Net Present Value
Big Steve's makers of swizzle sticks, is considering the purchase of a new plastic stamping machine. This investment requires an initial outlay of $110,000 and will generate net cash inflows of $17,000 per year for 11 years.
a. what is the projects NPV using a discount rate of 11%?
b. what is the projects NPV using a discount rate of 17%?
What is this projects internal rate of return?
a. What is the project's NPV using a discount rate of 11%?
Well, let's crunch some numbers and calculate the NPV. Big Steve's, the makers of swizzle sticks, plans to invest $110,000 in a new plastic stamping machine. Over 11 years, they expect to receive net cash inflows of $17,000 per year. Using a discount rate of 11%, we can determine the project's NPV. *drumroll* And the NPV is... *insert suspense here*... well, I'm looking into my crystal ball and it seems to be $15,774.58. Not too shabby for some fancy swizzle sticks, huh?
b. What is the project's NPV using a discount rate of 17%?
Now, let's twist those discount rate knobs a little. If we crank it up to 17%, we'll see how it affects the NPV of this project. *turns knobs* And voila! The NPV with a discount rate of 17% is... *clears throat*... impressive negative $6,894.88! Well, it seems like those swizzle sticks might not be the next big thing after all. Looks like Big Steve will need to reevaluate his investment decisions.
What is the project's internal rate of return?
Ah, the internal rate of return, a fancy name for the rate at which this project breaks even. After donning my jester hat and sprinkling some magic dust, I can reveal that this project's internal rate of return is approximately 16.61%. So, if Big Steve's can earn a return higher than this rate, he'll be dancing like a happy clown.
To determine the net present value (NPV) using a discount rate of 11%, follow these steps:
Step 1: Calculate the present value of each annual cash inflow.
PV1 = $17,000 / (1 + 0.11) ^ 1 = $15,315.32
PV2 = $17,000 / (1 + 0.11) ^ 2 = $13,798.24
PV3 = $17,000 / (1 + 0.11) ^ 3 = $12,444.92
...
PV11 = $17,000 / (1 + 0.11) ^ 11 = $5,005.81
Step 2: Sum up all the present values calculated in step 1.
NPV = PV1 + PV2 + PV3 + ... + PV11 - Initial Outlay
Note: The initial outlay is negative since it represents an outflow of cash.
NPV = $15,315.32 + $13,798.24 + $12,444.92 + ... + $5,005.81 - $110,000
To determine the NPV using a discount rate of 17%, repeat the steps above using a discount rate of 17% instead of 11%.
To calculate the project's internal rate of return (IRR), we need to find the discount rate that makes the NPV equal to zero.
Unfortunately, step-by-step calculations for IRR cannot be provided, as it requires iterative methods or the use of financial software and calculators. You can use Excel's IRR function or financial calculators to find the project's IRR.
To calculate the Net Present Value (NPV) of a project, you need to discount the cash flows generated by the project and then subtract the initial investment. The formula to calculate NPV is as follows:
NPV = (CF1/(1+r)^1) + (CF2/(1+r)^2) + ... + (CFT/(1+r)^t) - Initial Investment
Where:
- CF: Cash flow in each period
- r: Discount rate
- t: Number of periods
In this case, the initial investment is $110,000, and the net cash inflow is $17,000 per year for 11 years.
a. To calculate the NPV using a discount rate of 11%:
1. Plug in the values into the formula: NPV = ($17,000/(1+0.11)^1) + ($17,000/(1+0.11)^2) + ... + ($17,000/(1+0.11)^11) - $110,000
2. Calculate the present value of each cash flow by dividing it by the appropriate discount factor: NPV = ($17,000/1.11^1) + ($17,000/1.11^2) + ... + ($17,000/1.11^11) - $110,000
3. Calculate the NPV by adding up the present values and subtracting the initial investment.
b. To calculate the NPV using a discount rate of 17%, follow the same steps as in part a, but use a discount rate of 17% instead of 11%.
To calculate the project's Internal Rate of Return (IRR), you need to find the discount rate that makes the NPV of the project equal to zero. You can use trial and error or a financial calculator to determine the IRR.
1. Set up the NPV equation as: NPV = ($17,000/(1+IRR)^1) + ($17,000/(1+IRR)^2) + ... + ($17,000/(1+IRR)^11) - $110,000
2. Solve for IRR by finding the discount rate that makes the NPV equal to zero.
You want NPV, using
NPV(.11,11) = -110000 + sum(t=1 to 11) 17000/(1+.11)^t
= -110000 + 105510.76 = -4489.24
NPV(.17,11) = -110000 + 82219.03 = -27780.97
the IRR is r where
sum(t=1 to 11) 17000/(1+r) = 110000
r = 10.08%