Question

Zoe is thinking of replacing her old refrigerator which uses 1400 kilowatt hours (kWh) of electricity per year. A new, more efficient model will cost her $1700 and will use only 600 kWh per year. She pays 10 cents per kWh for her electricity.

Assume a time horizon of 4 years (i.e. t=0,1,2,3) and a discount rate of 10 percent. At the end of the three year period, the new fridge is worth $500 in the used fridge market and the old fridge is worth nothing. Assume that Zoe would buy this refrigerator at the beginning of year 0. Energy savings would be realized in full in all years.

(a) Compute the net present expected value of the costs associated with owning and operating the old refrigerator over the four year time horizon.

(b) Compute the net present value of the costs of owning and operating the new refrigerator over the four year time horizon.

(c) Using the standard discounted utility model discussed in class, we would expect that Zoe will choose to buy the new refrigerator. Why?

Answer 1

The cashflows from buying the new refrigerator are as follows:

At t = 0, cashflow = -$700 (cash outflow)

At t = 1, cashflow = -$(600)*0.10 = -$60 (cash inflow)

At t = 2, cashflow = -$(600)*0.10 = -$60 (cash inflow)

At t = 3, cashflow = -$(600)*0.10 + $500 = $440 (cash inflow)

where we get the value of the refrigerator at the end of third year ($500)

Also, we know that r = 10% = 0.1

(a) The expected net present value (NPV) of owning and operating the old refrigerator is calculated below:

(b) The net present value (NPV) of owning and operating the new refrigerator is calculated below:

(c) We see that the Net Present Value of costs is more for the old refrigerator (-1048.1593), whereas it is much lower for the new refrigerator (-473.5537). So, Zoe will choose to buy the new refrigerator.