Bell Mountain Vineyards is considering updating its current manual accounting system with a high-end electronic system. While the new accounting system would save the company money, the cost of the system continues to decline. The Bell Mountain’s opportunity cost of capital is 10 percent, and the costs and values of investments made at different times in the future are as follows:
Year Cost Value of Future Savings
(at time of purchase)
0 $5,000 $7,000
1 4,500 7,000
2 4,000 7,000
3 3,600 7,000
4 3,300 7,000
5 3,100 7,000
Calculate the NPV of each choice. (Round answers to the nearest whole dollar, e.g. 5,275.)
The NPV of each choice is:
NPV0 = $
NPV1 = $
NPV2 = $
NPV3 = $
NPV4 = $
NPV5 = $
I am in more need of knowing how to do it than just getting the answer.
To calculate the Net Present Value (NPV) of each choice, we need to discount the future savings back to their present value at the opportunity cost of capital, and then subtract the cost of the investment.
Step 1: Calculate the Present Value (PV) of future savings
The present value of future savings can be calculated using the formula:
PV = Future Value / (1 + r)^n
Where:
- PV is the present value
- Future Value is the value of savings in future years
- r is the discount rate (opportunity cost of capital)
- n is the number of years from the present
Step 2: Calculate the NPV for each choice
To calculate the NPV, subtract the cost of the investment from the PV of future savings:
NPV = PV - Cost of Investment
Let's calculate the NPV for each choice.
Choice 0 (current manual accounting system):
Cost = $5,000
PV of future savings = $7,000 / (1 + 0.10)^0 = $7,000
NPV0 = $7,000 - $5,000 = $2,000
Choice 1 (updating accounting system in 1 year):
Cost = $4,500
PV of future savings = $7,000 / (1 + 0.10)^1 = $7,000 / 1.10 = $6,363 (rounded to the nearest whole dollar)
NPV1 = $6,363 - $4,500 = $1,863
Continue this calculation for Choices 2, 3, 4, and 5 using the same steps.
Choice 2:
Cost = $4,000
PV of future savings = $7,000 / (1 + 0.10)^2 = $7,000 / 1.21 = $5,785 (rounded)
NPV2 = $5,785 - $4,000 = $1,785
Choice 3:
Cost = $3,600
PV of future savings = $7,000 / (1 + 0.10)^3 = $7,000 / 1.331 = $5,256 (rounded)
NPV3 = $5,256 - $3,600 = $1,656
Choice 4:
Cost = $3,300
PV of future savings = $7,000 / (1 + 0.10)^4 = $7,000 / 1.4641 = $4,781 (rounded)
NPV4 = $4,781 - $3,300 = $1,481
Choice 5:
Cost = $3,100
PV of future savings = $7,000 / (1 + 0.10)^5 = $7,000 / 1.6105 = $4,341 (rounded)
NPV5 = $4,341 - $3,100 = $1,241
So the NPV of each choice is as follows:
NPV0 = $2,000
NPV1 = $1,863
NPV2 = $1,785
NPV3 = $1,656
NPV4 = $1,481
NPV5 = $1,241