Consider the project with the following expected cash flows:
Year Cash flow
0 -$400,000
1 $100,000
2 $120,000
3 $850,000
•If the discount rate is 0%, what is the project's net present value?
•If the discount rate is 2%, what is the project's net present value?
•If the discount rate is 6%, what is the project's net present value?
•If the discount rate is 11%, what is the project's net present value?
•With a cost of capital of 5%, what is this project's modified internal rate of return?
Now draw (for yourself) a chart where the discount rate is on the horizontal axis (the "x" axis) and the net present value on the vertical axis (the Y axis). Plot the net present value of the project as a function of the discount rate by dots for the four discount rates. connect the four points using a free hand 'smooth' curve. The curve intersects the horizontal line at a particular discount rate. What is this discount rate at which the graph intersects the horizontal axis?
Consider the project with the following expected cash flows:
Year Cash flow
0 -$400,000
1 $100,000
2 $120,000
3 $850,000
•If the discount rate is 0%, what is the project's net present value?
•If the discount rate is 2%, what is the project's net present value?
•If the discount rate is 6%, what is the project's net present value?
•If the discount rate is 11%, what is the project's net present value?
•With a cost of capital of 5%, what is this project's modified internal rate of return?
Now draw (for yourself) a chart where the discount rate is on the horizontal axis (the "x" axis) and the net present value on the vertical axis (the Y axis). Plot the net present value of the project as a function of the discount rate by dots for the four discount rates. connect the four points using a free hand 'smooth' curve. The curve intersects the horizontal line at a particular discount rate. What is this discount rate at which the graph intersects the horizontal axis?
To calculate the net present value (NPV) of the project, we need to discount each cash flow to its present value and then sum them up.
To calculate the present value (PV) of each cash flow, we divide it by (1 + discount rate) raised to the power of the respective year.
For example, the present value of cash flow at year 1 would be: $100,000 / (1 + 0%)^1 = $100,000
Let's calculate the NPV for each discount rate:
1. At 0% discount rate:
- Year 0 cash flow: -$400,000 / (1 + 0%)^0 = -$400,000
- Year 1 cash flow: $100,000 / (1 + 0%)^1 = $100,000
- Year 2 cash flow: $120,000 / (1 + 0%)^2 = $120,000
- Year 3 cash flow: $850,000 / (1 + 0%)^3 = $850,000
NPV = -$400,000 + $100,000 + $120,000 + $850,000 = $670,000
2. At 2% discount rate:
Calculate the present value of each cash flow using the formula above and sum them up to find NPV.
3. At 6% discount rate:
Same as above, but use 6% as the discount rate.
4. At 11% discount rate:
Same as above, but use 11% as the discount rate.
To calculate the modified internal rate of return (MIRR), we need to find the discount rate that equates the present value of future cash inflows to the present value of outflows at the cost of capital (5% in this case).
To do this, we calculate the present value of future cash inflows at the cost of capital and sum them up. Then we calculate the present value of outflows and find the discount rate that makes the two present values equal.
Now, to draw the chart, create a horizontal axis representing the discount rate (0%, 2%, 6%, 11%) and a vertical axis representing the NPV calculated for each discount rate. Plot the NPV on the chart for each discount rate and connect the points with a smooth curve.
The discount rate at which the graph intersects the horizontal axis represents the internal rate of return (IRR) of the project. Calculate this intersection point and that will give you the discount rate at which the NPV becomes zero.