Greeting All,
I have been preparing for CMA part-2 from Gliem resource, However there is one thing in Unit 13 I couldn't understand, Which is the calculation of IRR
There is two examples in study unit 13.6 which calculate NPV, IRR, Payback period, and Profitability index. All the calculations in both examples are constant and uses the same formula except for IRR, the formula differs and I could not understand how we reach to it. However I will leave both examples and IRR solutions below.
Example 1
Hazman Company plans to replace an old piece of equipment that is obsolete and expected to be unreliable under the stress of daily operations. The equipment is fully depreciated, and no salvage value can be realized upon its disposal. One piece of equipment being considered as a replacement will provide an annual cash savings of $7,000 before income taxes and without regard to the effect of depreciation. The equipment costs $18,000 and has an estimated useful life of 5 years. No salvage value will be used for depreciation purposes because the equipment is expected to have no value at the end of 5 years.
Hazman uses the straight-line depreciation method on all equipment for both book and tax purposes. Hence, annual depreciation is $3,600. The company is subject to a 40% tax rate. Hazman's desired rate of return is 14%, so it will use the 14% column from a present value table.
Internal rate of return: The goal is to find the discount rate that most nearly equals the net investment.
| Net present value at 16% ($5,640 × 3.27) |
$ 18,443 |
| Net present value at 18% ($5,640 × 3.13) |
(17,653) |
|
|
| Difference |
$ 790
|
| Net present value at 16%: |
$ 18,443 |
| Initial investment |
(18,000) |
|
|
| Difference |
$ 443
|
| Estimated increment [($443 ÷ $790) × 2%] |
1.1% |
| Rate used |
+ 16.0%
|
| Internal rate of return |
17.1%
|
Example 2 The management of Flesher Farms is trying to decide whether to buy a new team of mules at a cost of $1,000 or a new tractor at a cost of $10,000. They will perform the same job. But because the mules require more laborers, the annual return is only $250 of net cash inflows. The tractor will return $2,000 of net cash inflows per year. The mules have a working life of 8 years, and the tractor has a working life of 10 years. Neither investment is expected to have a salvage value at the end of its useful life. Flesher Farms' desired rate of return is 6%.
Internal rate of return:
Mules: Initial investment ÷ Net cash inflows = $1,000 ÷ $250 = 4
On the 8-year line, a factor of 4 indicates a rate of return of approximately 18.7%.
Tractor: Initial investment ÷ Net cash inflows = $10,000 ÷ $2,000 = 5
On the 10-year line, a factor of 5 indicates a rate of return of approximately 15.2%.
I would really appreciate your support to understand the above examples. Thanks to all of you
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Hend Alutayri
Accountant
Yanbu
Saudi Arabia
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