Question

The market for widgets is increasing by 15% per year from current profits of $2,000,000. Investing in a design change will allow the profit per widget to stay steady; otherwise the price will drop by 3% per year. If inflation in the economy is 4%, what is the present worth in Year-1 dollars of the savings over the next 10 years? The interest rate is 10%.

Answer 1

If the price drops by 3%, profits also drops by 3%.

The dollar value of profits drop = 0.03 * $ 2,000,000

The dollar value of profits drop = $ 60,000

Thus by investing in design change, the savings per year will be $ 60,000 for the next 10 years.

The real rate of interest = [ ( 1+0.10) / ( 1 + 0.04) ] -1

Real rate of interest = 5.77%

The present worth in Year-1 dollars of the savings over the next 10 years = $ 60,000 1.0577¹ + $ 60,000 1.0577² + $ 60,000 1.0577³ + $ 60,000 1.0577⁴ + $ 60,000 1.0577⁵ + $ 60,000 1.0577⁶ + $ 60,000 1.0577⁷ + $ 60,000 1.0577⁸ + $ 60,000 1.0577⁹ + $ 60,000 1.0577¹⁰

The present worth in Year-1 dollars of the savings over the next 10 years = $ 446,457.50