Final answer:
The present worth of the sales for SKF Manufacturing can be found using the present value formula of a geometrically increasing annuity, accounting for the quarterly increase in sales and interest rate compounded quarterly.
Step-by-step explanation:
The present worth of the sales through a 5-year period for SKF Manufacturing, given sales of $150,000 in quarter one with an increase of $55,000 per quarter, and a nominal interest rate of 20% per year compounded quarterly, can be calculated using the formula for the present value of a geometrically increasing annuity. We start by determining the growth factor per quarter (1 plus the growth rate), the interest rate per quarter, and the number of periods. We then apply the present value formula for a geometric series:
Present Value Formula:
- PV = P * [(1 - (g/q)^(n)) / (i/q - g)] where,
- P = initial payment (the first quarter's sales),
- g = growth rate per period,
- i = nominal annual interest rate,
- q = number of periods per year,
- n = total number of periods.
First, we calculate:
- g = $55,000 increase per quarter,
- i = 20% annual interest,
- q = 4 (since interest is compounded quarterly),
- n = 5 * 4 = 20 total quarters over 5 years.
Next, we plug the values into the formula to find the present worth. Keep in mind that the calculations must be done carefully to account for the compounding of interest and the increase in sales per quarter.