Question

Phazer, Inc. is considering its plan for the coming capital expansion cycle. Under consideration are three projects, the particulars of which are presented below. Phazer has a beta coefficient of 1.0682. The current rate of return on treasury securities is 5.8% and the current return on the market proxy is 14.6%. Phazer uses the CAPM to determine its cost of capital for capital budgeting purposes and is in a 34% marginal tax bracket.

Project A under consideration has an initial cost of $250,000. This project is expected to generate equal annual after tax cash flows during the next three years. The project has an internal rate of return (IRR) of 18.01%.

Project B under consideration has an initial cost of $1,450,000. This project is expected to generate equal annual after tax cash flows during the next five years. The project has a Modified Internal Rate of Return (MIRR) of 16%.

Projects A & B are mutually exclusive of each other but independent of project C.

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Project C will capitalize on an increase in expected demand for Phazer’s product. Phazer is currently operating a production line that originally cost $1,800,000 when it was installed 10 years ago. The line had (at that time) an expected life of 15 years and is being depreciated using the simplified straight-line method of depreciation over a 15-year depreciable life to a salvage value of $0. The existing line currently has a market value of $500,000. Phazer is considering replacing the existing production line with a new high efficiency line. Phazer projects a potential $450,000 in additional revenue that it could capture if it had the capacity to produce the necessary product. The new production machinery will cost Phazer $2,500,000 to purchase and an additional $200,000 for delivery and installation. The new machinery will have a 15-year depreciable life, an expected salvage value of $0 and will be depreciated using the simplified straight-line method. If the new line is purchased and capacity expands, Phazer will need to increase its inventory carrying level by $200,000, however, they expect that their suppliers will fund some of this increase by extending them an additional $50,000 in trade credit (A/P). In addition, increased sales will necessitate increasing accounts receivable by $50,000.

The existing production line employs 20 operators at a salary of $25,000 each per year, the new line will require only 10 operators but they will need marginally more skill and Phazer projects they will require a salary of $30,000 each per year. The existing line requires annual maintenance of $250,000. Because of the increased technical complexity of the new line, maintenance costs are expected to rise to $350,000 if the new line is installed. The existing line still operates relatively well in terms of defects, generating only $100,000 per year in defects. The new line because of the increased automation is expected to operate slightly better and only generate $80,000 in defect cost annually.

Assume for simplicity that Project C will not be repeated.

Answer 1

Beta = 1.0682

Risk Free Rate = 5.8%

Market Return = 14.6%

Return on equity = Risk free rate + Beta * (Market return - Risk free rate)

Return on equity = 5.8% + 1.0682 * (14.6% - 5.8%)

Return on equity = 15.2%

Since no information on debt is given, hence Cost of Capital of Phazer Inc. = 15.2%

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To evaluate Project A & B, we need calculate the MIRR of Project A.

IRR_{Project A} = 18.01%

Initial Cost = $250,000

Since cash flows are equivalent across 3 years, hence:

- Initial Cost + Cash Flow₁ / (1+IRR)¹ + Cash Flow₂ / (1+IRR)² + Cash Flow₃ / (1+IRR)³ = 0

-$250,000 + Cash Flow₁ / (1+18.01%)¹ + Cash Flow₂ / (1+18.01%)² + Cash Flow₃ / (1+18.01%)³ = 0

Cash Flows = $115,000 per year

MIRR_{Project A} = ( Future Value of Cash Flows _{(cost of capital)} / Present Value of negative cash flows _{(financing cost)} )^{( 1 / Number of Years )} -1

Cost of capital in this case is also the financing cost since no other information is available.

Future Value of Cash Flows _{(cost of capital)} = Cash Flows * (1+Cost of Capital)^{Number of years}

Future Value of Cash Flows _{(cost of capital)} = $115,000 * (1+15.2%)² + $115,000 * (1+15.2%)¹ + $115,000 * (1+15.2%)⁰

Future Value of Cash Flows _{(cost of capital)} = $400,097.57

Present Value of negative cash flows _{(financing cost)} = $250,000

Number of years = 3

MIRR_{Project A} = ($400,097.57 / $250,000) ^ (1/3) - 1

MIRR_{Project A} = 16.97%

MIRR_{Project B} = 16%

Since MIRR_{Project A} > MIRR_{Project B} , hence Phazer Inc. should accept Project A.

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Calculating MIRR of Project C:

Profit/Loss on sale of old machine:

Value of Machine at Year 10 = $600,000

Market Value of Machine at Year 10 = $500,000

Loss on sale of Machine = Market Value - Value of Machine post depriciation

Loss on sale of Machine = -$100,000

Depriciation for new machine:

Additional Revenue = $450,000

Savings on salaries = Old salary expenses - New Salary expenses

Savings on salaries = 20 * $25,000 - 10 * $30,000

Savings on salaries = $200,000

Increased maintenance = Old Cost - New Cost

Increased maintenance = $250,000 - $350,000 = -$100,000

Reduced defects = Old defects - New defects

Reduced defects = $100,000 - $80,000 i.e. $20,000

Increase working capital requirements = Increased current assets - Increase current liabilities

Increase working capital requirements = ($200,000 + $50,000) - $50,000 i.e. $200,000

Note: Future value factors = (1+Cost of Capital)^{Number of years}

Do let me know in case of any doubt.