Question

You currently spend $6,000 to hire temporary workers for maintaining the garden in your house. You are planning to buy some equipment to automate the maintenance process. These equipment will result in savings of $1,000 for the next 10 years. Assume no taxes and discount rate to be 10%.

a) If the system costs $7,000 to install, what is the NPV of purchasing the new equipment?

b) If your answer to part a is negative, what additional savings per year is required for your to change your decision?

Please put in Excel and explain

Answer 1

Part a)

The NPV is calculated with the use of following table:

	0	1	2	3	4	5	6	7	8	9	10
Initial Investment	-7,000.00
Annual Savings		1000	1000	1000	1000	1000	1000	1000	1000	1000	1000
Annual Cash Flow	-7,000.00	1000	1000	1000	1000	1000	1000	1000	1000	1000	1000
Present Value [Free Cash Flow/(1+Discount Rate)^Years]	-7,000.00	909.09	826.45	751.31	683.01	620.92	564.47	513.16	466.51	424.10	385.54
NPV	-$855.43 (answer for Part a)

_____

Notes:

NPV is the sum of present value of annual cash flows from Year 0 to Year 10.

______

Part b)

In order to change the decision, the total present value of annual cash savings should atleast be equal to the cost of machine (which is $7,000). The value of annual savings to achieve a total present value of $7,000 is arrived with the use of equation given below:

Cost of Machine = Annual Savings*PVA(Rate,Years) where PVA indicate Present Value of An Annuity of $1

Substituting values in the above formula, we get,

7,000 = Annual Savings*PVA(10%,10)

Using PVA table, we get,

7,000 = Annual Savings*6.14457

Rearranging values, we get,

Annual Savings = 7,000/6.14457 = $1,139.22

Additional Savings Per Year = Annual Savings as Calculated Above - Current Annual Savings = 1,139.22 - 1,000 = $139.22 (Answer for Part b)