Question

Case Study:

A manufacturing company is evaluating two options for new equipment to introduce a new product to its suite of goods. The details for each option are provided below:

Option 1                                                                                                        

·         $65,000 for equipment with useful life of 7 years and no salvage value.                                                  

·         Maintenance costs are expected to be $2,700 per year and increase by 3% in Year 6 and remain at that rate.                      

·         Materials in Year 1 are estimated to be $15,000 but remain constant at $10,000 per year for the remaining years.                  

·         Labor is estimated to start at $70,000 in Year 1, increasing by 3% each year after.          

Revenues are estimated to be: 

Year 1	Year 2	Year 3	Year 4	Year 5	Year 6	Year 7
-	75,000	100,000	125,000	150,000	150,000	150,000

 

 

 

 

 

 

 

Option 2 

 

·         $85,000 for equipment with useful life of 7 years and a $13,000 salvage value 

·         Maintenance costs are expected to be $3,500 per year and increase by 3% in Year 6 and remain at that rate. 

·         Materials in Year 1 are estimated to be $20,000 but remain constant at $15,000 per year for the remaining years. 

·         Labor is estimated to start at $60,000 in Year 1, increasing by 3% each year after. 

Revenues are estimated to be:

 

Year    1	Year    2	Year    3	Year    4	Year    5	Year    6	Year    7
-	80,000	95,000	130,000	140,000	150,000	160,000

 

The company’s required rate of return and cost of capital is 8%.

Management has turned to its finance and accounting department to perform analyses and make a recommendation on which option to choose. They have requested that the three main capital budgeting calculations be done: NPV, IRR, and Payback Period for each option.

For this assignment, compute all required amounts and explain how the computations were performed. Evaluate the results for each option and explain what the results mean. Based on your analysis, recommend which option the company should pursue.

Answer 1

Requirement 1;

Option - 1: Determination of the Annual Cash Flows: Particulars Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Revenue 75,000 1,00,000 1,25,000 1,50,000 1,50,000 1,50,000 10,000 72,100 2,700 10,000 74,263 2,700 10,000 76,491 2,700 10,000 78,786 2,700 10,000 81,149 2,781 10,000 83,584 2,781 Less : - Material - Labor - Maintenance - Initial Investment Depreciation Net Income Add : Depreciation Annual Cash Flow 15,000 70,000 2,700 65,000 9,286 -65,000 -96,986 9,286 -65,000 -87,700 9,286 -19,086 9,286 -9,800 9,286 3,751 9,286 13,037 9,286 26,523 9,286 35,809 9,286 49,229 9,286 58,514 9,286 46,784 9,286 56,070 9,286 44,350 9,286 53,635 Year 2 80,000 Year 3 95,000 Year 4 1,30,000 Year 5 1,40,000 Year 6 1,50,000 Year 7 1,60,000 Option - 2: Determination of the Annual Cash Flows: Particulars Year 0 Year 1 Revenue Less : - Material 20,000 - Labor 60,000 - Maintenance 3,500 - Initial Investment 85,000 15,000 61,800 3,500 15,000 63,654 3,500 15,000 65,564 3,500 15,000 67,531 3,500 15,000 69,556 3,605 15,000 71,643 3,605 - Depreciation Net Income Add : Depreciation Annual Cash Flow 10,286 -85,000 -93,786 10,286 | -85,000 -83,500 10,286 -10,586 10,286 -300 10,286 2,560 10,286 12,846 10,286 35,651 10,286 45,936 10,286 43,684 10,286 53,969 10,286 51,553 10,286 61,839 10,286 59,466 10,286 69.752

Calculation of NPV : Particulars Discount Factor Option - 1 Discounted Cash Flow Option - 2 Discounted Cash Flow -77,313 -87,700 -257 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Salvage Value - Year 7 Discounted Cash Flow Less : Initial Investment Net Present Value 0.92590 0.85730 0.79380 0.73500 0.68060 0.63020 0.58350 0.58350 -9,800 13,037 35,809 58,514 56,070 53,635 -81,201 -8,402 10,349 26,320 39,825 35,335 31,296 -83,500 -300 12,846 45,936 53,969 61,839 69,752 13,000 10,197 33,763 36,732 38,971 40,700 7,586 90,379 -85,000 5,379 53,522 -65,000 -11,478 Therefore, Option - 2 has the highest NPV.

Calculation of IRR: IRR is the Rate of Return at which the NPV of the Project is ZERO. This will be calculated as follows: Option -1 Let us try the NPV at 6 % and 7 % Option - 1 Option - 1 PV Factor @ PV Factor Particulars Discounted Discounted 6% Cash Flow @ 7% Cash Flow Cash Flows Cash Flows Year O 1.0000 $ (65,000) $ (65,000) 1.0000 $ (65,000) $ (65,000). Year 1 | 0.9434 $ (87,700) $ (82,736) 0.9346 $ (87,700) $ (81,963). Year 2 0.8900 $ (9,800 $ (8,722) 0.8734 $ (9,800) $ (8,560) Year 3 0.8396 $ 13,037 $ 10,946 0.8163 $ 13,037 $ 10,642 Year 4 T 0 .7921 $ 35,809 $ 28,364 0.7629 $ 35,809 $ 27,319 Year 5 0.7473 $ 58,514 $ 43,725 0.7130 $ 58,514 $ 41,720 Year 6 0.7050 $ 56,070 $ 39,527 0.6663 $ 56,070 $ 37,362 Year 7 0.6651 $ 53,635 $ 35,671 0.6227 $ 53,635 $ 33,401 $ 1,775 $ 5,079) Since, NPV becomes Negative at 7%, it means that the NPV is between 6 % and 7 %. Change in % Change in NPV 1% $ 6,854 $ 1,775 Change = $ 1,775 / $ 6,854 * 1 % Change = 0.2590 % Therefore, IRR = 6 % + 0.2590 % = 6.259 %

Option - 2 Let us try the NPV at 7 % and 8 % Particulars PV Factor @ 8% Cash Flow Discounted Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 1.0000 0.9259 0.8573 0.7938 0.7350 0.6806 0.6302 0.5835 $ $ $ $ $ $ $ $ Option - 2 PV Factor @ 9% Cash Flows (85,000) $ (85,000)| (83,500) $ (77,315). 0.9174 (300 $ (257) 0.8417 12,846 $ 10,198. 0.7722 45,936 $ 33,765 0.7084 53,969 $ 36,731 0.6499 61,839 $ 38,969 0.5963 82,752 $ 48,285 0.5470 5,375 Option - 2 Cash Flow Discounted Cash Flows (85,000) $ (85,000). (83,500) $ (76,606). (300) $ (253) 12,846 $ 9,919 45,936 $ 32,542 $ 53,969 $ 35,076 $ 61,839 $ 36,872 $ 82,752 $ 45,268 $ (2,179) Since, NPV becomes Negative at 9 %, it means that the NPV is between 8 % and 9 %. Change in % Change in NPV 1% $ 7,554 $ 5,375 Change = $ 5,373 / $ 7,554 * 1 % Change = 0.7115 % Therefore, IRR = 8 % + 0.7115 % = 8.7115 % Based on IRR, Option - 2 shall be selected as its return (IRR) is more than the Option - 1.

Computation of Payback Period : Option - 1: Option - 2: Particulars Particulars A A Cash Flow $ (65,000) (87,700) (9,800) 13,037 35,809 $ 58,514 $ 56,070 $ 53,635 Year o Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Cumulative Cash Flows $ (65,000) $ (1,52,700) $ (1,62,500) $ (1,49,463) $ (1,13,654) $ (55,140) $ 930 $ 54,566 A Cash Flow Cumulative Cash Flows $ (85,000) $ (85,000) $ (83,500) $ (1,68,500) $ (300) $ (1,68,800) $ 12,846 $ (1,55,954) 45,936 $ (1,10,018) $ 53,969 $ (56,048) $ 61,839 $ 5,790 $ 82,752 $ 88,542 Year o Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 A Payback Period = 5 + $ 55,140 / $ 56,070 Payback period = 5 + 0.98 Therefore, Payback Period = 5.98 Years Payback period = 5 + $ 56,048 / $ 61,839 Payback period = 5 + 0.91 Therefore, Payback period = 5.91 Years Therefore, Option - 2 has the faster payback period.

Computation of ARR: Average Rate of Return = Average Annual Income / Average Investment Average Annual Income = [Revenue - Expenses (including depreciation)] / No. of Years Average Investment = [Investment at the Beginning + Investment at the ending] / 2 Option - 1: Particulars Year 1 Year 2 Year 3 Year 4 Net Income -96,986 -19,086 3,751 26,523 Average Income 7,795 Average Investment 32,500 ARR 23.98% Year 5 49,229 Year 6 46,784 Year 7 44,350 Year 2 -10,586 Year 3 2,560 Option - 2: Particulars Net Income Average Income Average Investment ARR Year 4 35,651 Year 5 43,684 Year 6 51,553 Year 7 59,466 Year 1 -93,786 12,649 32,500 38.92% Sometimes, Instead of Average Investment, Initial Investment is also used. In such case, ARR is calculated as follows: Option - 1: Particulars Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 | Year 7 Net Income -96,986 - 19,086 3,751 26,523 49,229 46,784 44,350 Average Income 7,795 Initial Investment 65,000 ARR 11.99%

Requirement 2:

Option - 2: Particulars Net Income Average Income Initial Investment ARR Year 2 -10,586 Year 3 2,560 | Year 4 35,651 | Year 5 43,684 | Year 6 51,553 | Year 7 59,466 Year 1 -93,786 12,649 85,000 14.88%

A Computation of NPV 31 32 Year Amount -85000 -83,500 -300 12,846 45,937 53,970 33 34 35 2 36 3 37 38 39 61,839 82,752 8% 40 41 Rate of return 42 IRR Formula 43 IRR =npv(B40,B33:B39)+B32 5375.75

A Computation of IRR 17 18 Year Amount -85000 -83,500 -300 12,846 45,937 53,970 61,839 82,752 19 20 21 2 22 3 23 24 25 26 27 IRR Formula 28 IRR =irr(B18:B25) 9% 29

Year Cumlative Amount -85000 -85000 -83500 -168500 -300l -168800 2 12846 -155954 45937 -110017 3 4 53970 -56047 5792 88544 61839 82752 88544

Payabck Period = year 5 + 56047/61839 %3D 5+ 0.90634 5.09 years

ARR = Average net profit / Initial investment 24792/85000 0.29167 Average profit = sum of inflow /7 1,73,544 /7 24792

Year Computation of net cash Flow 2 3 4 Annual Revenue o 75000 100000 125000 Less : maintenance Costs -2700 -2700 -2700 -2700 Material Expenses -15,000 -10,000 -10,000 -10,000 Labor -70,000 -72100 -74263 -76,491 Net Cash Flow -87,7001 -9,8001 13,037] 35,809 Note: no ise to deduct depreciation and add beack because there is no tax saving 150000 -2700 -10,000 -78785 58,515 150000 -2781.00 -10,000 -81149 56,0701 150000 -2781.00 -10,000 -83584 53,635|

16 Computation of IRR Amount 6 17 Year 18 19 -65000 -877001 -9800 130371 358091 58515 56070 53635 23 :5 aasta 25 irr(B18:B25) 26 IRR Formula 27 IRR 6%

A 30 Computation of NPV 31 Year Amount -65000 -87700 -9800 13037 35809 58515 56070 53635 40 Rate of return 8% 41 IRR Formula Enpv(B40, B33:B39)+B32 42 IRR -11482.31) vooWNO 39

ARR = Average net profit / Initial investment 17081/65000 0.26278 Average profit = sum of inflow /7 119566 /7 17080.9

Year Amount AWNA Cumlative -65000 -65000 -87700 -152700 -9800 -162500 13037 -149463 358091 -113654 58515 -55139 560701 931 53635 54566 54566

Payabck Period = year 5 + 55139/56070 5+ 0.9834 = 5.98yeras

Answer 2

Option - 1: Determination of the Annual Cash Flows: Particulars Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Revenue 75,000 1,00,000 1,25,000 1,50,000 1,50,000 1,50,000 10,000 72,100 2,700 10,000 74,263 2,700 10,000 76,491 2,700 10,000 78,786 2,700 10,000 81,149 2,781 10,000 83,584 2,781 Less : - Material - Labor - Maintenance - Initial Investment Depreciation Net Income Add : Depreciation Annual Cash Flow 15,000 70,000 2,700 65,000 9,286 -65,000 -96,986 9,286 -65,000 -87,700 9,286 -19,086 9,286 -9,800 9,286 3,751 9,286 13,037 9,286 26,523 9,286 35,809 9,286 49,229 9,286 58,514 9,286 46,784 9,286 56,070 9,286 44,350 9,286 53,635 Year 2 80,000 Year 3 95,000 Year 4 1,30,000 Year 5 1,40,000 Year 6 1,50,000 Year 7 1,60,000 Option - 2: Determination of the Annual Cash Flows: Particulars Year 0 Year 1 Revenue Less : - Material 20,000 - Labor 60,000 - Maintenance 3,500 - Initial Investment 85,000 15,000 61,800 3,500 15,000 63,654 3,500 15,000 65,564 3,500 15,000 67,531 3,500 15,000 69,556 3,605 15,000 71,643 3,605 - Depreciation Net Income Add : Depreciation Annual Cash Flow 10,286 -85,000 -93,786 10,286 | -85,000 -83,500 10,286 -10,586 10,286 -300 10,286 2,560 10,286 12,846 10,286 35,651 10,286 45,936 10,286 43,684 10,286 53,969 10,286 51,553 10,286 61,839 10,286 59,466 10,286 69.752

Calculation of NPV : Particulars Discount Factor Option - 1 Discounted Cash Flow Option - 2 Discounted Cash Flow -77,313 -87,700 -257 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Salvage Value - Year 7 Discounted Cash Flow Less : Initial Investment Net Present Value 0.92590 0.85730 0.79380 0.73500 0.68060 0.63020 0.58350 0.58350 -9,800 13,037 35,809 58,514 56,070 53,635 -81,201 -8,402 10,349 26,320 39,825 35,335 31,296 -83,500 -300 12,846 45,936 53,969 61,839 69,752 13,000 10,197 33,763 36,732 38,971 40,700 7,586 90,379 -85,000 5,379 53,522 -65,000 -11,478 Therefore, Option - 2 has the highest NPV.

Calculation of IRR: IRR is the Rate of Return at which the NPV of the Project is ZERO. This will be calculated as follows: Option -1 Let us try the NPV at 6 % and 7 % Option - 1 Option - 1 PV Factor @ PV Factor Particulars Discounted Discounted 6% Cash Flow @ 7% Cash Flow Cash Flows Cash Flows Year O 1.0000 $ (65,000) $ (65,000) 1.0000 $ (65,000) $ (65,000). Year 1 | 0.9434 $ (87,700) $ (82,736) 0.9346 $ (87,700) $ (81,963). Year 2 0.8900 $ (9,800 $ (8,722) 0.8734 $ (9,800) $ (8,560) Year 3 0.8396 $ 13,037 $ 10,946 0.8163 $ 13,037 $ 10,642 Year 4 T 0 .7921 $ 35,809 $ 28,364 0.7629 $ 35,809 $ 27,319 Year 5 0.7473 $ 58,514 $ 43,725 0.7130 $ 58,514 $ 41,720 Year 6 0.7050 $ 56,070 $ 39,527 0.6663 $ 56,070 $ 37,362 Year 7 0.6651 $ 53,635 $ 35,671 0.6227 $ 53,635 $ 33,401 $ 1,775 $ 5,079) Since, NPV becomes Negative at 7%, it means that the NPV is between 6 % and 7 %. Change in % Change in NPV 1% $ 6,854 $ 1,775 Change = $ 1,775 / $ 6,854 * 1 % Change = 0.2590 % Therefore, IRR = 6 % + 0.2590 % = 6.259 %

Option - 2 Let us try the NPV at 7 % and 8 % Particulars PV Factor @ 8% Cash Flow Discounted Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 1.0000 0.9259 0.8573 0.7938 0.7350 0.6806 0.6302 0.5835 $ $ $ $ $ $ $ $ Option - 2 PV Factor @ 9% Cash Flows (85,000) $ (85,000)| (83,500) $ (77,315). 0.9174 (300 $ (257) 0.8417 12,846 $ 10,198. 0.7722 45,936 $ 33,765 0.7084 53,969 $ 36,731 0.6499 61,839 $ 38,969 0.5963 82,752 $ 48,285 0.5470 5,375 Option - 2 Cash Flow Discounted Cash Flows (85,000) $ (85,000). (83,500) $ (76,606). (300) $ (253) 12,846 $ 9,919 45,936 $ 32,542 $ 53,969 $ 35,076 $ 61,839 $ 36,872 $ 82,752 $ 45,268 $ (2,179) Since, NPV becomes Negative at 9 %, it means that the NPV is between 8 % and 9 %. Change in % Change in NPV 1% $ 7,554 $ 5,375 Change = $ 5,373 / $ 7,554 * 1 % Change = 0.7115 % Therefore, IRR = 8 % + 0.7115 % = 8.7115 % Based on IRR, Option - 2 shall be selected as its return (IRR) is more than the Option - 1.

Computation of Payback Period : Option - 1: Option - 2: Particulars Particulars A A Cash Flow $ (65,000) (87,700) (9,800) 13,037 35,809 $ 58,514 $ 56,070 $ 53,635 Year o Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Cumulative Cash Flows $ (65,000) $ (1,52,700) $ (1,62,500) $ (1,49,463) $ (1,13,654) $ (55,140) $ 930 $ 54,566 A Cash Flow Cumulative Cash Flows $ (85,000) $ (85,000) $ (83,500) $ (1,68,500) $ (300) $ (1,68,800) $ 12,846 $ (1,55,954) 45,936 $ (1,10,018) $ 53,969 $ (56,048) $ 61,839 $ 5,790 $ 82,752 $ 88,542 Year o Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 A Payback Period = 5 + $ 55,140 / $ 56,070 Payback period = 5 + 0.98 Therefore, Payback Period = 5.98 Years Payback period = 5 + $ 56,048 / $ 61,839 Payback period = 5 + 0.91 Therefore, Payback period = 5.91 Years Therefore, Option - 2 has the faster payback period.

Computation of ARR: Average Rate of Return = Average Annual Income / Average Investment Average Annual Income = [Revenue - Expenses (including depreciation)] / No. of Years Average Investment = [Investment at the Beginning + Investment at the ending] / 2 Option - 1: Particulars Year 1 Year 2 Year 3 Year 4 Net Income -96,986 -19,086 3,751 26,523 Average Income 7,795 Average Investment 32,500 ARR 23.98% Year 5 49,229 Year 6 46,784 Year 7 44,350 Year 2 -10,586 Year 3 2,560 Option - 2: Particulars Net Income Average Income Average Investment ARR Year 4 35,651 Year 5 43,684 Year 6 51,553 Year 7 59,466 Year 1 -93,786 12,649 32,500 38.92% Sometimes, Instead of Average Investment, Initial Investment is also used. In such case, ARR is calculated as follows: Option - 1: Particulars Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 | Year 7 Net Income -96,986 - 19,086 3,751 26,523 49,229 46,784 44,350 Average Income 7,795 Initial Investment 65,000 ARR 11.99%

Option - 2: Particulars Net Income Average Income Initial Investment ARR Year 2 -10,586 Year 3 2,560 | Year 4 35,651 | Year 5 43,684 | Year 6 51,553 | Year 7 59,466 Year 1 -93,786 12,649 85,000 14.88%