For the following set of cash flows, |
Year | Cash Flow |
0 | –$8,000 |
1 | 4,800 |
2 | 3,500 |
3 | 5,200 |
a. What is the NPV at a discount rate of 0 percent? |
b. What is the NPV at a discount rate of 15 percent? |
c. What is the NPV at a discount rate of 23 percent? |
d. What is the NPV at a discount rate of 28 percent? |
Net present value is the present value of cash inflows minus the initial investment. For calculating the present value in this question, we will use the present value of $1 table.
(a) At discount rate of 0%, present value of cash inflows will be the sum of all cash inflows.
Sum of cash inflows = $4800 + $3500 + $5200 = $13500
Initial investment = $8000
Net present value (NPV) = Present value of cash inflows - Initial investment
Net present value (NPV) = $13500 - $8000 = $5500
(b) At discount rate of 15%, present value of cash inflows is:
Present value of cash inflows = $4800 * PVIF (15%, 1 year) + $3500 * PVIF (15%, 2 year) + $5200 * PVIF (15%, 3 year)
where, PVIF is the present value of $1 at 15% for various years.
We will now use the present value tables to find the value of PVIF at 15% for various years and put the values in the equation above as per below:
Present value of cash inflows = ($4800 * 0.870) + ($3500 * 0.756) + ($5200 * 0.658)
Present value of cash inflows = $4176 + $2646 + $3421.6
Present value of cash inflows = $10243.6
Initial investment = $8000
Net present value (NPV) = Present value of cash inflows - initial investment
Net present value (NPV) = $10243.6 - $8000 = $2243.6
(c) At discount rate of 23%, present value of cash inflows is:
Present value of cash inflows = $4800 * PVIF (23%, 1 year) + $3500 * PVIF (23%, 2 year) + $5200 * PVIF (23%, 3 year)
where, PVIF is the present value of $1 at 23% for various years.
We will now use the present value tables to find the value of PVIF at 23% for various years and put the values in the equation above as per below:
Present value of cash inflows = ($4800 * 0.81) + ($3500 * 0.66) + ($5200 * 0.54)
Present value of cash inflows = $3888 + $2310+ $2808
Present value of cash inflows = $9006
Initial investment = $8000
Net present value (NPV) = Present value of cash inflows - initial investment
Net present value (NPV) = $9006 - $8000 = $1006
(d) At discount rate of 28%, present value of cash inflows is:
Present value of cash inflows = $4800 * PVIF (28%, 1 year) + $3500 * PVIF (28%, 2 year) + $5200 * PVIF (28%, 3 year)
where, PVIF is the present value of $1 at 28% for various years.
We will now use the present value tables to find the value of PVIF at 28% for various years and put the values in the equation above as per below:
Present value of cash inflows = ($4800 * 0.78) + ($3500 * 0.61) + ($5200 * 0.48)
Present value of cash inflows = $3744 + $2135 + $2496
Present value of cash inflows = $8375
Initial investment = $8000
Net present value (NPV) = Present value of cash inflows - initial investment
Net present value (NPV) = $8375 - $8000 = $375
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