A fast-food establishment is thinking of buying a new cooking grill and refrigeration unit.
The costs of these new machines are $12,500 and $9,000, respectively. The installation costs
of the new equipment will run about $800. It is estimated that 10% more customers can be
served with the new equipment, which would mean an additional annual net cash flow of
approximately $4,500. The salvage value of the old grill and refrigeration unit is estimated
to be $1,000.
The firm’s cost of capital is 12%. The equipment should last 10 years, at a minimum.
Required:
Using the net present value method, should the company purchase the new equipment?
(Ignore income tax effects.)
is four eigths greater than four tenths
To determine whether the company should purchase the new equipment using the net present value (NPV) method, we need to calculate the NPV of the investment.
NPV is calculated by subtracting the initial investment from the present value of future cash flows.
Step 1: Calculate the present value of the net cash flows over the 10-year period.
The net cash flow in the first year will be the additional annual cash flow ($4,500) minus the installation cost ($800) which equals $3,700.
In the subsequent years, the net cash flow will be the initial cash flow plus the additional annual cash flow, so it will be $4,500.
We will calculate the present value of these cash flows using the formula:
PV = CF / (1 + r)^t
Where:
PV - Present Value
CF - Cash Flow
r - Discount rate (cost of capital)
t - Time period
Given that the cost of capital is 12% and the equipment will last for 10 years, let's calculate the present value of cash flows.
Year 0:
Initial Investment: -$12,500 - $9,000 - $800 = -$22,300
Present Value: -$22,300 / (1 + 0.12)^0 = -$22,300
Years 1-10:
Net Cash Flow: $4,500
Present Value: $4,500 / (1 + 0.12)^t
Year 1: $4,500 / (1 + 0.12)^1 = $4,018.75
Year 2: $4,500 / (1 + 0.12)^2 = $3,581.03
.
.
.
Year 10: $4,500 / (1 + 0.12)^10 = $890.90
Step 2: Calculate the salvage value of the old equipment.
The salvage value is estimated at $1,000.
Step 3: Calculate the total present value of cash inflows and outflows.
Add up the present values of the net cash flows and the salvage value of the old equipment.
Total PV = PV of net cash flows + Salvage value
Total PV = -$22,300 + $4,018.75 + $3,581.03 + ... + $890.90 + $1,000
Step 4: Calculate the NPV.
The NPV is calculated by subtracting the initial investment from the total present value.
NPV = Total PV - Initial investment
NPV = [-$22,300 + $4,018.75 + $3,581.03 + ... + $890.90 + $1,000] - (-$22,300)
If the NPV is positive, the investment is considered profitable. If it is negative, the investment is not considered profitable.
Now calculate the NPV using the given formula:
NPV = [Total PV] - (-$22,300)
I will perform the calculations and provide you with the result.