What is the Net Present Value (NPV) of spending $400 today on an appliance that saves $85 a year for 4 years, with an alternative investment earning 13%?

To determine the Net Present Value (NPV) of spending $400 today on an appliance that will generate savings of $85 annually for four years with an alternative investment earning a 13% return, you first need to calculate the present value of the future savings and then subtract the initial cost of the appliance.

The formula for the present value of future cash flows is:

[ PV = \frac{C}{(1 + r)^n} ]

where:

• ( PV ) is the present value,
• ( C ) is the cash flow per period,
• ( r ) is the discount rate (the alternative investment rate, in this case, 0.13 or 13%),
• ( n ) is the year number.

Here, you will calculate the present value for each year’s savings and then sum them up.

1. Year 1:

• ( PV_1 = \frac{85}{(1 + 0.13)^1} = \frac{85}{1.13} \approx 75.22 )

2. Year 2:

• ( PV_2 = \frac{85}{(1 + 0.13)^