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 $92,000. The annual cash inflows for the next three years will be:

Determine the internal rate of return using interpolation. Use Appendix B and Appendix D. (Round "PV Factor" and intermediate to 3 decimal places. Round final answer to 2 decimal places. Omit the "%" sign in your response.)

With a cost of capital of 10 percent, should the machine be purchased?

Home Security Systems is analyzing the purchase of manufacturing equipment that will cost $92,000. The annual cash inflows for the next three years will be:

Explanation / Answer

Part a We will solve part a of this problem using a six-step process, as follows:

Step 1 Average the Inflows ($41000 + $39,000 + $34,000) / 3 = $114000 / 3 = $38000

Step 2 Divide the inflows by the assumed annuity in Step 1

Investment = $92000,

Annuity $38000

= 92000/38000 = 2.421

Step 3         Go to Appendix D for the 1st approximation.
The value in Step 2 (for n = 3) falls between
11% and 12%.

Step 4     Try a first approximation of discounting back the inflows. Because the inflows are biased toward
the early years, we will use the higher rate of 12%.

Year   Cash Flow     PVIF at 12%   Present Value

1         $41000              .893                  $ 36607

2           39000              .797                       31091

3           34000              .712                      24201

                                                                  $91898

Step 5    Since the NPV is slightly lower $92000, we need to try a lower rate. We will try 11%.

Year   Cash Flow     PVIF at 11%   Present Value

1         $41000              .900                  $ 36937

2           39000              .812                       31653

3           34000              .731                      24861

                                                                  $93451

Because the NPV is now higher than $92,000, we know the IRR is between 11% and 12%. We will interpolate.

$93451............ PV @ 11%      $93451............. PV @ 12%

–91898............ PV @ 12%      –92000............. Cost

$     1553                                $      1451

    11% + ($1451/$1553) (1%)

= 11.009% IRR

b.       Since the IRR of 11.009% is greater than the cost of capital of 10%, the project should be accepted

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