Question

A firm must purchase an electronic control device. Device A costs $10,000 and lasts for 3 years. Annual maintenance costs in each of the years are $1,800 $1,400 and $1,300 respectively. Device B costs $15,000 and lasts for 4 years. Annual maintenance costs in each of the years are $1,700, $1,100, $1,070, and $1,100 respectively. These two devices service the same purpose (i.e., are mutually exclusive) and the firm needs to use this device for its day-to-day operations. If the cost of capital is 7.00%, which device should the firm purchase?

NPV of Device A: ?

EAA of Device A: ?

NPV of Device B: ?

EAA of Device B: ?

2. You own a rental building in the city and are interested in replacing the heating system. You are faced with the following alternatives: a. A solar heating system, which will cost $9,328 to install and $527 a year to run and will last forever (assume that your building will, too). b. A gas heating system, which will cost $6,459 to install and $1,127 a year to run and will last 23 years. c. An oil heating system, which will cost $3,561 to install and $1,130 a year to run and will last 15 years. If your opportunity cost is 8.00% percent, which of these three options is best for you?

NPV of Solar heating system: ?

EAA of Solar heating system: ?

NPV of Gas heating system: ?

EAA of Gas heating system: ?

NPV of Oil heating system: ?

EAA of Oil heating system: ?

Answer 1

Prepare the table to compute the present value of Device A as follows:

The result of the above table is as follows:

So, the net present value of the cost of Device A is $13,966.24445.

Compute the equivalent annual annuity (EAA) using the equation as shown below:

EAA = ( Rate * Net present value) / ( 1 – ( 1+ Rate) ^{– Period}

         = ( 7% * $13,966.24445) / ( 1 – ( 1 + 7% ) ^{– 3}

         = $977.6371115/ 0.1837021231

        =   $5,321.8607111

Hence, EAA of the cost of device A is $5,321.8607111.

Prepare the table to compute the present value of Device B as follows:

The result of the above table is as follows:

So, the net present value of the cost of Device B is $19,262.19111.

Compute the equivalent annual annuity (EAA) using the equation as shown below:

EAA = ( Rate * Net present value) / ( 1 – ( 1+ Rate) ^{– Period}

         = ( 7% * $19,262.19111) / ( 1 – ( 1 + 7% ) ^{– 4}

         = $1,348.3533777/ 0.23710478795

        = $5,686.7404

Hence, EAA of the cost of device B is $5,686.7404.

Both NPV and EAA of the cost of device A are less than the Device B. So, the firm should purchase device A.