Question

Aerotron electronics is considering the purchase of water filtration system to assist in circuit board manufacturing. The system cost $40,000. it has an expected life of 7 years at which time its salvage value will be $7,500. Operating and maintenance expenses are estimated to be $2,000 per year. if the filtration system is not purchased. Aerotron electronics will have to pay Bay City $12,000 per year for water purification. If system is purchased, no water purification from Bay City will be needed Aerotron Electronics must be borrow half of the purchase price but they cannot start repaying the loan for two years. The bank has agreed to three equal annual payments with the first payment due at end of year . the loan interest rate is 8% compounded annually. Aerotron Electronics MARR is 10% compounded annually. Find the MIRR, Make a recommendation should Aerotron invest?   

Answer 1

MARR = 10%

initial cost = 40000

Salvage value = 7500 after 7 yrs

annual O&M cost = 2000

If filtration system is not bought then Aerotron will pay = 12000

Annual savings if system is bought = 12000 - 2000 = 10000

Half of the cost will be loan so, loan amount = 40000/2 = 20000

Loan interest rate = 8%

Loan term = 3 yrs annual payments

Loan amount after 1 yrs = 20000*(F/P,8%,1) = 20000*1.08 = 21600

Loan payments at EOY 2, 3, 4 = 21600*(A/P,8%,3) = 21600*0.388033 = 8381.51

PW of the outflows = 20000 + 8381.51*(P/A,10%,3)*(P/F,10%,1)

= 20000 + 8381.51*2.486851*0.909090

= 38948.677

FW of inflows = 10000*(F/A,10%,7) + 7500 = 10000*9.487171 + 7500 = 102371.71

Let MIRR be I%

Then

38948.677 * (1+i)^7 = 102371.71

I = (102371.71 / 38948.677)^(1/7) - 1

I = 1.148035 - 1 = 0.148035 = 14.80%

As MIRR > MARR, so this project should be selected