1. Find out the power consumption of the device in kilowatts (kW).
2. Estimate how long the device will be used for each day.
3. Multiply the power consumption by the number of hours, to get the energy use per day in kilowatt hours (kWh).
4. Multiply this by the number of days in a year (365).
5. This will then give you the energy use of the device for the year.
6. Repeat the above with the old device you are replacing.
7. Subtract the new device energy use from the old device energy use.
8. Calculate the cost of this energy, if for example the average UK cost of electricity is abot 12p per kWh, in the US it is about the same in cents.   The average UK gas price is about 3p per kWh, there is a full listing here.
9. So all you do now is multiply the cost of the saved energy by the cost per unit.
10. Don’t forget to get the units right, 12 pence is 0.12 pounds.
11. The final step to estimating a payback time is to divide the cost of the new device by the financial value of the energy saving per year.

You are buying a new refrigerator, and the power consumption of the old unit is 0.05kW, a refrigerator is on all day, so its energy consumption is 0.05 x 24 hours, giving 1.2 kWh, it is on all year, so for the year this is 438 kWh, with an electricity cost of 0.12 Pounds (use your currency unit, e.g. Dollars or Euros), this would cost 52.6 pounds per year to operate.
The new fridge power consumption is 0.04kW, and using the same method, this costs 42.05 pounds per year to operate, so the cost saving per year in energy bills is 52.6 - 42.06 = 10.54 pounds.   If the fridge costs 200 pounds then on purely energy cost grounds the investment will take 19 years to pay back.

You can also use this method to calculate whether it is worth buying the more expensive energy saving model.  We should all try to save energy, but manufacturers charge an unnecessary premium for the energy efficient badge, and are often deceiving customers making them spend much more for little energy saving gain.  Forewarned is forearmed!