No Free Lunch: Economics for a Fallen World: Third Edition, Revised

Chapter Sixteen: Valuing the Future - Concepts in Capital & Finance 411 APPLICATION OF FINANCE: OTHER EXAMPLES While the basic formula of finance is found in equation 4 earlier, there are many ways you may see financial problems presented in the world; we’ll review several types below. This section is intended to be more of a “how to” rather than a more conceptual development, so our discussion will be abbreviated. COMPARISON OF TWO DIFFERENT INVESTMENT OPPORTUNITIES WITHIN A FIRM Let’s say a firm has two possible independent investments, each with a series of cash flows. Investment A will cost the firm $25,000 for initial activation (fixed cost), and cost $2,000 annually (variable cost) for the life of the investment (four years of CFs) beginning at the end of year one, and will yield $10,000 per year. Assume that the fixed cost initial capital has no value at the end of the project. Investment B will not require any additional fixed investment, but will cost the firm $15,000 per year for four years beginning at project approval, and yield four cash flows of $22,000 per year beginning at the end of the 1st year until the project is completed at the end of year four. Each project faces an interest rate of 8% and is considered of equal risk. Should either of these projects be done? If only one can be initiated, which offers the most value to the firm? As seen in Figure 16.6 , the net present value of investment A’s cash flows is slightly positive. Pursuit of this investment will add value to the firm. If no other investment opportunities were available, this project should be pursued. If capital is limited (and capital is almost always limited at some point) for a firm, the increase in present value must be compared to other alternatives, such as investment B, as in Figure 16.7 . Investment B contributes far more to the firm’s worth than investment A; ideally a firm would be able to do both, but if choosing between the two, investment B is significantly more profitable. Figure 16.6, Present discounted value investment A. Each year’s net CF must be discounted back to present value. No discount is applied to the initial $25,000 investment, since it is made upon project initiation. Each subsequent year’s CFs are summed ($8,000) and discounted fot the number of periods. In this case, the project adds some value to the firm. -25,000.00 -2,000 -2,000 -2,000 -2,000 10,000 10,000 10,000 10,000 0 1 2 3 4 8% -25,000 5,880.24 1,497.02 = PV 6,350.66 6,858.71 7,407.41 Figure 16.7, Present discounted value investment B. Each year’s net CFs must be discounted back to present value. No discount is applied to the initial $15,000 investment, since it is made upon project initiation. Each subsequent year’s CFs are summed and discounted for the appropriate number of periods. In this case, the project adds significantly more value to the firm than investment A. -15,000.00 -15,000 -15,000 -15,000 23,000 23,000 23,000 23,000 0 1 2 3 4 8% -15,000 16,905.68 22,522.47 = PV 6,350.66 6,858.71 7,407.41