Question 2 A firm wants to buy a machine costing 100000 The

Question 2 A firm wants to buy a machine costing $100,000. The machine has a $5,500 annual maintenance cost and an $8,000 salvage value at the end of 10 years. If annual revenue from the machine is 20,000 and the MARR is 12%, is this acceptable for the firm? Show the reason for your answer. (5 marks)

Solution

Solution: Cost of machine, IC = $100,000

Annual maintenance cost = $5,500, Annual revenues = $20,000, so anuual returns, AR = 20000 - 5500 = $14,500

Salvage value, SV = $8,000; life period, N= 10 years; MARR = 12%

To check if deal is good, or firm should invest in this machine, we calculate IRR (Internal rate of return).

If IRR > MARR, the deal is good, and this investment should happen ... (1)

Present worth,PW = -IC + AR(P/A,i,N) + SV(P/F,i,N)

IRR is rate for which present worth = 0

PW of this machine = -100,000 + 14,500 (P/A,12%, 10) + 8,000 (P/F, 12%, 10)

For IRR, 100,000 = 14,500 (P/A,i,10) + 8000 (P/F, i,10)

(P/A,i,10) = ((1+i)¹⁰-1)/i(1+i)¹⁰

(P/F,i,10) = (1+i)^-10

so, 100000 = 14500*((1+i)¹⁰-1)/i(1+i)¹⁰  + 8000 (1+i)^-10

On solving, we get i = 0.0821 (approx). So, IRR = 8.21% < 12% = MARR

Following (1), the firm shouldn\'t invest.