Big Steve's makers of swizzle sticks, is considering the purchase of a new plastic stamping machine. This investment requires an initial outlay of $95,000 and will generate net cash inflows of $16,000 per year for 8 years.
a. What is the project's NPV using a discount rate of 7 percent? Should the project be accepted? Why or why not?
b. What is the project's NPV using a discount rate of 17 percent? Should the project be accepted? Why or why not?
c. What is this project's internal rate of return? Should the project be accepted? Why or why not?
To calculate the project's NPV, we need to discount each year's cash inflows at the given discount rate and subtract the initial outlay.
a. Using a discount rate of 7 percent:
NPV = -$95,000 + $16,000 / (1 + 0.07) + $16,000 / (1 + 0.07)^2 + ... + $16,000 / (1 + 0.07)^8
= -$95,000 + $14,953.27 + $13,944.18 + $12,975.07 + $12,037.54 + $11,129.61 + $10,248.62 + $9,392.27 + $8,558.65
= $38,238.14
Since the NPV is positive, the project should be accepted. A positive NPV indicates that the present value of the future cash inflows exceeds the initial investment, resulting in a net gain.
b. Using a discount rate of 17 percent:
NPV = -$95,000 + $16,000 / (1 + 0.17) + $16,000 / (1 + 0.17)^2 + ... + $16,000 / (1 + 0.17)^8
= -$95,000 + $13,675.21 + $11,710.18 + $9,997.39 + $8,511.42 + $7,229.88 + $6,133.06 + $5,202.70 + $4,422.34
= -$6,528.83
Since the NPV is negative, the project should not be accepted. A negative NPV indicates that the present value of the future cash inflows is lower than the initial investment, resulting in a net loss.
c. To find the internal rate of return (IRR), we need to find the discount rate that makes the NPV equal to zero. We can use IRR formula or trial and error method.
By calculating using trial and error, we find that the IRR is approximately 12.1%. Since this rate is higher than the discount rate of 7% and lower than the discount rate of 17%, the project should be accepted. The IRR represents the annualized rate of return generated by the project, and if it exceeds the cost of capital, the project is considered profitable.
To calculate the project's NPV, we need to use the formula:
NPV = ∑(CFt / (1+r)^t) - Initial Outlay
where:
NPV = Net Present Value
CFt = net cash inflow in year t
r = discount rate
t = time period
Let's calculate the NPV for each scenario:
a. Discount rate = 7%
NPV = -95,000 + (16,000 / (1+0.07)^1) + (16,000 / (1+0.07)^2) + ... + (16,000 / (1+0.07)^8)
Calculating this equation, the NPV is $26,710.51.
Since the NPV is positive, the project should be accepted because it is expected to generate more cash inflows than the initial investment.
b. Discount rate = 17%
NPV = -95,000 + (16,000 / (1+0.17)^1) + (16,000 / (1+0.17)^2) + ... + (16,000 / (1+0.17)^8)
Calculating this equation, the NPV is -$14,431.43.
As the NPV is negative, the project should not be accepted, as it is expected to generate lower cash inflows than the initial investment.
c. To find the Internal Rate of Return (IRR), we need to find the discount rate that makes the project's NPV equal to zero.
Using a financial calculator or Excel, the project's IRR is approximately 12.43%.
Since the IRR is greater than the discount rate of 7%, the project should be accepted. The IRR represents the rate at which the project's net cash inflows equal the initial outlay, indicating that the project is expected to generate a return greater than 7%.
In summary:
a. NPV at 7% = $26,710.51, project should be accepted.
b. NPV at 17% = -$14,431.43, project should not be accepted.
c. IRR = 12.43%, project should be accepted as the IRR is greater than the discount rate of 7%.