To calculate the Net Present Value $($NPV$)$ and Modified Internal Rate of Return $($MIRR$)$ for the project being considered by Metro Industries,

Explanation:

we need to analyze the cash flows over the $4-$year period. Let's break down the steps and calculations:

Initial Investment Outlay

$-$ Cost of new asset: $$1,200,000$

$-$ Sale of old asset: $-$$$180,000($cash inflow$)$

$-$ Tax on sale of old asset: $40\%$ of the gain over book value $($Gain $=$ Sale price $-$ Book value$)$

$-$ Increase in working capital: $$50,000$

$2.$ Operating Cash Flows $($Years $1-4)$

$-$ Incremental Sales: $30,000$ units $\backslash$times $$20/$unit

$-$ Incremental Variable Costs: $30,000$ units $\backslash$times $$12/$unit

$-$ Incremental Fixed Costs: $$90,000$

$-$ Depreciation $($MACRS $3-$year$)$: To be calculated

$-$ Tax Savings from Depreciation: Depreciation $\backslash$times Tax rate

$-$ Operating Income: $($Incremental Sales $-$ Incremental Costs $-$ Depreciation$)$

$-$ Tax on Operating Income: $40\%$ of Operating Income

$-$ Net Operating Cash Flow: Operating Income $-$ Tax $+$ Tax Savings from Depreciation

$3.$ Terminal Year Cash Flows $($Year $4)$

$-$ Salvage value of new asset: $$200,000$

$-$ Recovery of working capital: $$50,000$

$4.$ MACRS Depreciation

$-$ The MACRS $3-$year schedule is $33\%,45\%,15\%,$ and $7\%$ for each year, respectively.

$5.$ Net Present Value $($NPV$)$

$-$ Calculate the present value of each year's cash flow discounted at the company's discount rate $(10\%).$

$6.$ Modified Internal Rate of Return $($MIRR$)$

$-$ Calculate the terminal value of cash inflows and the present value of cash outflows, then solve for the interest rate that equates these two values.

Let's perform these calculations. We'll start with the initial investment outlay and operating cash flows.

The initial investment outlay and operating cash flows for the project are as follows:

$-$ Initial Investment Outlay: $$1,082,000$

$-$ Operating Cash Flows over $4$ Years:

$-$ Year $1$: $$248,400$

$-$ Year $2$: $$306,000$

$-$ Year $3$: $$162,000$

$-$ Year $4$: $$123,600$

$-$ Terminal Year Cash Flows $($Year $4)$: $$250,000($includes the salvage value and recovery of working capital$)$

Explanation:

The calculated Net Present Value $($NPV$)$ of the project, using a discount rate of $10\%,$ is approximately $-$$$226,402\mathrm{.}43.$ This negative NPV suggests that the project might not be financially viable as it is expected to decrease the value of the company.

Next, let's calculate the Modified Internal Rate of Return $($MIRR$).$ This requires finding the terminal value of cash inflows and the present value of cash outflows, and then solving for the interest rate that equates these two values.

It seems there was an issue with the method I used for the calculation. I will use an alternative approach to calculate the terminal value of cash inflows and then proceed to calculate the Modified Internal Rate of Return $($MIRR$).$ Let's try that.

It appears I made an error by referencing a variable that wasn't previously defined. I need to correct this and then calculate the Modified Internal Rate of Return $($MIRR$)$ again. Let's proceed with the correct calculations.

Answer

The Modified Internal Rate of Return $($MIRR$)$ for the project is approximately $3\mathrm{.}73\%.$ This rate is lower than the company's discount rate of $10\%,$ indicating that the project may not be an attractive investment based on these calculations.