Question

The cost required to maintain an electron microscope is known to increase by a fixed percentage each year. A high tech equipment maintenance company has offered it services for a fee of $25,000 for the first year (i.e., end of year 1) with increases of 6% per year thereafter. The biotechnology company wants to take advantage of a tax loop hole by paying for the 3-year contract immediately.

At an interest rate of 15% per year, what should the company be willing to pay immediately(P)?

Show cash flow diagram if possible.

Answer 1

payment of 25000 in first year increasing at a rate of 6% annually uptil 3 years

interest rate = 15%

We need to find the present value of this geometric series

The formula for calculation of present value of geometric series is

P= C *[((1+g)^n/(1+i)^n - 1)] / (g-i)

C= initial amount = 25000

g= increase in gradient = 0.06

i = 0.15

n=3

P= 25000 *[((1+0.06)^3/(1+0.15)^3 - 1)] / (0.06-0.15)

P= 25000 *[((1.06)^3/(1.15)^3 - 1)] / (-0.09)

P= 25000 *[(0.78311235 - 1)] / (-0.09)

P= 25000 *(-0.2168876) / (-0.09)

P = 25000 * 2.4098622

P = 60246.56

Biotechnolgy company needs to 60246.56 right now to take the benefit of tax loop

Cash flow from the veiw of biotechnology company