Question

A company is considering the purchase of a machine costing $800,000 and requiring an additional $40,000 outlay for shipping and installation.

The machine will require an initial investment in additional net working capital of $15,000. The machine will be used for 5 years, and then sold for an expected $200,000. Annually, the machine is expected to boost the company’s revenue by $195,000 but it will require operating costs (not including depreciation) of $20,000 annually. If purchased, the machine is to be fully depreciated straight line over an 8-year schedule. The firm faces a tax rate of 20%.

The company’s debt consists of bonds paying interest semiannually, that have 10 years left until maturity. These have a book value of $2m, and a coupon rate of 6%. They are currently trading for $900 per $1000 of face value.

The company’s perpetual preferred stock has a fixed dividend of $7.25 per share per year, and a per-share par of $100. The book value of preferred is $1m. Each share of preferred is trading at $88.

There are 180,000 shares of common stock outstanding for this company. Each share is currently trading for $60. Analysts expect the company to pay a dividend of $3.45 per share next year, and they expect that the company’s earnings and per share dividends will grow at a constant rate of 4% for the foreseeable future.

The risk-free rate is 2.5%, and the expected return on the market portfolio is 8%. The company’s equity beta is 1.15.

A survey of institutional investors suggests that they would require a premium of 3% over the company’s 10-year bond yield if investing in the company’s common stock.

Should the company invest in the new machine, assuming that it has the same level of risk as that for the company as a whole?

*This should be solved using an Excel workbook.

Answer 1

WACC = (weight of debt * cost of debt) + (weight of preferred stock * cost of preferred stock) + (weight of common stock * cost of common stock)

market value of debt = book value of bonds * (price per bond / face value per bond)

market value of preferred stock = book value of stock * (price per share / face value per share)

market value of common stock = shares outstanding * market price per share

weight of debt = market value of debt / total market value

weight of preferred stock = market value of preferred stock / total market value

weight of common stock = market value of common stock / total market value

YTM is calculated using RATE function in Excel with these inputs :

nper = 10*2 (10 years to maturity with 2 semiannual coupon payments each year)

pmt = 1000 * 6% / 2 (semiannual coupon payment = face value * annual coupon rate / 2. This is a positive figure as it is an inflow to the bondholder)

pv = -900 (current bond price. This is a negative figure as it is an outflow to the buyer of the bond)

fv = 1000 (face value of the bond receivable on maturity. This is a positive figure as it is an inflow to the bondholder)

The RATE calculated is the semiannual YTM. To calculate the annual YTM, we multiply by 2. Annual YTM is 7.44%

after-tax cost of debt = YTM * (1 - tax rate)

cost of preferred stock = dividend / price per share

cost of equity (CAPM) = risk free rate + (beta * (expected market return - risk free rate)

cost of equity (Gordon model) = (next year dividend / current share price) + constant growth rate

cost of equity (bond yield plus risk premium approach) = bond YTM + risk premium

cost of equity = average of three methods

total cost of machine = purchase cost + installation cost

Operating cash flow (OCF) each year = income after tax + depreciation

In year 5, the entire working capital investment is recovered.

loss on sale of equipment at end of year 5 = book value - sale price

book value = original cost - accumulated depreciation

after-tax salvage value = salvage value + tax benefit on loss on sale of equipment (the loss is tax deductible, and hence reduces the tax outgo. This is treated as a cash inflow)

NPV is calculated using NPV function in Excel

NPV is -$50,928

No, the company should not invest in the machine because the NPV is negative.