• 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.
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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:
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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: