Question

3. Computer Systems:

We estimate it will cost $300,000 to upgrade our computer systems. It will take about three years to convert over to new computers and implement our proprietary technology, but after those three years, these new computers will allow us to earn an additional $70,000 per year for the next 10 years due to increased productivity. If our cost of capital is 12 percent, please use the net present value method to determine if we should undertake this project.

Please show ALL work

Answer 1

Answer)

Net Present Value: It is measure of viability or profitability of a capital budgeting decision. Net present value is calculated by subtracting Present value of cash outflows from the present value of cash inflows. If the value arrived at is positive, the capital budgeting decision is set to be profitable and vice-versa.

Net Present Value = Present value of cash inflows – Present value of cash outflows

                                  = $ 281,520 - $ 300,000

                                 = -$ 18,480

Conclusion: Since the Net present value of the project is negative (i.e. -$ 18,480), it is advisable to not to undertake the project

Working Notes:

Calculation of Present Value of Cash outflows:

Present Value of Cash outflows = Cash Outflow to be done today X Present value factor (at 12%)

                                                        = $ 300,000 X 1.00

                                                         = $ 300,000

Therefore the present value of cash outflow is $ 300,000. We have assumed that the entire cash outflow will be done at the beginning of year 1.

Calculation of Present Value of Cash Inflows:

Present Value of Cash Inflows = (Annual Cash inflow X Cumulative Present Value from year 4 to year 13 at 12%) - (Annual Cash inflow X Cumulative Present Value from year 1 to year 3 at 12%)]

                                            = ($ 70,000 X 4.02172) – (0 X 2.40183)

                                            = $ 281,520 (rounded off)

Alternatively, the present value of cash inflows can be calculated as follows:

Year ending	Additional Cash Inflow	Present Value factor (@12%)	Present Value of cash inflow
1	0	0.89286	-
2	0	0.79719	-
3	0	0.71178	-
4	$ 70,000	0.63552	$ 44,486.27
5	$ 70,000	0.56743	$ 39,719.88
6	$ 70,000	0.50663	$ 35,464.18
7	$ 70,000	0.45235	$ 31,664.45
8	$ 70,000	0.40388	$ 28,271.83
9	$ 70,000	0.36061	$ 25,242.70
10	$ 70,000	0.32197	$ 22,538.13
11	$ 70,000	0.28748	$ 20,123.33
12	$ 70,000	0.25668	$ 17,967.26
13	$ 70,000	0.22917	$ 16,042.19
Total			$ 2,81,520.20

Working Note:

The formula for calculation of Present Value is:

Present Value = Future Value X [1/ (1+ i)^n]

Where,

“i” is the cost of capital to be used as discounting factor for calculation of Present Value

“n” is the number of years. (For example, for year 1, the value of “n” will be “1”. For year 2, the value of “n” will be “2” and so on)

Present value of $ 1 at the end of various years will be calculated as follows:

Present value of $ 1 at the end of Year 1:

Present Value = Future Value X [1/ (1+ i)^n]

                          = $ 1 X [1/(1+0.12)^1]

                          = $ 1/1.12

                          = $ 0.89286

Therefore the present value of $ 1 at the end year 1 will be $ 0.89286.     

Present value of $ 1 at the end of Year 2:

Present Value = Future Value X [1/ (1+ i)^n]

                          = $ 1 X [1/(1+0.12)^2]

                          = $ 1/[(1.12)^2]

                          = $ 0.79719

Therefore the present value of $ 1 at the end year 2 will be $ 0.79719.

Present value of $ 1 at the end of Year 3:

Present Value = Future Value X [1/ (1+ i)^n]

                          = $ 1 X [1/(1+0.12)^3]

                          = $ 1/[(1.12)^3]

                          = $ 0.71178

Therefore the present value of $ 1 at the end year 3 will be $ 0.71178.

Note: The present value from year 4 to year 13 is calculated in the similar manner by inputting the relevant year at “n” in the following formula and by taking “i” as 12% or 0.12.

Present Value = Future Value X [1/ (1+ i)^n]