Your firm has the option of making an investment in new software that wil cost $130,000 today and is estimated to provide the savings shown in the table over5 years.

year savings estimate
1 $35,000
2 50,000
3 45,000
4 25,000
5 15,000
should the firm make this investment if it requires a minimum annual return of 9% on all investments?

84491.08

To determine if the firm should make this investment, we need to calculate the net present value (NPV) of the investment. NPV is the sum of the present values of all future cash flows associated with the investment, discounted at the required rate of return.

First, let's calculate the present value (PV) of each year's savings estimate using the formula:

PV = CF / (1 + r)^n

where CF is the cash flow, r is the required rate of return, and n is the number of years.

Using a required rate of return of 9%, the present value of each year's savings estimate is as follows:

Year 1: PV = $35,000 / (1 + 0.09)^1 = $32,110.09
Year 2: PV = $50,000 / (1 + 0.09)^2 = $41,741.77
Year 3: PV = $45,000 / (1 + 0.09)^3 = $34,614.33
Year 4: PV = $25,000 / (1 + 0.09)^4 = $17,371.99
Year 5: PV = $15,000 / (1 + 0.09)^5 = $10,012.29

Now, let's calculate the total present value by summing up the present values of all years:

Total PV = $32,110.09 + $41,741.77 + $34,614.33 + $17,371.99 + $10,012.29 = $135,850.47

Finally, let's calculate the net present value (NPV) of the investment by subtracting the initial cost of $130,000 from the total present value:

NPV = Total PV - Initial Cost = $135,850.47 - $130,000 = $5,850.47

Since the NPV is positive ($5,850.47), the firm should make this investment as it exceeds the required minimum annual return of 9%.

To determine whether the firm should make this investment, we can calculate the net present value (NPV) of the investment. NPV measures the profitability of an investment by comparing the present value of its future cash flows to the initial investment.

To calculate the NPV, we need to discount each year's savings estimate to its present value and then sum them up.

The formula to calculate the present value (PV) is:
PV = CF / (1 + r)^n

Where:
- CF is the cash flow (savings estimate) for a given year
- r is the rate of return (discount rate)
- n is the number of years in the future

In this case, the discount rate is 9% or 0.09. Let's calculate the present value of each year's savings estimate:

Year 1: PV = 35,000 / (1 + 0.09)^1 = 32,110.09
Year 2: PV = 50,000 / (1 + 0.09)^2 = 41,285.79
Year 3: PV = 45,000 / (1 + 0.09)^3 = 35,359.13
Year 4: PV = 25,000 / (1 + 0.09)^4 = 17,797.42
Year 5: PV = 15,000 / (1 + 0.09)^5 = 9,399.87

Now, sum up all the present values to calculate the NPV:

NPV = -130,000 + 32,110.09 + 41,285.79 + 35,359.13 + 17,797.42 + 9,399.87
= 5,952.30

The NPV of this investment is $5,952.30 positive. Since the NPV is positive, it indicates that the investment has a positive expected return and is potentially worthwhile. Therefore, the firm should make this investment if it requires a minimum annual return of 9% on all investments.