Question

K (Present value of a growing perpetuity) Your firm has taken on cost saving measures that will provide a benefit of $16,000 in the first year. These cost savings will decrease each year at a rate of 3 percent forever. If the appropriate interest rate is 8 percent, what is the present value of these savings? The present value of these cost savings is S (Round to the nearest cent.)​

Answer 1

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.