October 28

# October 28 - • Replacement Chain • Repeat projects...

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Unformatted text preview: • Replacement Chain • Repeat projects until they begin and end at the same time. • Compute NPV for the “repeated projects.” • The Equivalent Annual Cost Method Mom's Cookies Inc. is considering the purchase of a new cookie oven. The original cost of the old oven was \$30,000; it is now 5 years old, and it has a current market value of \$13,333.33. The old oven is being depreciated over a 10­year life towards a zero estimated salvage value on a straight line basis, resulting in a current book value of \$15,000 and an annual depreciation expense of \$3,000. The old oven can be used for 6 more years but has no market value after its depreciable life is over. Management is contemplating the purchase of a new oven whose cost is \$25,000 and whose estimated salvage value is zero. Expected before­tax cash savings from the new oven are \$4,000 a year over its full MACRS depreciable life. Depreciation is computed using MACRS over a 5­year life, and the required rate of return is 10 percent. Assume a 40 percent tax rate. What is the net present value of the new oven? You have been asked by the president of your company to evaluate the proposed acquisition of a new special­purpose truck. The truck's basic price is \$50,000, and it will cost another \$10,000 to modify it for special use by your firm. The truck falls into the MACRS three­year class, and it will be sold after three years for \$20,000. Use of the truck will require an increase in net working capital (spare parts inventory) of \$2,000. The truck will have no effect on revenues, but it is expected to save the firm \$20,000 per year in before­tax operating costs, mainly labor. The firm's marginal tax rate is 40 percent. Equivalent Annual Cost (EAC) • Applicable to a much more robust set of circumstances than the replacement chain • The EAC is the value of the level payment annuity that has the same PV as our original set of cash flows. • For example, the EAC for the Cadillac air cleaner is \$750.98. • The EAC for the Cheapskate air cleaner is \$763.80, which confirms our earlier decision to reject it. • Consider an investment that costs \$100,000 and has a cash inflow of \$25,000 every year for 5 years. The required return is 9%, and payback cutoff is 4 years. • • • • • What is the payback period? What is the discounted payback period? What is the NPV? What is the IRR? Should we accept the project? • What method should be the primary decision rule? • When is the IRR rule unreliable? Break­Even Analysis • Common tool for analyzing the relationship between sales volume and profitability • There are three common break­even measures • Accounting break­even: sales volume at which net income = 0 • Cash break­even: sales volume at which operating cash flow = 0 • Financial break­even: sales volume at which net present value = 0 Dollar Return = Dividend + Change in Market Value Holding Period Returns • A famous set of studies dealing with rates of returns on common stocks, bonds, and Treasury bills was conducted by Roger Ibbotson and Rex Sinquefield. • They present year­by­year historical rates of return starting in 1926 for the following five important types of financial instruments in the United States: • • • • • Large­company Common Stocks Small­company Common Stocks Long­term Corporate Bonds Long­term U.S. Government Bonds U.S. Treasury Bills • The history of capital market returns can be summarized by describing the: • average return • the standard deviation of those returns • the frequency distribution of the returns Historical Returns, 1926­2004 • The Risk Premium is the added return (over and above the risk­free rate) resulting from bearing risk. • One of the most significant observations of stock market data is the long­run excess of stock return over the risk­free return. • The average excess return from large company common stocks for the period 1926 through 2005 was: 8.5% = 12.3% – 3.8% • The average excess return from small company common stocks for the period 1926 through 2005 was: 13.6% = 17.4% – 3.8% • The average excess return from long­term corporate bonds for the period 1926 through 2005 was: 2.4% = 6.2% – 3.8% • Suppose that The Wall Street Journal announced that the current rate for one­year Treasury bills is 5%. • What is the expected return on the market of small­company stocks? • Recall that the average excess return on small company common stocks for the period 1926 through 2005 was 13.6%. • Given a risk­free rate of 5%, we have an expected return on the market of small­company stocks of 18.6% = 13.6% + 5% • There is no universally agreed­ upon definition of risk. • The measures of risk that we discuss are variance and standard deviation. • The standard deviation is the standard statistical measure of the spread of a sample, and it will be the measure we use most of this time. • Its interpretation is facilitated by a discussion of the normal distribution. Normal Distribution • A large enough sample drawn from a normal distribution looks like a bell­shaped curve. The probability that a yearly return will fall within 20.2 percent of the mean of 12.3 percent will be approximately 2/3. • The 20.2% standard deviation we found for large stock returns from 1926 through 2005 can now be interpreted in the following way: if stock returns are approximately normally distributed, the probability that a yearly return will fall within 20.2 percent of the mean of 12.3% will be approximately 2/3. • Recall our earlier example: • Note that the geometric average is not the same as the arithmetic average: • To address the time relation in forecasting returns, use Blume’s formula: ...
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