You have been asked to analyze the possibility of replacing a bocce ball machine
ID: 2769162 • Letter: Y
Question
You have been asked to analyze the possibility of replacing a bocce ball machine that your company bought 5 years ago. It had an expected life of 10 years at the time of purchase and cost $1,200,000 to purchase. Your firm has been depreciating the equipment using MACR 10-year depreciation. The old machine would be sold if the project is taken on. It is estimated that it could be sold for $800,000 at that time. It is expected that if the machine is not replaced, it could be sold for $100,000 at the end of its economic life. A consultant hired by your firm has determined that the best replacement machine is made by PMBA Inc. She determined that the new machine will save somewhere between $350,000 and $450,000 a year in manufacturing costs (expected cost reduction is $400,000). The cost of the machine is $2,100,000 and has an expected life of 5 years. Even though it has a five-year life IRS guidelines allow your firm to use a 3-year MACR schedule for depreciation on the machine. The new machine will require a one-time increase in working capital of $150,000. Your firm has a tax rate of 35%, and a required rate of return on the project of 12.00%(firm’s WACC). What is the NPV, MIRR, and IRR of the project if the expected saving are obtained? What level of savings would be the economic breakeven? Assuming that the worst case is saving of $350,000, a discount rate of 13%, how does it change the results? What is the saving was $450,000, what would the results be?
Explanation / Answer
Year
Basis
%
Depreciation Expense
Accumulated Depreciation
Ending Book Value
1
$1,200,000.00
10.000%
$120,000.00
$120,000.00
$1,080,000.00
2
$1,200,000.00
18.000%
$216,000.00
$336,000.00
$864,000.00
3
$1,200,000.00
14.400%
$172,800.00
$508,800.00
$691,200.00
4
$1,200,000.00
11.520%
$138,240.00
$647,040.00
$552,960.00
5
$1,200,000.00
9.216%
$110,592.00
$757,632.00
$442,368.00
As we can see that the ending book value of the old machinery in year 5 is $442,368. So, the after tax value of the machine, if sold = $800,000 – [($800,000 - $442,368) x (tax rate)] = $674,828.8
So, initial investment = Cost of new machine – after-tax value of old machine + NWC
=> $2,100,000 - $674,828.8 + $150,000 = $ 1,575,171.2
Depreciation of new machine as per 3-years schedule:
Year
Basis
%
Depreciation Expense
Accumulated Depreciation
Ending Book Value
1
$2,100,000.00
33.333%
$700,000.14
$700,000.14
$1,399,999.86
2
$2,100,000.00
44.444%
$933,333.45
$1,633,333.59
$466,666.41
3
$2,100,000.00
14.815%
$311,119.20
$1,944,452.79
$155,547.21
4
$2,100,000.00
7.407%
$155,547.21
$2,100,000.00
$0.00
Operating Cash flow from the project:
Year
1
2
3
4
5
Savings
$400,000.00
$400,000.00
$400,000.00
$400,000.00
$400,000.00
Less: Depreciation
$700,000.00
$933,333.45
$311,119.20
$155,547.21
$0.00
Before tax savings
-$300,000.00
-$533,333.45
$88,880.80
$244,452.79
$400,000.00
Less: Tax @ 35%
-$105,000.00
-$186,666.71
$31,108.28
$85,558.48
$140,000.00
After-tax Savings
-$195,000.00
-$346,666.74
$57,772.52
$158,894.31
$260,000.00
Add: Depreciation
$505,000.00
$586,666.71
$368,891.72
$314,441.52
$260,000.00
Add: Recovery of NWC
$0.00
$0.00
$0.00
$0.00
$150,000.00
Operating Cash Flow
$310,000.00
$239,999.97
$426,664.24
$473,335.84
$670,000.00
NPV = -$1,575,171.2 + [($310,000)/(1.12)] + [($239,999.97)/(1.12)2] + [($426,664.24)/(1.12)3] + [($473,335.84)/(1.12)4] + [($670,000)/(1.12)5] =-$122,378.33
IRR:
0 = -$1,575,171.2 + [($310,000)/(IRR)] + [($239,999.97)/(IRR)2] + [($426,664.24)/(IRR)3] + [($473,335.84)/(IRR)4] + [($670,000)/(IRR)5] = 9.2421%
MIRR using reinvestment approach:
In the reinvestment approach, we find the future value of all cash except the initial cash flow at the end of the project using the reinvestment rate. So, the reinvesting the cash flows to time 5, we find:
Time 5 Cash Flow:
[($310,000)*(1.12)4] + [($239,999.97)*(1.12)3] + [($426,664.24)*(1.12)3] + [($473,335.84)*(1.12)1] + [($670,000)] = $2,560,317.44
So, the MIRR using the reinvestment approach:
0 = -$1,575,171.2 + [($2,560,317.44) / (1+MIRR)5]
$1,575,171.2 = [($2,560,317.44) / (1+MIRR)5]
(1+MIRR)5 = $2,560,317.44 / $1,575,171.2
(1+MIRR)5 = 1.625421696
MIRR = (1.625421696)1/5 – 1 = 0.1020 or 10.20%
Year
Basis
%
Depreciation Expense
Accumulated Depreciation
Ending Book Value
1
$1,200,000.00
10.000%
$120,000.00
$120,000.00
$1,080,000.00
2
$1,200,000.00
18.000%
$216,000.00
$336,000.00
$864,000.00
3
$1,200,000.00
14.400%
$172,800.00
$508,800.00
$691,200.00
4
$1,200,000.00
11.520%
$138,240.00
$647,040.00
$552,960.00
5
$1,200,000.00
9.216%
$110,592.00
$757,632.00
$442,368.00
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