Question

Appledale Dairy is considering upgrading an old ice-cream maker. Extensive upgrading costs $10600 and saves $8540 in the first year. The savings then decrease by 18 percent each year thereafter. If the upgraded ice-cream maker will last for seven years, what is the present worth of the upgrade?

Answer 1

The present worth of upgrading the ice-cream maker for seven years, considering an initial cost of $10,600 and savings decreasing by 18 percent annually, is approximately $31,338.84.

Step-by-step explanation:

To calculate the present worth, we use the Net Present Value (NPV) formula, taking into account the initial cost and the savings over the seven-year period. The initial cost of $10,600 is subtracted from the savings each year, discounted by the decreasing rate of 18 percent. The formula for NPV is:

Where:

- C is the initial cost,

- S_t is the savings in year t,

- r is the rate of decrease, and

- n is the number of years.

In this scenario, C = $10,600, r = 0.18, and n = 7. The savings for each year are calculated by multiplying the previous year's savings by
`(1 - \(r\)).`The result of this calculation provides the present worth of upgrading the ice-cream maker, taking into account the initial investment and the decreasing savings over the seven-year period.

In conclusion, the present worth of the upgrade reflects the net financial impact, considering both the initial investment and the expected savings over the seven-year lifespan of the upgraded ice-cream maker, while accounting for the annual decrease in savings. This financial analysis assists Appledale Dairy in making an informed decision about the upgrade.