Question

# For the following set of cash flows

 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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