Question

The Elberta Fruit Farm of Ontario always has hired transient workers to pick its annual cherry crop. Janessa Wright, the farm manager, just received information on a cherry picking machine that is being purchased by many fruit farms. The machine is a motorized device that shakes the cherry tree, causing the cherries to fall onto plastic tarps that funnel the cherries into bins. Ms. Wright has gathered the following information to decide whether a cherry picker would be a profitable investment for the Elberta Fruit Farm:

1. Currently, the farm is paying an average of $200,000 per year to transient workers to pick the cherries.
2. The cherry picker would cost $250,000. It would be depreciated using the straight-line method and it would have no salvage value at the end of its 8-year useful life.
3. Annual out-of-pocket costs associated with the cherry picker would be: cost of an operator and an assistant, $98,000; insurance, $5,000; fuel, $15,000; and a maintenance contract, $20,000.

Click here to view Exhibit 13B-1 and Exhibit 13B-2, to determine the appropriate discount factor using tables.

Required:

1. Determine the annual savings in cash operating costs that would be realized if the cherry picker were purchased.

2a. Compute the simple rate of return expected from the cherry picker.

2b. Would the cherry picker be purchased if Elberta Fruit Farm’s required rate of return is 18%?

3a. Compute the payback period on the cherry picker.

3b. The Elberta Fruit Farm will not purchase equipment unless it has a payback period of five years or less. Would the cherry picker be purchased?

4a. Compute the internal rate of return promised by the cherry picker.

4b. Based on this computation, does it appear that the simple rate of return is an accurate guide in investment decisions?

Answer 1

Solution :

PART 2a : Simple rate of return :

Simple rate of return is arrived by dividing the net income by Initial investment (cost of the asset).

Net Income = Annual Cash Savings - Depreciation

Depreciation = (Cost of the Asset -Salvage) Useful Life

= ($250,000) 8

= $31,250

Therefore, Net income = $62,000 - $31,250 = $30,750

Simple rate of return = ($30,750 $250,000) x 100 = 12.30%

PART 2b : Should Cherry picker be purchased if the expected rate of return is 18% :

The required rate of return from Cherry picker is 18%. However, the return expected from the cherry picker is only 12.30% as computed above.
Since, the cherry picker fails to fulfil the required return of 18%, it shall not be purchased.

PART 3a : Payback period :

Payback period is the time taken by the investment to recover its cost incurred in full.

It is calculated as follows :  Initial investment Annual savings in cash operating cost

= $250,000 $62,000

= 4.03 years

Part 3b : Should Cherry picker be purchased if the expected payback period is 5 years :

The enterprise expects the investment to be recovered in 5 years, however, as per the above calculations in Part 3a, the investment cost is recovered within 4.03 years.

Hence, the cherry picker should be purchased

Part 4a : Computation of internal rate of return :

Let internal rate of return be "i".

$62,000 x Cumulative PV Factor at i for 8 periods =$250,000 $62,000 = 4.0322

Cumulative PV Factor at i for 8 periods = 4.0322

This PV factors falls between i at 18% and 19%

Cumulative PV Factor at 18% = 4.078

Cumulative PV Factor at 19% = 3.954

IRR = 18% + [ (4.078 -   4.032) (4.078 - 3.954) ]

IRR = 18% + [(0.046) (0.124) ]

IRR = 18% + 0.3709

IRR = 18.0379%

*The IRR rate may vary due to rounding off differences

Part 4 b : Comparing IRR with Simple return rate :

IRR = 18.0379%

Simple return rate = 12.30%

There is a significant difference between IRR & Simple return rate. The decision taken by comparing the simple return with the expected return yielded that the cherry picker should not be purchased as it yielded a return less than 18%.

However, when we compare the IRR with the expected return, we can see that the cherry picker has yielded more than the expected return of 18%..

Hence, it can be concluded that simple return rate is an inaccurate guide to decision making.

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