Question

You are thinking of building a new machine that will save you $ 4 comma 000$4,000 in the first year. The machine will then begin to wear out so that the savings decline at a rate of 1 %1% per year forever. What is the present value of the savings if the interest rate is 9 %9% per​ year?

Answer 1

The present value of the savings=$37,064.22

Step-by-step explanation:

The present value of the savings is the amount that it worths today, this would be done in two stages;

The first stage is to determined the present of the first cash savings as follows:

PV of the first payment = 4,000 × (1.09)^(-1)=3,669.72

Second step is to determine the present value of the declining perpetuity

PV of declining perpetuity. A perpetuity is the series of cash flow occurring for the foreseeable future of years.

A- 4,000, g-negative growth rate = 1%,

interest rate = 9%

PV in year 1 = 4,000× (1-0.09)/(0.09+0.01)

= 36,400

PV in year 0 = 36,400 × (1.09)^(-1) = 33,394.49

The present value of the savings = 33,394.49 + 3,669.72= 37,064.22

The present value of the savings=$37,064.22