Question

The HVAC engineer for a company that constructed one of the world’s tallest buildings requested that $500,000 be spent on software and hardware to improve efficiency of the environmental control system. This is expected to save $10,000 per year for 10 years in energy costs and $700,000 at the end of the 10 years in equipment refurbishment costs. Find the rate of return

Answer 1

The rate of return for the software and hardware investment is 142%.

Step-by-step explanation:

To calculate the rate of return, we need to compare the total cost of the investment to the total amount saved over 10 years.

The total cost of the investment is the initial cost of $500,000.

The total savings over the 10 years is the sum of the annual energy cost savings of $10,000 and the equipment refurbishment cost savings of $700,000, which equals $710,000.

Next, we calculate the rate of return by dividing the total savings by the total cost of the investment:

Rate of return = (Total savings / Total cost) × 100

Rate of return = ($710,000 / $500,000) × 100

Rate of return = 142%

Therefore, the rate of return for the software and hardware investment is 142%.

Answer 2

5.16%

Step-by-step explanation:

PW=0 equation.

0 = -500,000 + 10,000(P/A, i*,10) + 700,000(P/F, i*,10)

Now let use the estimation procedure to determine i* mean while All income will be regarded as a single F in year 10 so that the P/F factor can be used.

Therefore The P/F factor is selected because most of the cash flow ($700,000) which already fits this factor and errors.

P =$500,000, n =10,

F =10(10,000) + 700,000 = $800,000. .

Now we can state that 500,000 =

800,000(P/F,i,10)(P/F,i,10) = 0.625

Roughly estimated i* is between 4% and 5%.

Let use 5% as the first trial because this approximate rate for the P/F factor is lower than the true value when the time value of money is considered.

At i* =5%, the IRR equation is

0 = -500,000 + 10,000(P/A,5%,10) + 700,000(P/F,5%,10)0 < $6946

The result is positive, indicating that the return is more than 5%.

Let Try i*= 6%.

0 = -500,000 + 10,000(P/A,6%,10) + 700,000(P/F,6%,10)0 > $-35,519

Since the interest rate of 6% is too high, linearly interpolate between 5% and 6%

i* = 5.00 + 6946/(6946 + 35519) = 5.16%

Therefore the RATE OF RETURN is 5.16%