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Unformatted text preview: ount that must be borrowed to fund this year’s consumption is: Amount to borrow = $100,000 – 80,000 = $20,000 Interest will be charged the amount borrowed, so the repayment of this loan next year will be: Loan repayment = $20,000(1.10) = $22,000 So, the consumption potential next year is the salary minus the loan repayment, or: Consumption potential = $90,000 – 22,000 = $68,000 2. The potential consumption for a saver next year is the salary during the year, plus the savings from the current year and the interest earned. The amount saved this year is: Amount saved = $50,000 – 35,000 = $15,000 The saver will earn interest over the year, so the value of the savings next year will be: Savings value in one year = $15,000(1.12) = $16,800 So, the consumption potential next year is the salary plus the value of the savings, or: Consumption potential = $60,000 + 16,800 = $76,800 3. Financial markets arise to facilitate borrowing and lending between individuals. By borrowing and lending, people can adjust their pattern of consumption over time to fit their particular preferences. This allows corporations to accept all positive NPV projects, regardless of the inter-temporal consumption preferences of the shareholders. 108 4. a. The present value of labor income is the total of the maximum current consumption. So, solving for the interest rate, we find: $86 = $40 + $50/(1 + R) R = .0870 or 8.70% b. The NPV of the investment is the difference between the new maximum current consumption minus the old maximum current consumption, or: NPV = $98 – 86 = $12 c. The total maximum current consumption amount must be the present value of the equal annual consumption amount. If C is the equal annual consumption amount, we find: $98 = C + C/(1 + R) $98 = C + C/(1.0870) C = $51.04 5. a. The market interest rate must be the increase in the maximum current consumption to the maximum consumption next year, which is: Market interest rate = $90,000/$80,000 – 1 = 0.1250 or 12.50% b. Harry will invest $10,000 in financial assets and $30,000 in productive assets today. c. NPV = –$30,000 + $56,250/1.125 NPV = $20,000 109 CHAPTER 5 NET PRESENT VALUE AND OTHER INVESTMENT RULES
Answers to Concepts Review and Critical Thinking Questions 1. Assuming conventional cash flows, a payback period less than the project’s life means that the NPV is positive for a zero discount rate, but nothing more definitive can be said. For discount rates greater than zero, the payback period will still be less than the project’s life, but the NPV may be positive, zero, or negative, depending on whether the discount rate is less than, equal to, or greater than the IRR. The discounted payback includes the effect of the relevant discount rate. If a project’s discounted payback period is less than the project’s life, it must be the case that NPV is positive. Assuming conventional cash flows, if a project has a positive NPV for a certain discount rate, then it will also have a positive NPV for a zero discount rate; thus, the payback period must be less than the project life. Since discounted payback is calculated at the same discount rate as is NPV, if NPV is positive, the discounted payback period must be less than the project’s life. If NPV is positive, then the present value of future cash inflows is greater than the initial investment cost; thus, PI must be greater than 1. If NPV is positive for a certain discount rate R, then it will be zero for some larger discount rate R*; thus, the IRR must be greater than the required return. a. Payback period is simply the accounting break-even point of a series of cash flows. To actually compute the payback period, it is assumed that any cash flow occurring during a given period is realized continuously throughout the period, and not at a single point in time. The payback is then the point in time for the series of cash flows when the initial cash outlays are fully recovered. Given some predetermined cutoff for the payback period, the decision rule is to accept projects that pay back before this cutoff, and reject projects that take longer to pay back. The worst problem associated with the payback period is that it ignores the time value of money. In addition, the selection of a hurdle point for the payback period is an arbitrary exercise that lacks any steadfast rule or method. The payback period is biased towards shortterm projects; it fully ignores any cash flows that occur after the cutoff point. The IRR is the discount rate that causes the NPV of a series of cash flows to be identically zero. IRR can thus be interpreted as a financial break-even rate of return; at the IRR discount rate, the net value of the project is zero. The acceptance and rejection criteria are: If C0 < 0 and all future cash flows are positive, accept the project if the internal rate of return is greater than or equal to the discount rate. If C0 < 0 and all future cash flows are positive, reject the project if the internal rate of return is less than the discount rate. If C0 > 0 and all future cash flows are negative, accept the project if th...
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