To calculate the present value of the cost savings, we can use the formula for the present value of a growing perpetuity. The formula is:
K = C / (r - g)
Where:
K = Present value of the growing perpetuity
C = Cash flow in the first year
r = Interest rate
g = Growth rate
In this case, C = $16,000, r = 8% (or 0.08), and g = -3% (or -0.03). We use a negative sign for the growth rate since the cost savings are decreasing each year.
Now we can substitute the values into the formula and calculate the present value:
K = 16000 / (0.08 - (-0.03))
K = 16000 / 0.11
K ≈ $145,454.55
Therefore, the present value of these cost savings is approximately $145,454.55.