Question

Case study: Healthy Vegetable Producers
Healthy Vegetable Producers grow a variety of vegetables to sell to a major processing plant. John Brady, the new manager of Healthy Vegetable, is considering several changes in the business, including the purchase of a new harvesting machine that can dramatically reduce the number of workers the firm employs at harvest. Perhaps you can help John by applying some of the decision tools discussed in this week’s material to the decision he faces.

The cost of the new harvesting machine is $450,000, with an expected life of five years. The machine is very specialized, so it is not expected to have any appreciable salvage value. However, there will be significant labor savings involved. Initially, the new equipment will require little maintenance and repair, but, as it gets older the cost of maintenance, and repair will go up sharply. Generally, the owners and management of Healthy Vegetable feel that a 12 percent return should be expected from any new investment project before it can be undertaken. In addition, they would like a payback period of less than three years and an accounting rate of return (ARR) of 25%. The business tax rate for the company is 30%. Expected net returns before depreciation and taxes from the investments and estimated depreciation expenses are shown in the following Table.

Year	Net profit before depreciation and taxes	Depreciation
1	$275,000	$90,000
2	250,000	90,000
3	225,000	90,000
4	175,000	90,000
5	160,000	90,000

1. Initially, beore any calculations, what is your general reaction? Should the Vegetable Producers invest in the new equipment? (2 point)

2. What is the payback period for this investment (4 points)

3. What is the average rate of return (ARR) for this investment? (4 points)

4. What is the net present value (NPV) of this investment, using 12% minimum return

   required by the owners? (4 points)

5. What is profitability index at 12%? (2 points)

6. What is the internal rate of return (IRR) for the investment? Calculate using interpolation

   method. (5 points)

7. In the final analysis, do you believe this investment project would be good for Healthy

   Vegetable? Why or why not? (4 points)

Answer 1

Since, there are multiple parts to the question, I have answered the first five.

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Part A)

The general reaction would be to invest in the equipment as it would help the company in reducing the labor cost that forms a significant portion of total costs incurred by the company in its vegetable production business.

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Part B)

Step 1: Calculate Annual Cash Flow

The value of annual cash flow is arrived as below:

	Cash Flow
	Year 1	Year 2	Year 3	Year 4	Year 5
Net Profit before Depreciation and Taxes	275,000	250,000	225,000	175,000	160,000
Less Depreciation	90,000	90,000	90,000	90,000	90,000
Net Profit after Depreciation but before Taxes	185,000	160,000	135,000	85,000	70,000
Less Taxes	55,500	48,000	40,500	25,500	21,000
Net Profit after Taxes	129,500	112,000	94,500	59,500	49,000
Add Depreciation	90,000	90,000	90,000	90,000	90,000
Annual Cash Flow	$219,500	$202,000	$184,500	$149,500	$139,000

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Step 2: Calculate Payback Period

The payback period is calculated as below:

Year	Cash Flow	Cumulative Cash Flow
0	-450,000	-450,000
1	219,500	-230,500
2	202,000	-28,500
3	184,500	156,000
4	149,500
5	139,000

As can be seen from the above table that cumulative cash flows turn positive from negative between Year 2 and Year 3, the payback period will lie between these two years. The formula for payback period is arrived as below:

Payback Period = Years Upto which Partial Recovery is Made + Balance/Cash Flow of the Year in which Full Recovery is Made = 2 + 28,500/184,500 = 2.15 Years

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Part C)

The accounting rate of return is calculated as below:

Accounting Rate of Return = Average Accounting Income/Average Investment*100

Here,

Average Accounting Income = Sum of Net Profit After Depreciation and Taxes for all Years/Number of Years = (129,500 + 112,000 + 94,500 + 59,500 + 49,000)/5 = $88,900

Average Investment = (Initial Investment + Salvage Value)/2 = (450,000 + 0)/2 = $225,000

Substituting these values in the above formula for ARR, we get,

Accounting Rate of Return = 88,900/225,000*100 = 39.51%

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Part D)

The net present value can be calculated with the use of formula given below:

Net Present Value = Cash Flow Year 0 + Cash Flow Year 1/(1+Required Rate of Return)^1 + Cash Flow Year 2/(1+Required Rate of Return)^2 + Cash Flow Year 3/(1+Required Rate of Return)^3 + Cash Flow Year 4/(1+Required Rate of Return)^4 + Cash Flow Year 5/(1+Required Rate of Return)^5

Substituting these values in the above formula for NPV, we get,

NPV = - 450,000 + 219,500/(1+12%)^1 + 202,000/(1+12%)^2 + 184,500/(1+12%)^3 + 149,500/(1+12%)^4 + 139,000/(1+12%)^5 = $212,221.05

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Part E)

The value of profitability index is determined as follows:

Profitability Index = Present Value of Cash Inflows/Initial Investment

Here,

Present Value of Cash Inflows = Cash Flow Year 1/(1+Required Rate of Return)^1 + Cash Flow Year 2/(1+Required Rate of Return)^2 + Cash Flow Year 3/(1+Required Rate of Return)^3 + Cash Flow Year 4/(1+Required Rate of Return)^4 + Cash Flow Year 5/(1+Required Rate of Return)^5 = 219,500/(1+12%)^1 + 202,000/(1+12%)^2 + 184,500/(1+12%)^3 + 149,500/(1+12%)^4 + 139,000/(1+12%)^5 = $662,221.05

and Initial Investment = $450,000

Substituting these values in the above formula for Profitability Index, we get,

Profitability Index = 662,221.05/450,000 = 1.47