Home Security Systems is analyzing the purchase of manufacturing equipment that

Question

Home Security Systems is analyzing the purchase of manufacturing equipment that will cost $40,000. The annual cash inflows for the next three years will be:

Year

1 .................... 2 .................... 3 ....................

Cash Flow

$20,000 18,000 13,000

Determine the internal rate of return using interpolation. With a cost of capital of 12 percent, should the machine be purchased?

Please calculate the present value at 14% for year 1, 2, and 3

Example to fill in:

STEP 1: Average the inflows $17,000 STEP 2: Divide investment by annuity from step 1 2.353 STEP 3: Find the rate that corresponds to the value in Step 2: STEP 4: Calculate the Present Value at 14% Because the inflows are biased toward the early years, we will use the higher rate of 14%. Year Cash Flow PVIF @ 14% Present Value 1 $20,000 2 $18,000 3 $13,000 STEP 5: Calculate the Present Value at 15% Since the NPV is slightly over $40,000, we need to try a higher rate. We will try 15%. Year Cash Flow PVIF @ 15% Present Value 1 $20,000 0.870 $17,391 2 $18,000 0.756 $13,611 3 $13,000 0.658 $8,548 ($450) PV @ 14% ($450) PV @ 15% PV @ 14% Cost IRR =

Explanation / Answer

PV @ 14%= (20000/1.14)+(18000/1.14^2)+(13000/1.14^3)= $ 40168.905

PV @ 15%= (20000/1.15)+(18000/1.15^2)+(13000/1.15^3)= $ 39549.60

Therefore IRR= 14+.27= 14.27%

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