Question

Johnson thermal products used austenitic nickel chromium alloys to manufacture resistance heating wire. The company is considering a new annealing drawing process to reduce costs. Assume that the companies mar is a real 12% per year and the inflation rate is 3% per year. If the new process will cost $3.7 million now, how much must be saved each year to recover the investment in 5 years? a. $2,103,784.b. $603,784.c. $1,103,784.d. $1,603,784.

Answer 1

Answer:

The correct option is c. $1,103,784.

Explanation:

This can be calculated using the formula for calculating the present value of an ordinary annuity as follows:

PV = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)

Where;

PV = Present value or cost of the new process = $3.7 million = $3,700,000

P = Annual savings to recover the investment in 5 years = ?

r = interest rate = MARR + Inflation rate = 12% + 3% = 15%, or 0.15

n = number of years = 5

Substitute the values into equation (1)  and solve for P, we have:

$3,700,000 = P * ((1 - (1 / (1 + 0.15))^5) / 0.15)

$3,700,000 = P * 3.3521550980114

P = $3,700,000 / 3.3521550980114

P = $1,103,768

From the options, the closet figure to $1,103,768 is c. $1,103,784. The difference is due the difference I rounding. Therefore, the correct option is c. $1,103,784. That is, the amount that must be saved each year to recover the investment in 5 years is $1,103,784.