# 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.

1. A) Calculate the project’s NPV ( ), IRR ( ), and MIRR (   )
2. 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

1. 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
1. 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%

1. 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\$

1. 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