财务管理证券估价

股票估价 ，增长率的推导：假设你预期下一年Longs药店要支付每股0.56美元股利，并在年末股票按每股45.50美元交易。如果与郎石同等风险投资的期望回报率是6.80%，你今天会为郎石股票最多支付多少？在这个价格上你预期的股利收益率和资本利得率是多少？解答应用公式9.1，我们有 在这个价格下，郎石的股利收益率是。期望的每股资本利得是45.50美元43.13美元=2.37美元，资本利得率是2.37/43.13=5.50%。因此，在这个价格下郎石的期望总回报率是1.30%+5.50%=6.80%，这等于其权益资本成本。Consolidated Edison公司是一个管理公共事业的企业，服务于纽约市地区。假设公司计划在下一年支付每股2.3美元的股利。如果其权益资本成本是7%，并在未来每年股利期望增长2%，估计股票价值。解答如果股利每年期望按2%的比例永续地增长，股票的每股价格：Crane Sporting Goods预期来年每股收益是6美元。公司计划把所有的收益都作为股利支付。对于没有增长的预期，目前每股价格是60美元。假设在可预见的未来，公司可以削减其股利支付率到75%，并且用留存收益开设新商店。这些新商店的投资回报率预期是12%。假定其权益资本成本不变，新政策对股价有什么影响？现在假设新投资的回报率是8%而不是12%，又将如何？解答首先，让我们估计科云的权益资本成本。目前，科云计划支付等于其每股收益6美元的股利。给出的每股价格是60美元，科云的股利收益率是6美元/60美元=10%。没有预期增长（），我们可以运用公式9.7来估计：换句话说，在目前的政策下调整科云的股票价格，市场内具有同等风险的其他股票的期望回报率一定是10%。其次，我们考虑新政策下的结果。如果科云减少其股利支付率到75%，那么从公式9.8可知，下一年的股利将下降到。同时，因为公司现在要留存其收益的25%投资新商店，由公式9.12，其增长率将增加到假定科云可以按这个比率持续增长，我们可以计算在新政策下的每股价格，使用公式9.6的稳定股利增长模型：因此，如果科云削减股利来增加投资和增长，科云的每股价格将从60美元增加到64.29美元，意味着投资具有正的NPV。两阶段模型：持续价值：Small Fry公司正发明一种薯片，它的外表和口感都像油炸薯条。给出市场对这个产品的反应，公司把所有收益进行再投资以扩大经营。过去的一年收益是每股2美元，并且每年期望增长率是20%，直到第4年末。在那时，其他公司可能生产出竞争产品。分析师计划在第4年末，将削减投资并开始把60%的收益作为股利支付，其增长将放缓为长期增长率4%。如果权益资本成本是8%，今天的每股价值是多少？解答从第0年的2美元开始到第4年末，EPS每年增长20%，之后增长放缓为4%。股利支付率在第4年之前都是零，当竞争减少了其投资机会后公司的支付率上升到60%。用EPS乘以股利支付率，我们预计出未来股利，见第4行。从第4年往后，股利每年将按期望长期增长率4%增长。因此我们可以使用稳定股利增长模型来预计第3年末每股价格。给出其权益资本成本是8%，然后我们把这个最终价值代入，应用股利贴现模型（公式9.4）：注释：To be precise, by cash we are referring to the firms cash in excess of its working capital needs, which is the amount of cash it has invested at a competitive market interest rate.Solution:估价乘数：基于可比公司的估价We can compute a firms P/E ratio by using either trailing earnings (earnings over the prior 12 months) or forward earnings (expected earnings over the coming 12 months), with the resulting ratio called the trailing P/E or forward P/E, respectively.Valuations from multiples are based on the low, high, and average values of the comparable firms from table above.Red and blue regions show the variation between the lowest-multiple/ worst-case scenario and the highest-multiple/best-case scenario. KCPs actual share price of $26.75 is indicated by the gray line. 信息、竞争与股票价格 竞争与有效市场The idea that markets aggregate the information of many investors, and that this information is reflected in security prices, is a natural consequence of investor competition. If information were available that indicated that buying a stock had a positive NPV, investors with that information would choose to buy the stock; their attempts to purchase it would then drive up the stocks price. By a similar logic, investors with information that selling a stock had a positive NPV would sell it and the stocks price would fall.The idea that competition among investors works to eliminate all positive-NPV trading opportunities is referred to as the efficient markets hypothesis. It implies that securities will be fairly priced, based on their future cash flows, given all information that is available to investors.Public, Easily Interpretable Information.Private or Difficult-to-Interpret Information.Implications for Corporate Managers. If stocks are fairly valued according to the models we have described, then the value of the firm is determined by the cash flows that it can pay to its investors. This result has several key implications for corporate managers: Focus on NPV and free cash flow. A manager seeking to boost the price of her firms stock should make investments that increase the present value of the firms free cash flow. Thus the capital budgeting methods are fully consistent with the objective of maximizing the firms share price. Avoid accounting illusions.Many managers make the mistake of focusing on accounting earnings as opposed to free cash flows. With efficient markets, the accounting consequences of a decision do not directly affect the value of the firm and should not drive decision making. Use financial transactions to support investment.With efficient markets, the firm can sell its shares at a fair price to new investors. Thus, the firm should not be constrained fromraising capital to fund positive NPV investment opportunities.The efficient markets hypothesis is best expressed in terms of returns. It states that securities with equivalent risk should have the same expected return. The efficient markets hypothesis is therefore incomplete without a definition of “equivalent risk.” Furthermore, different investors may perceive risks and returns differently (based on their information and preferences). There is no reason to expect the efficient markets hypothesis to hold perfectly; it is best viewed as an idealized approximation for highly competitivemarkets. 债 券 估 价债券现金流、价格与收益相关概念：息票利率、面值等。zero-coupon bond, a bond that does not make coupon payments. The only cash payment the investor receives is the face value of the bond on the maturity date. Treasury bills（国库券）, which are U.S. government bonds with a maturity of up to one year, are zero-coupon bonds.The yield to maturity of a bond is the discount rate that sets the present value of the promised bond payments equal to the current market price of the bond.零息票债券在理解即期和远期利率时要频繁用到。Consequently, we will often refer to the yield to maturity of the appropriate maturity, zero-coupon risk-free bond as the risk-free interest rate. Some financial professionals also use the term spot interest rates （即期利率）to refer to these default-free, zero-coupon yields.息票债券：现金流时间线债券价格的动态变化：ProblemConsider a 30-year bond with a 10% coupon rate (annual payments) and a $100 face value. What is the initial price of this bond if it has a 5% yield to maturity? If the yield to maturity is unchanged, what will the price be immediately before and after the first coupon is paid?以30年期的零息票债券为例来探讨利率变化、时间变化与债券价格的关系：Yield to Maturity and Bond Price Fluctuations Over Time图像说明：The graphs illustrate changes in price and yield for a 30-year zero-coupon bond over its life. The top graph illustrates the changes in the bonds yield to maturity over its life. In the bottom graph, the actual bond price is shown in blue. Because the yield to maturity does not remain constant over the bonds life, the bonds price fluctuates as it converges to the face value over time. Also shown is the price if the yield to maturity remained fixed at 4%, 5%, or 6%.夏普投资学：债券的凸性债券价格与到期日之间的关系：图形略，溢价或折价均随着到期日的临近而加速减少。债券资产组合管理与免疫资产，债券的久期（夏普投资学）收益曲线与债券套利Using the Law of One Price, we show that given the spot interest rates, which are the yields of default-free zero-coupon bonds, we can determine the price and yield of any other default-free bond. As a result, the yield curve provides sufficient information to evaluate all such bonds.复制债券组合：By the Law of One Price, the three-year coupon bond must trade for a price of $1153. If the price of the coupon bond were higher, you could earn an arbitrage profit by selling the coupon bond（卖空息票债券） and buying the zero-coupon bond portfolio（购买零息票债券组合）. If the price of the coupon bond were lower, you could earn an arbitrage profit by buying the coupon bond and short selling the zero-coupon bonds.运用零息票债券收益率为息票债券估价解得：Because the coupon bond provides cash flows at different points in time, the yield to maturity of a coupon bond is a weighted average of the yields of the zero-coupon bonds of equal and shorter maturities. The weights depend (in a complex way) on the magnitude of the cash flows each period. In this example, the zero-coupon bonds yields were 3.5%, 4.0%, and 4.5%. For this coupon bond, most of the value in the present value calculation comes from the present value of the third cash flow because it includes the principal, so the yield is closest to the three-year, zero-coupon yield of 4.5%.例题：l 总结：根据前面的例题得知，具有相同期限、但息票利率不同的息票债券，其到期收益率YTM不同，换言之，同一期限的不同息票债券的到期收益率取决于它们各自的息票利率。息票债券的到期收益率是零息票债券到期收益率的加权平均。当息票利息增加，在计算净现值时，早期现金流比后期现金流相对更重要。如果即期到期收益率曲线向右上方倾斜（恰如上例所示），则随着息票利率的增加，早期现金流比后期现金流相对更重要，早期收益率的权重更大些，而早期收益率较小（向右上方倾斜），故加权平均的YTM将下降。反之则，或平坦的即期收益曲线则l 公司债券（存在违约或信用风险）Because the cash flows promised by the bond are the most that bondholders can hope to receive, the cash flows that a purchaser of a bond with credit risk expects to receive may be less than that amount. As a result, investors pay less for bonds with credit risk than they would for an otherwise identical default-free bond. Because the yield to maturity for a bond is calculated using the promised cash flows, the yield of bonds with credit risk will be higher than that of otherwise identical default-free bonds. 无违约风险情形确信违约，仅能支付90，收到的900无风险，故仍为0.04的利率，The 15.56% yield to maturity of Avants bond is much higher than the yield to maturity of the default-free Treasury bill. But this result does not mean that investors who buy the bond will earn a 15.56% return. Because Avant will default, the expected return of the bond equals its 4% cost of capital:Note that the yield to maturity of a defaultable bond is not equal to the expected return of investing in the bond. Because we calculate the yield to maturity using the promised cash flows rather than the expected cash flows, the yield will always be higher than the expected return of investing in the bond.l 违约风险The two examples were extreme cases, of course. In the first case, we assumed the probability of default was zero; in the second case, we assumed the company would definitely default. In reality, the chance that the company will default lies somewhere in between these two extremes (and for most firms, is probably much closer to zero).To illustrate, again consider the one-year, $1000, zero-coupon bond issued by Avant. This time, assume that the bond payoffs are uncertain. In particular, there is a 50% chance that the bond will repay its face value in full and a 50% chance that the bond will default and you will receive $900. Thus, on average, you will receive $950.Lets suppose investors demand a risk premium of 1.1% for this bond, so that the appropriate cost of capital is 5.1%. Then the present value of the bonds cash flow is:=10.63%债券的评级（Bond Ratings）投资级（标准普尔：AAA、AA、A、BBB）、投机级(标准普尔:BB、B、CCC、CC、C、D)根据前述分析，违约风险越高，则YTM越高。l 远期利率：A forward interest rate (or forward rate) is an interest rate that we can guarantee today for a loan or investment that will occur in the future. we will consideronly interest rate forward contracts for investments of one year. For example, when we refer to the forward rate for year 5, we mean the rate available today on a one-year investment that begins four years from today and is repaid five years from today.，对远期利率的解释：假定现在签定一个合约，规定资金在一年以后借出，两年后偿还，这样一个合约是一个远期合约。一年借期的利率在合约上规定（利息在两年后到期时必须偿付），这个利率就是远期利率。区分这个利率与从现在起一年以后通行的一年期借款利率（那时的即期利率）是很重要的。一个远期利率在现在签定的合约中规定，但与一段未来时期相联系。根据合约的特性，利率条件已经确定，但实际交割将在以后进行。换一个人，他可能愿意等待一年，在那时的即期市场签定借款合约，那时，利率条件可能变得好于、也可能坏于今天的远期利率，因为未来的即期利率不能被完全地预知。利率的期限结构：参见夏普的投资学上册第83页。无偏差预期理论、流动性偏好理论、市场分割理论利率期限结构的经验验证债券久期地计算及解释：参见夏普的投资学上册第319、320页如何构造免疫资产：参见夏普的投资学上册第323页。