets being retired, alongside purchase and operating costs. Comparing scenarios by year of purchase requires assigning each cash flow to the appropriate time and discounting it consistently. The explanation accepts the assumption that the old machine can be sold promptly at its stated value because it will lose value and cannot meet the full service requirement. It does not show the full present-value calculation or test whether transaction costs, resale limits, or other replacement scenarios change the preferred decision.
Key ideas
- Replacement analysis should include proceeds from selling the existing asset as well as the new purchase cost.
- The sale of the current machine offsets part of the purchase and operating outflows in the first-year scenario.
- Present-value comparisons depend on assigning cash flows to the correct dates and discounting them consistently.
- The proposed offset assumes the old machine can be sold immediately at its stated value.
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Full text
# Cash Flow for Operating Cost, Sheldon Ross Question # Cash Flow for Operating Cost, Sheldon Ross Question In his An Elementary Introduction to Mathematical Finance, 3rd Edition book, pg. 55, Sheldon Ross has a question - > A company needs a certain type of machine for the next five years. They presently own such a machine, which is now worth 6,000 (dollars) but will lose 2,000 in value in each of the next three years, after which it will be worthless and unuseable. The (beginning-of-the-year) value of its yearly operating cost is 9,000, with this amount expected to increase by 2,000 in each subsequent year that it is used. A new machine can be purchased at the beginning of any year for a fixed cost of 22,000. The lifetime of a new machine is six years, and its value decreases by 3,000 in each of its first two years of use and then by 4,000 in each following year. The operating cost of a new machine is 6,000, plus an additional 1,000 every following year. He does Present Value Analysis on cash flows for alternate scenarios, that is, whether a new machine is bought at year 1, 2, 3.. His cash flow for year 1 purchase seems incorrect though. The flow is (in 1000 dollars) 22, 7, 8, 9, 10, −4 It says 22 for year 1 purchase of the new machine - but if the company is buying in the beginning of year 1, shouldn't they pay 22K + 6K = 28K, that is, including the operating costs? The year 2 above shows 7K for operating expense, which looks correct. Any ideas? ## Answer by Quantuple (score 0, accepted) https://quant.stackexchange.com/a/25655 22k seems fine to me, assuming a new machine is bought on the first year. Indeed, you face a cost of 22k (sell price of new machine) plus 6k (operating cost of new machine), but you also earn 6k by selling your current machine at its face value (since it won't last 5 years as required and it will only lose value from now on, better sell it asap).
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