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?
1467.90
To determine whether the firm should make the investment, we need to calculate the present value of the savings estimates and compare it to the initial cost.
Step 1: Calculate the present value of each year's savings estimate.
Using the formula for present value (PV) = FV / (1+r)^n, where FV = future value, r = annual discount rate, and n = number of years:
For year 1: PV = $35,000 / (1+0.09)^1 = $35,000 / 1.09 = $32,110.09
For year 2: PV = $50,000 / (1+0.09)^2 = $50,000 / 1.1881 = $42,058.51
For year 3: PV = $45,000 / (1+0.09)^3 = $45,000 / 1.29503 = $34,764.03
For year 4: PV = $25,000 / (1+0.09)^4 = $25,000 / 1.41158 = $17,720.74
For year 5: PV = $15,000 / (1+0.09)^5 = $15,000 / 1.53862 = $9,751.82
Step 2: Calculate the total present value by summing up the present values of all years.
Total PV = $32,110.09 + $42,058.51 + $34,764.03 + $17,720.74 + $9,751.82 = $136,405.19
Step 3: Compare the total present value to the initial cost.
If the total present value is greater than or equal to the initial cost, then the firm should make the investment.
In this case, the initial cost is $130,000. Since the total present value ($136,405.19) is greater than the initial cost, the firm should make this investment.
To determine whether the firm should make the investment in the new software, we need to calculate the net present value (NPV) of the investment. NPV is a financial metric that takes into account both the initial cost and the estimated savings over a specified period, while considering the required minimum annual return.
To calculate the NPV, we first need to discount the estimated savings from each year to their present value. The formula for discounting future cash flows is:
PV = FV / (1 + r)^n
Where PV is the present value, FV is the future value, r is the discount rate (expressed as a decimal), and n is the number of years.
Let's calculate the present value of the estimated savings for each year:
Year 1:
PV1 = $35,000 / (1 + 0.09)^1 = $35,000 / 1.09 = $32,110.09
Year 2:
PV2 = $50,000 / (1 + 0.09)^2 = $50,000 / 1.1881 = $42,088.02
Year 3:
PV3 = $45,000 / (1 + 0.09)^3 = $45,000 / 1.29503 = $34,763.30
Year 4:
PV4 = $25,000 / (1 + 0.09)^4 = $25,000 / 1.41158 = $17,727.20
Year 5:
PV5 = $15,000 / (1 + 0.09)^5 = $15,000 / 1.53862 = $9,757.00
Next, we sum up the present values of the estimated savings:
PVTotal = PV1 + PV2 + PV3 + PV4 + PV5
= $32,110.09 + $42,088.02 + $34,763.30 + $17,727.20 + $9,757.00
= $136,445.61
Now, we can calculate the net present value by subtracting the initial cost of the investment:
NPV = PVTotal - Initial Cost
= $136,445.61 - $130,000
= $6,445.61
If the NPV is positive, it means the investment is expected to generate more value than its cost. In this case, the NPV is $6,445.61, indicating that the investment is expected to provide a positive return.
Therefore, based on a minimum required annual return of 9%, the firm should make this investment in the new software as the expected return exceeds the required return.