**Determine Net Present Value and Net Operating Working Capital**

MMG Manufacturing is considering a new machine that costs $300,000 and would reduce pretax manufacturing costs by $92,000 annually. Holmes would use the 3-year MACRS method to depreciate the machine, and management thinks the machine would have a value of $33,000 at the end of its 5-year operating life. The applicable depreciation rates are 33%, 45%, 15%, and 7%. Net operating working capital would increase by $30,000 initially, but it would be recovered at the end of the project’s 5-year life. Holmes’s marginal tax rate is 35%, and a 11.0% WACC is appropriate for the project.

- A) Calculate the project’s NPV ( ), IRR ( ), and MIRR ( )
- B) Assume management is unsure about the $92,000 cost savings — this figure could deviate by as much as plus or minus 20%.

What would the NPV be under each of these situations?

Situation1 (cost saving increase by 20%): ( )

Situation2 (Cost savings decrease by 20%): ( )

Suppose the CFO wants you to do a scenario analysis with different values for the cost savings, the machine’s salvage value, and the net operating working capital (NOWC) requirement. She asks you to use the following probabilities and values in the scenario analysis:

Scenario Probability Cost Savings Salvage Value NOWC

Worst Case 0.25 $70,000 $26,000 $32,000

Base Case 0.50 $92,000 $33,000 $30,000

Best Case 0.25 $110,000 $40,000 $28,000

- C) Calculate the project’s expected NPV ( ), its standard deviation ( ), nd its coefficient of variation ( ).

HINT: based on the answers you get in b: E(NPV)= P1*NPV1(scenario1) + P2*NPV2(scenario2) + P3*NPV3(Scenario3)

Hint to question a. Please calculate the cash flows from the table below (90% of the answer is already provided to you), in order to be able to calculate NPV, IRR, MIRR, and payback period.

**Solution**

__NPV Calculations__

__NPV Calculations__

- Initial investment: $3,00,000

Operating cost increase: $30,000 -> Total investment is 3,30,000$

Cost of machine at the end of 5 years: $33,000

By 3 yr MACRS model, the depreciation rates are 33% 45% 15% 7%

Thus depreciation expenses can be calculated as follows:

Year |
Depreciation expense |
Saving |
Savings – Depreciation |
Tax deductions |
Net amount |

1 | 108900 | 92000 | -16900 | 9776.65 | -7123.35 |

2 | 148500 | 92000 | -56500 | 32685.25 | -23814.75 |

3 | 49500 | 92000 | 42500 | -24586.25 | 17913.75 |

4 | 23100 | 92000 | 68900 | -39858.65 | 29041.35 |

5 | 0 | 92000 | 92000 | -53222 | 38778 |

By 5% inflation rate, adjusted amounts are as follows:

Net amount |
Adjusted amount |

-7123.35 | -6784.142857 |

-23814.75 | -21600.68027 |

17913.75 | 15474.57078 |

29041.35 | 23892.39052 |

38778 | 30383.57768 |

NPV can thus be calculated as sum of these values and sum with final salvage value/ (1.05)^{5}

Thus NPV = $67,222

Calculating the discount rate for which the NPV is calculated to be ZERO comes out to be:

0.6858 (68.58%). IRR is calculated using Solver from excel varying the Discount rate and equalizing NPV to ZERO

MIRR can be calculated by the formula below:

After calculations, MIRR can be calculated as: 21.56%

- Worst case scenario:

Year |
Depreciation expense |
Saving |
Savings – Depreciation |
Tax deductions |
Net amount |

1 | 109560 | 70000 | -39560 | 22885.46 | -16674.54 |

2 | 149400 | 70000 | -79400 | 45932.9 | -33467.1 |

3 | 49800 | 70000 | 20200 | -11685.7 | 8514.3 |

4 | 23240 | 70000 | 46760 | -27050.66 | 19709.34 |

5 | 0 | 70000 | 70000 | -40495 | 29505 |

Net amount |
Adjusted amount |

-16674.54 | -15880.51429 |

-33467.1 | -30355.64626 |

8514.3 | 7354.972465 |

19709.34 | 16214.92279 |

29505 | 23117.93954 |

NPV can be calculated as: 20,823$ taking Salvage value as 28,000$

Best case scenario:

Year |
Depreciation expense |
Saving |
Savings – Depreciation |
Tax deductions |
Net amount |

1 | 108240 | 110000 | 1760 | -1018.16 | 741.84 |

2 | 147600 | 110000 | -37600 | 21751.6 | -15848.4 |

3 | 49200 | 110000 | 60800 | -35172.8 | 25627.2 |

4 | 22960 | 110000 | 87040 | -50352.64 | 36687.36 |

5 | 0 | 110000 | 110000 | -63635 | 46365 |

Net amount |
Adjusted amount |

741.84 | 706.5142857 |

-15848.4 | -14374.96599 |

25627.2 | 22137.73891 |

36687.36 | 30182.78187 |

46365 | 36328.19071 |

NPV can be calculated as: 1,06,321$ taking salvage value as 40,000$

- Taking probabilities of worst case to be 0.25, base case to be 0.5 and best case to be 0.25, we can calculate expected value of NPV as:

E(NPV) = It comes out to be $65,399

Initial Capital | |||||

328000 |

Year |
Depreciation expense |
Saving |
Savings – Depreciation |
Tax deductions |
Net amount |

1 | 108240 | 110000 | 1760 | -1018.16 | 741.84 |

2 | 147600 | 110000 | -37600 | 21751.6 | -15848.4 |

3 | 49200 | 110000 | 60800 | -35172.8 | 25627.2 |

4 | 22960 | 110000 | 87040 | -50352.64 | 36687.36 |

5 | 0 | 110000 | 110000 | -63635 | 46365 |

** **

0.05 | 106321.3064 | 40000 | |

Discount rate |
NPV | Salvage rate |

Net amount |
Adjusted amount |

741.84 | 706.5142857 |

-15848.4 | -14374.96599 |

25627.2 | 22137.73891 |

36687.36 | 30182.78187 |

46365 | 36328.19071 |