Would you be able to show me how to get all 4 parts of the question? Thank you!

Question

Would you be able to show me how to get all 4 parts of the question? Thank you! I'm an engineering econ student. This is problem 5-51 from Engineering Economy 16th ed by Sullivan.

A computer call center is going to replace all of its incandescent lamps with more energy efficient fluorescent lighting fixtures. The total energy savings are estimated to be S1,395 per year, and the cost of purchasing and installing the fluorescent fixtures is S5,000. The study period is seven years, and terminal market values for the fixtures are negligible. a. What is the IRR of this investment? b. What is the simple payback period of the investment? c. Is there a conflict in the answers to Parts (a) and (b)? List your assumptions. d. The simple payback "rate of return" is 1/. How close does this metric come to matching your answer in Part (a)? a. The IRR of the investment isM. (Round to one decimal place.)

Explanation / Answer

a.

Cashflow in year 0 = $5000

Cashflow in year 1 to 7 = $1,395

Let IRR be r%

Then, NPV at r% will be 0.

i.e -5000 + 1395/(1+r) + .... + 1395/(1+r)^7 = 0

Solve for r using guess technique.

Let r1 = 20%.

NPV1 = -5000 + PV(20%,7,-1395) = -5000+5028.41 = $28.41

As the NPV is very close to 0, rate should be close to 20% and higher (at a lower rate, NPV will be higher).

Let r2 = 22%

NPV2 = -5000 + PV(22%,7,-1395) = -5000 + 4764.63 = -235.37

IRR = r1 + NPV1 * (R2-R1)/(NPV1-NPV2)

= 20% + 28.41 * (22% - 20%)/(28.41 + 235.37) = 20% + 2% * 28.41/263.78 = 20% + 0.2154% ~ 20.2%

b. Calculate the cumulative cashflows

As seen from the table the payback period is between 3 and 4 years

= 3 + |-815|/1395 = 3.58 years

C. The simple payback period ignores the discount rate, i.e it does not confirm to the time value of money. It just calculates the time by which the initial investment will be recovered if the discount rate were 0%.

The IRR on the other hand is the discount rate at which the investment will give a no profit no loss.

D. Simple payback rate = 1/3.58 = 27.90%

This rate has a difference of about 7.7% from the IRR. This is because the simple payback rate did not consider any discounting/time value of money. Payback considers a $ earned in 2nd or 3rd year as equal to the $ earned in year 1 but in reality that is not the case.

Year Cashflows Cumulative 0 -5000 -5000 1 1395 -3605 2 1395 -2210 3 1395 -815 4 1395 580 5 1395 1975 6 1395 3370 7 1395 4765

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