Question

ACME manufacturing is considering replacing an existing production line with a new line that has a greater output capacity and operates with less labour than the existing line. The existing line, which was purchased several years ago, originally cost $500,000 and currently has a book value of $250,000.

The new line would cost $750,000 and would be depreciated on a straight-line basis over a useful life of 5 years. At the end of five years, the new line could be sold as scrap for $75,000. The existing unit is being depreciated at $50,000 per year and will be fully depreciated at the end of year 5. ACME can sell the existing unit today for $275,000. Assume ACME’s tax rate is 30%.

Because the new line is more automated, it would require fewer operators, operating costs (exclusive of depreciation) are expected to decrease by $20,000 per annum, and revenues are expected to increase by $100,000 per annum (due to increased additional sales). ACME estimates that in addition it will require an initial increase in net working capital of $40,000. At the end of year 5, this amount will be fully recovered.

ACME’s equity beta is 1.8 and its pre‐tax cost of debt is 7.14% per annum. The risk free rate is 6% per annum and the market return is 11% per annum. ACME’s debt to equity ratio is 1.

Required:

a) Calculate the company’s weighted average cost of capital. 


b) What is the NPV of the new production line? Advise whether the company should replace the existing line or not?

Answer 1

Answer 1: The values provided in the question for WACC (weighted average cost of capital) are as follows:

1. Market value of equity = $ 275,000 (existing unit current selling price).
2. Market Value of debt = $ 40,000 (working capital Cost)
3. Total Value of financing = $ 890,000 {current price of new line ($ 750,000) + additional operating cost ($ 20,000) + working capital cost ($ 40,000)}
4. Cost of equity = $ 750,000 (current price of new machine)
5. Cost of debt = $ 750,000 (it is equivalent to cost of equity because debt to equity ratio = 1)
6. Tax Rate = 30%

The formula for calculating WACC is as follows:

WACC = Market Value of Equity Total Value of Financing * Cost of Equity) Market Value of Debt + Total Value of Financing * Cost of Debt (1 - Tax Rate)

Using the values provided in the question,

WACC = $ 275,000 $ 890,000 $ 40,000 +$ 890,000 * $ 750,00 $ 750,000 + (1 - 30%)

WACC = $ 255,337.08

Answer 2: The values provided in the question for NPV (Net Present Value) are as follows:

1. Total Cash inflows = $ 360,000 { expected revenue to increase per annum is $ 100,000 – operating cost per annum is $ 20,000 – working capital cost per annum is $ 8,000 ($ 40,000/5) = $ 72,000} * (life of new line = 5).
2. Discount rate (risk free rate) = 6%
3. Time Period (life of new line) = 5

The formula for calculating NPV is as follows:

[Total cash flows NPV = (1 + R)

Using the values provided in the question,

NPV = $360,000 (1 + 6% 5

NPV = $ 76,595.74

ACME should replace existing line because NPV is coming positive with a value of $ 76,595.75 plus it would save an additional $ 19,662.92 (Current market price of existing line = $ 275,000 less WACC of new line = $ 255,337.08)