Expected cash flows

Discounted Ca.sh Flows. Because the flows below the cash flow box in Figure 1 tend to be arbitrary management decisions that are generally difficult to predict, the prediction of profitabiUty is based on the expected cash flows instead of earnings. As a result, some logical assumptions to account for the cost of capital and the recovery of the investment must be made. 

Despite the fact that project B s expected cash flow is riskier than that of project A, that risk is largely diversifiable, because it is unique to the project and depends only on the Medicare coverage decision which, we can assume, is unaffected by the state of the economy. Project A s risk, on the other hand, may reflect undiversifiable, or systematic, risk because demand for analgesics may vary with the state of the economy. Although the total risk of project B is much... 

How does the cost of capital affect decisions to invest in R D projects To assess whether the investment is worth its 10 million R D cost, company managers (on behalf of their investors) would compute the net present value (NPV) of the investment by converting all future expected cash flows (both into and out of the firm) into their present value at the time the investment decision is made using the cost of capital appropriate to the project as the discount rate." The algebraic sum of the present values of all the expected cash flows is the NPV of the investment. If the NPV is greater than zero, the investment is worth it and will compensate investors at a rate of return that exceeds the cost of capital. 

Considering the example shown in Table A1 of a hypothetical bond with coupons and principal linked to the inflation. We assume a 5-year inflation-linked bond with a 2% annual coupon payment. The expected cash flows, coupons and principal, are discounted with a discount rate of 3%. The valuation is performed by the following steps. 

The option-adjusted spread (OAS) is the most important measure of risk for bonds with embedded options. It is the average spread required over the yield curve in order to take into account the embedded option element. This is, therefore, the difference between the yield of a bond with embedded option and a government benchmark bond. The spread incorporates the future views of interest rates and it can be determined with an iterative procedure in which the market price obtained by the pricing model is equal to expected cash flow payments (coupons and principal). Also a Monte Carlo simulation may be implemented in order to generate an interest rate path. Note that the option-adjusted spread is influenced by the parameters implemented into the valuation model as the yield curve, but above all by the volatility level assumed. This is referred to volatility dependent. The higher the volatility, the lower the option-adjusted spread for a callable bond and the higher for a putable bond. 

To calculate the value of these bonds, it is preferable to use the binomial tree model. The value of a straight bond is determined as the present values of expected cash flows in terms of coupon payments and principal repayment. For bonds with embedded options, since the main variable that drives their values is the interest rate, the binomial tree is the most suitable pricing model. 

The approaches to shareholder value include all aspects of corporate governance that aim at the shareholder s property. The value of the corporation can be computed as its expected cash flows discounted with its... 

Cash flow is simply the cash that is expected to be received in the future from owning a financial asset. For a fixed-income security, it does not matter whether the cash flow is interest income or repayment of principal. A security s cash flows represent the sum of each period s expected cash flow. Even if we disregard default, the cash flows for some fixed-income securities are simple to forecast accurately. Noncallable benchmark government securities possess this feature since they have known cash flows. For benchmark government securities, the cash flows consist of the coupon interest payments every year up to and including the maturity date and the principal repayment at the maturity date. 

For securities that fall into the first category, a key factor determining whether the owner of the option (either the issuer of the security or the investor) will exercise the option to alter the security s cash flows is the level of interest rates in the future relative to the security s coupon rate. In order to estimate the cash flows for these types of securities, we must determine how the size and timing of their expected cash flows will change in the future. For example, when estimating the future cash flows of a callable bond, we must account for the fact that when interest... 

Once the expected (estimated) cash flows and the appropriate interest rate or interest rates that should be used to discount the cash flows are determined, the final step in the valuation process is to value the cash flows. The present value of an expected cash flow to be received t years from now using a discount rate / is... 

The value of a financial asset is then the sum of the present value of all the expected cash flows. Specifically, assuming that there are N expected cash flows ... 

The procedure for calculating the yield to call is the same as that for the yield to maturity determine the interest rate that will make the present value of the expected cash flows equal to the market price plus accrued interest. The expected cash flows are the coupon payments to a particular call date in the future and the call price. 

There are valuation models that can be used to value bonds with embedded options. These models take into account how changes in yield will affect the expected cash flows. Thus, when V and V+ are the values produced from these valuation models, the resulting duration takes into account both the discounting at different interest rates and how the expected cash flows may change. When duration is calculated in this manner, it is referred to as effective duration or option-adjusted duration or OAS duration. Below we explain how effective duration is calculated based on the lattice model and the Monte Carlo model. 

The prices used in equation (4.4) to calculate convexity can be obtained by either assuming that when the yield changes the expected cash flows either do not change or they do change. In the former case, the resulting convexity is referred to as modified convexity. (Actually, in the industry, convexity is not qualified by the adjective modified. ) In contrast, effective convexity assumes that the cash flows do change when yields change. This is the same distinction made for duration. 

RiskMetrics Group CDOManager is designed to analyze cash and synthetic CDO structures. It helps assess the risk associated with a CDO and calculate prices. CDOManager produces expected cash flow from the assets and feeds them into a waterfall to determine the cash flow to the notes. Exhibit 22.16 provides a screenshot from CDOManager. 

As explained in chapter 1, yield is conventionally defined as the rate at which a bond s expected cash flows must be discounted so that the sum of their present values will equal the bond s clean price— that is, the price excluding any accrued interest. This is known as the bond s redemption... 

The OAS-derived yield spread is based on the present values of expected cash flows discounted using government bond—derived forward rates. The spread berween the cash flow yield and the government bond yield is based on yields to maturity. The OAS spread is added to the entire yield curve, whereas a yield spread is over a single point on the government bond yield curve. For these reasons, the two spreads are not strictly comparable. 

The modified duration of a bond measures its price sensitivity to a change in yield. It is essentially a snapshot of one point in time. It assumes that no change in expected cash flows will result from a change in market interest rates and is thus inappropriate as a measure of the interest rate risk borne by a mortgage-backed bond, whose cash flows are affected by rate changes because of the prepayment effect. 

Effective duration is essentially approximate duration where P and P are obtained using a valuation model—such as a static cash flow model, a binomial model, or a simulation model—that incorporates the eflFect of a change in interest rates on the expected cash flows. The values of P and T, depend on the assumed prepayment rate. Generally analysts assume a higher prepayment rate when the interest rate is at the lower level of the two rates—interest and prepayment. 

The first step in calculating the E[NPV] in our example is to estimate (predict) the health effects of implementing the cable system, and then as the second step to determine the effect on the expected cash flows. The perspective taken is the society s viewpoint. The estimated cost of implementing the cable system in all Norwegian schools is about 150 million. 

Starting at period T, work back to Period 0, identifying the optimal decision and the expected cash flows at each step. Expected cash flows at each state in a given period should be discounted back when included in the previous period. 

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