Chapter 5-7 Flashcards
If you invest money at a given interest rate, what will be the future value of your investment?
An investment of $1 earning an interest rate of r will increase in value each period by the factor (1 + r). After t periods its value will grow to $(1 + r)t. This is the future value of the $1 investment with compound interest.
What is the present value of a cash flow to be received the future?
The present value of a future cash payment is the amount that you would need to invest today to produce that future payment. To calculate present value, we divide the cash pay- ment by (1 + r)t or, equivalently, multiply by the discount factor 1/(1 + r)t. The discount factor measures the value today of $1 received in period t.
How can we calculate present and future values of streams of cash payments?
A level stream of cash payments that continues indefinitely is known as a perpetuity; one that continues for a limited number of years is called an annuity. The present value of a stream of cash flows is simply the sum of the present value of each individual cash flow. Similarly, the future value of an annuity is the sum of the future value of each individual cash flow. Shortcut formulas make the calculations for perpetuities and annuities easy.
How should we compare interest rates quoted over different time intervals, for example, monthly versus annual rates?
Interest rates for short time periods are often quoted as annual rates by multiplying the per- period rate by the number of periods in a year. These annual percentage rates (APRs) do not recognize the effect of compound interest; that is, they annualize assuming simple interest. The effective annual rate annualizes using compound interest. It equals the rate of interest per period compounded for the number of periods in a year.
What is the difference between real and nominal cash flows and between real and nominal interest rates?
A dollar is a dollar, but the amount of goods that a dollar can buy is eroded by inflation. If prices double, the real value of a dollar halves. Financial managers and economists often find it helpful to reexpress future cash flows in terms of real dollars—that is, dollars of constant purchasing power.
Be careful to distinguish the nominal interest rate and the real interest rate—that is, the rate at which the real value of the investment grows. Discount nominal cash flows (that is, cash flows measured in current dollars) at nominal interest rates. Discount real cash flows (cash flows measured in constant dollars) at real interest rates. Never mix and match nomi- nal and real.
What are the differences between the bond’s coupon rate, current yield, and yield to maturity?
A bond is a long-term debt of a government or corporation. When you own a bond, you receive a fixed interest payment each year until the bond matures. This payment is known as the coupon. The coupon rate is the annual coupon payment expressed as a fraction of the bond’s face value. At maturity the bond’s face value is repaid. In the United States most bonds have a face value of $1,000. The current yield is the annual coupon payment expressed as a percentage of the bond price. The yield to maturity measures the rate of return to an investor who purchases the bond and holds it until maturity, accounting for coupon income as well as the difference between purchase price and face value.
How can one find the market price of a bond given its yield to maturity or find a bond’s yield given its price? Why do prices and yields vary inversely?
Bonds are valued by discounting the coupon payments and the final repayment by the yield to maturity on comparable bonds. The bond payments discounted at the bond’s yield to maturity equal the bond price. You may also start with the bond price and ask what interest rate the bond offers. The interest rate that equates the present value of bond payments to the bond price is the yield to maturity. Because present values are lower when discount rates are higher, price and yield to maturity vary inversely.
Why do bonds exhibit interest rate risk?
Bond prices are subject to interest rate risk, rising when market interest rates fall and falling when market rates rise. Long-term bonds exhibit greater interest rate risk than short-term bonds.
What is the yield curve and why do investors pay attention to it?
The yield curve plots the relationship between bond yields and maturity. Yields on long-term bonds are usually higher than those on short-term bonds. These higher yields compensate holders for the fact that prices of long-term bonds are more sensitive to changes in interest rates. Investors may also be prepared to accept a lower interest rate on short-term bonds when they expect interest rates to rise.
Why do investors pay attention to bond ratings and demand a higher interest rate for bonds with low ratings?
Investors demand higher promised yields if there is a high probability that the borrower will run into trouble and default. Credit risk implies that the promised yield to maturity on the bond is higher than the expected yield. The additional yield investors require for bearing credit risk is called the default premium. Bond ratings measure the bond’s credit risk.
What information is included in stock trading reports, and how can stock-price information about other firms be used to help you value a particular firm?
Large companies usually arrange for their stocks to be traded on a stock exchange. The stock listings report the stock’s price, price change, volume, dividend yield, and price-earnings (P/E) ratio.
To value a stock financial analysts often start by identifying similar firms and looking at how much investors in these companies are prepared to pay for each dollar of earnings or book assets.
How can one calculate the present value of a stock given forecasts of future dividends and future stock price, and how do a company’s growth opportunities show up in its stock price and price- earnings ratio?
Stockholders generally expect to receive (1) cash dividends and (2) capital gains or losses. The rate of return that they expect over the next year is defined as the expected dividend per share DIV1 plus the expected increase in price P1 − P0, all divided by the price at the start of the year P0.
Unlike the fixed interest payments that the firm promises to bondholders, the dividends that are paid to stockholders depend on the fortunes of the firm. That’s why a company’s common stock is riskier than its debt. The return that investors expect on any one stock is also the return that they demand on all stocks subject to the same degree of risk.
The present value of a share is equal to the stream of expected dividends per share up to some horizon date plus the expected price at this date, all discounted at the return that investors require. If the horizon date is far away, we simply say that stock price equals the present value of all future dividends per share. This is the dividend discount model.
If forecast dividends grow at a constant rate, g, then the value of a stock is P0 = DIV1/ (r − g). This is the constant-growth dividend discount model. Sometimes, it is feasible to discount forecasted dividends for the next few years and then to discount the expected price at the end of this period. The expected price is often estimated using the constant- growth model.
You can think of a share’s value as the sum of two parts—the value of the assets in place and the present value of growth opportunities, that is, of future opportunities for the firm to invest in high-return projects. The price-earnings (P/E) ratio reflects the market’s assess- ment of the firm’s growth opportunities.
How can these stock valuation formulas be used to infer the value of an entire business?
Similar valuation methods can be used to estimate the value of an entire business. In this case, you need to forecast and discount the free cash flows provided by the business. These are the cash flows that are not plowed back into the business but can be used to pay dividends or repurchase stock.
How does competition among investors lead to efficient markets?
Competition between investors will tend to produce an efficient market—that is, a market in which prices rapidly reflect new information and investors have difficulty making consistently superior returns. Of course, we all hope to beat the market, but if the market is efficient, all we can rationally expect is a return that is sufficient on average to compensate for the time value of money and for the risks we bear.
The evidence for market efficiency is voluminous, and there is little doubt that skilled professional investors find it difficult to win consistently. Nevertheless, there remain some puzzling instances where markets do not seem to be efficient. Some financial economists attribute these apparent anomalies to behavioral foibles.
