Question

You are contemplating the purchase of a new $1,840,000 computer-based dairy cow feeding system. The system will be depreciated straight-line over its ten-year life and have no value at the end of its life. You will earn $250,000 before taxes in the first year from additional milk production and expect an annual growth rate of 4%. Your tax rate is 25%, equity cost 10%, and debt cost 7%. Currently, your farm's debt to asset ratio is 0.25 and you would like to keep the same financial ratio.

Compute the following for this project using after-tax cash flows: 1) payback period, 2) NPV, and 3) internal rate of return. Please also list the cash flows for each year.

Answer 1

First let us find the Weighted Average Cost of Capital (WACC) for this project.

Debt to asset ratio is 0.25, that is 25% of the assets is financed by debt.

Cost of equity is given as 10% and cost of debt is given as 7%. So we need to find after tax cost of debt.

Which is = Interest (1-tax rate)

= 7(1-0.25) = 5.25%

Now to find WACC we have a formula:

WACC = (Cost of debt * Percentage of debt) + (Cost of equity * Percentage of Equity)

= (5.25% * 25%) + (10% * 75%)

= 8.81%

We will use this WACC as the required rate of return to find the NPV of this project.

1) Payback Period:

From the above table we can see the cumulative cash flows. But we need to ignore the negative sign.

2) NPV:

NPV is nothing but the sum of discounted cash flows during the life of the project minus the initial cash outflow.

NPV =  $1,890,459.30 -  $1,840,000.00

= 50,459.30

Since the NPV is above '0' we can accept the project. NPV is above '0' means it is giving over and above the required rate of return.

3) Internal Rate of Return (IRR):

IRR is a rate of return at which NPV becomes '0'.

For this project IRR comes to 9.39%

Excel formula is given below.