Money, Banking, and International Finance ( PDFDrive )

Money, Banking, and International Finance

government or corporation could sell the bond for a greater market price, reducing the investor’s return. Higher market price means the bond issuer sold the bond for a premium.

A corporation, for example, has a $1,000 bond that pays interest twice a year. Interest rate on the bond is 8%, equaling $80 a year or $40 every six months. If the bond matures in two years, then the present value formula has 4 periods.

Market interest rate currently is 4% a year, or 2% for a payment period. If the market interest rate drops to 4%, the corporation would not sell this bond at face value because the corporation would pay a higher interest rate than the market. Consequently, the corporation can sell this bond for a greater price, reflecting the market interest rate. We calculate the bond market price in Equation 3, and it, PV0, equals $1,076.15. Therefore, a corporation pays 4% interest on bonds with an 8% interest coupon rate.

Market interest rate could swing in the opposite direction. Consequently, the corporations and governments could sell bonds at a discount if the market interest rate exceeds the bond’s interest rate. For example, a corporation sells a $1,000 bond that pays 8% interest rate that pays twice a year. Thus, the corporation pays $80 a year in interest, or $40 every six months. Furthermore, the bond matures in two years, or 4 periods in the present value formula. If the market interest rate rises to 12% a year (or 6% for a payment period), an investor would never buy this bond at face value. They would earn 8% interest year. However, the corporation could sell this bond for a lower price, compensating the investors for a greater market interest rate. We calculate the bond market price in Equation 4, and the bond’s market price, PV0, equals $930.70. Consequently, investors would earn a 12% return on their 8% interest bonds.

A government or corporation could issue a bond that never matures, which we call a consul or perpetuity. Consequently, the bond has no maturity date, but the bondholder receives interest payments forever. A government or corporation rarely issues these bonds because most people and government like end dates for loans. However, this bond possesses nice mathematical properties.

A government, for example, sold a consul that pays $50 interest per year, and the bond never matures. If the market interest rate equals 8%, then calculate the market price, PV0, of this consul. Since all interest payments are equal, subsequently, all future values, FV, are the same in the present value formula. Thus, the present value becomes an infinite series, which reduces to FV ÷ i. Consequently, we calculate the market price of this consul as $625 in Equation 5.

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YTM = 0.1411

As you can see, this calculation becomes very complicated. If you calculate the discount rate manually, then you must calculate the PV0 by selecting various discount rates, such as 0%, 5%, 10%, and 20%. Next, you insert your particular discount rate, r, into the Equation 7, and select the discount rate that has a present value, PV0 close to $1,600. Mathematicians wrote programs that can solve for the discount rate. If you visit the author’s website, www.kenszulczyk.com, he has a JavaScript program that can solve for the discount rate.

Yield to maturity generates two important rules on bonds, which are:

Market interest rate (or yield to maturity) and the market price (or present value) of the securities are inversely related. For example, if you examine the present value formula, the interest rate, or yield to maturity is located in the denominators of the fractions. Thus, the market price falls as the interest rate rises, and vice versa.

If a bond has a shorter maturity, subsequently, its price will fluctuate less for a change in the market interest rate. We show this by an example.

For example, we have two bonds with a face value of $5,000 and a coupon interest rate of 10%, paid annually. In our case, both bonds pay $500 once a year. First bond matures in one year while the other bond matures in 10 years. If the market interest rate rises to 16%, then the one-year bond has a market price of $4,741.38 while the 10-year bond has a market value of $3,550. Consequently, the interest rate change affected the 10-year bond more than the one-year bond. We calculated the market value of the one-year bond in Equation 8 and the ten-year bond in Equation 9. As this example illustrates, investors prefer money market securities because they fluctuate less when the interest rate changes.

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Money, Banking, and International Finance

An investor values his stock, P0, at time 0 that equals the discounted dividend he receives next year and the market price the investor receives if he sells the stock. Furthermore, if the investor is in the first time period, then the investor faces the same choice for Period 2 in Equation 13. Thus, we moved the time subscripts ahead by one period.

We obtain Equation 14 by substituting Equation 13 into Equation 12.

Then we build our sequence by examining an investor’s decision for Period 3, and substitute that equation into Equation 14 for variable P2. We continue to examine an investor’s future decision for each time period until we derive an infinite sequence in Equation 15.

If the corporation pays the same dividends, then D= D1 = D2 = , subsequently, the market price becomes a perpetuity, where we simplify a stock’s value to Equation 16.

As an illustration, you purchase stock as a long-term investment. Your annual rate of return is 5%, and you expect the corporation to pay $2 per share indefinitely. Consequently, you compute the market value of this stock of $40 per share in Equation 17.

If you want to know the market value of this stock for one year, then this becomes a trick question. Since you expect to earn the same dividend year after year, subsequently the market price is still $40.00. Thus, the investor does not experience any capital gains or losses.

Many investors want their dividends to grow over time, and Equation 16 can include a dividend growth rate. If the dividend grows at g percent per year, then we update the present

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per year. Compute the rate of return on this investment. We calculate a rate of return of 8% per year in Equation 23.

Some corporations, especially in high-tech industries, pay low dividends in the beginning. Subsequently, the corporation grows rapidly over time, and it begins paying higher dividends. We can modify the present value formula to handle this situation. Present value formula has two components:

Non-steady state – we use the present value to write out all cash flows, when the dividend growth rate is not constant. Non-steady state occurs for a new corporation.

Steady state – the corporation begins paying dividends over time that increase at a constant rate. This occurs after the corporation becomes mature. Consequently, we calculate the cash flows as a perpetuity.

As an illustration, we set the rate of return to 10%. A corporation pays a dividend of $6 at time 1. Corporation expects to increase the dividend by 2% for the first year, 4% for the second year, and 6% for year 3. After Year 3, the dividend grows at a constant rate of 6% per year. In this case, we solve for the dollar value of the dividend for each year with no fixed growth rate. We calculate the following:

Year 1: D1 = $6(1+0.02) = $6.12

Year 2: D2 = $6.12(1+0.04) = $6.3648

Year 3: D3 = $6.3648(1+0.06) = $6.746688

Third year becomes the perpetuity because the corporation begins increasing the dividend at a constant rate. For this example, we must observe the time subscripts. Remember, we calculate the stock price, P, one period before the dividend payment, D, in Equation 24.

Finally, we can calculate the market value of the stock share in the time period 0 by discounting the future cash flows of the stock in Equation 25.

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3.A T-bill has a face value of $20,000 with a yield to maturity of 3%, and this bill matures in 270 days. Calculate the market value of this T-bill.

4.If a consul pays $100 of interest every year and the market interest rate equals 6%, compute the market value of this consul.

5.A bond has a face value of $2,000, an interest rate of 10%,and pays interest twice a year. If the yield to maturity is 5% and the bond matures in three years, calculate the market value of this bond.

6.A bond has a face value of $2,000, an interest rate of 10% and pays interest twice a year. If the yield to maturity is 20% and the bond matures in three years, compute the market value of this bond.

7.Explain why money market securities make better investments than capital market securities.

8.If you expect the central bank to lower interest rates, define a good investment strategy.

9.You bought a discount bond for $4,500. If the bond matures in 3 years with a face value of $5,000, calculate your yield-to-maturity (YTM).

10.If a corporation expects to pay $1 dividend every year that grows 3% per year while the market interest rate is 4%, compute the market value of this stock.

11.A new internet company does not pay dividends for the first two years. However, in Year 3, the company will pay a $1 dividend that grows at 5% per year. Calculate the market price of this stock if the interest rate is 10%.

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8. Determining the Market Interest Rates

We explain in this chapter which factors determine interest rates by using the market forces of supply and demand for bonds. Furthermore, several factors shift the supply and demand functions, which alter the bond's market quantity, market price, and market interest rate. These shifts allow analysts and economists to predict changes in the interest rates and bond prices. Moreover, we use demand and supply functions to explain interest rate behavior during business cycles and recessions and explain the Fisher Effect. Finally, we introduce a loanable funds market for a small country. Then we expand the supply and demand for bonds to include a world’s real interest rate. Consequently, the world's interest rate either causes loanable funds to enter or leave a small country.

The Supply and Demand for Bonds

Interest rates have fluctuated substantially in the United States during the second half of the 20th century. For example, interest rates on 3-month T-bills were 1% in the early 1950s. Then, the interest rates on T-bills soared to over 15% in 1981 and subsequently, plummeted to below 6% in the mid-1980s and 1990s. Currently, T-bill rates have fallen below 1% after the 2008 Financial Crisis.

Everyone closely watches the interest rates. They determine whether consumers should save or buy, whether families should buy a house or purchase bonds. Furthermore, the interest rates influence business decisions to invest in new equipment or invest their money into financial securities. From Chapter 2, you have learned the major financial instruments. All these instruments represent credit market instruments. All these instruments are loans, where one party lends funds to another party except corporate stock. Stock conveys ownership in a corporation and is not a loan.

Companies and governments issue a variety of credit instrument with different maturities. Therefore, each credit instrument has an interest rate associated with it. Financial markets have hundreds of financial instruments, which create hundreds of interest rates. Good news is all interest rates usually move together. If one interest rate increases, then the other interest rates rise too. For our analysis, we assume a market has one interest rate.

Bond’s supply and demand determine the interest rate in the bond market, and a bond becomes the tradable commodity. Investors buy bonds while businesses and government supply bonds. Consequently, the intersection of supply and demand functions in the bond market determines the bond’s market price and quantity.

Demand function reflects the relationship between the quantity demanded and the market price of bonds, when we hold all other economic variables constant. We show a demand function in Figure 1. Demand function has a negative slope because as you move from point A to point B, the price of bonds becomes lower, so investors buy more bonds for a cheaper price. Just imagine bonds are similar to a product. For example, if the price of a soda becomes cheaper, then consumers buy more sodas. Please note as you move from point A to point B, the

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