Question

Just because a​ project's payback period is relatively long​ doesn't mean it is not profitable in the long run. Consider an investment in LED lights with a price tag of $226,000. The estimated annual savings in electricity and routine maintenance is $40,900 and the life of the LED lights is 21 years. Assume that the payback period of three years or less is desired by the investor.

a. What is the simple payback period for the​ lights? (I already know answer is 5.5 years don't bother doing this.)

b. What is the IRR of this​ investment? (Show work on Chegg or paper but not excel and make sure answer is correct.)

c. What do you conclude from Part ​(a) and Part (b)​?

Answer 1

Initial Investment = $226,000

Annual Savings = $40,900

Life = 21years

a. What is the simple payback period for the​ lights? (I already know answer is 5.5 years don't bother doing this.)

Initial investment = $226,000

Annual Savings = $40,900

Simple payback period = Investment / Annual Savings

Simple payback period = $226,000/$40,900=5.5 years

Desired Payback period = 3 years

As the actual payback period is more than the desired payback period, the project should not be accepted. It must be rejected.

b. What is the IRR of the investment?

Using the trial and error method for the calculation of IRR

Let interest rate is 15%.

At 15% the NPW of the above cash flow series will be

NPW = -$226,000 + $40,900 (P/A, 15%, 21)

NPW = -$226,000 + $40,900 (6.3125) = 32,181

As the NPW is positive, increase the rate of interest to get negative NPW. Increase the rate of interest to 18% and calculate the NPW at 18%.

NPW = -$226,000 + $40,900 (P/A, 18%, 21)

NPW = -$226,000 + $40,900 (5.3837) = -5,807

Using interpolation

IRR = 15% + [32,181 – 0 ÷ 32,181 – (-5,807)]*3% = 17.5%

IRR of the investment will be 17.5%

c. What do you conclude from Part ​(a) and Part (b)​?

From part (a)

Desired Payback period = 3 years

As the actual payback period is more than the desired payback period, the project should not be accepted. It must be rejected.

From part (b)

IRR calculated above = 17.5%

But MARR is not given in the question. Unless MARR we cannot justify whether the project is acceptable or not. However, the simple payback period assumes that the investment should be recovered within three years which the investment is not able to do. By seeing the cash flows of the first three years it can be seen that the PW for the first three years savings will be less than the PW of the cash outflows (initial investment). So project cannot be acceptable.

However, without the MARR, the acceptability of the project cannot be determinable.