# Interest rates, risk-free rate, expectation, liquidity, 1 year treasury bond,

1. The interest rate on 1-year Treasury securities is 5 percent. The interest rate on 2-year Treasury securities is 6 percent. The expectations theory is assumed to be correct. If the real risk-free rate is assumed to be 3% every year, what is the inflation expected in year-2?

2. The real risk-free rate of interest is 3 percent. Inflation is expected to be 4 percent this coming year, jump to 5 percent next year, and increase to 6 percent the year 3. According to the expectations theory, what should be the interest rate on 3-year, risk-free securities today?

3. Assume that the expectations theory holds, and that liquidity and maturity risk premiums are zero. If the annual rate of interest on a 2-year Treasury bond is 10.5 percent and the rate on a 1-year Treasury bond is 12 percent, what rate of interest should you expect on a 1-year Treasury bond one year from now?

4. The real risk-free rate is expected to remain constant at 3 percent. Inflation is expected to be 2 percent a year for the next 3 years, and then 4 percent a year thereafter. The maturity risk premium is 0.1%(t - 1), where t equals the maturity of the bond. (The maturity risk premium on a 5-year bond is 0.4 percent.) A 5-year corporate bond has a yield of 8.4 percent. What is the yield on a 7-year corporate bond that has the same default risk and liquidity premiums as the 5-year corporate bond?

5. Two years back a firm had issued $1,000 par value bonds carrying the coupon rate of 12% payable annually. These bonds' maturity was 10 years at the time of issue, and the firm would pay 5% premium on maturity. Calculate,

(a) The cost of these bonds to the firm, if the firm's marginal tax rate is 38%? (Use Excel spreadsheet)

(b) An investor bought these bonds recently at $990 and intends to hold for the rest of the maturity period. If the investor is in 15% marginal tax rate, what is the after-tax return of the investor? (Use Excel spreadsheet)

6. If these bonds are currently traded at $975, and if the firm wants to issue the new bonds to day what coupon rate should the firm offer on the new bonds? Assume that the new bonds will be issued and paid on maturity at par. (Don't ignore maturity value effect.)

#### Solution Preview

Please refer to the attachments.

The expectations theory is a theory that purports to explain the shape of the yield curve, or the term structure of interest rates. According to this theory, longer-term rates are determined by investor expectations of future short-term rates.

In mathematical terms, the theory suggests that:

(1 + R2)2 = (1 + R1) x (1 + E(R1))

where

R2 = the rate on two-year securities,

R1 = the rate on one-year securities,

E(R1) = the rate expected on one-year securities one year from now.

E(R1) = (1 + Rf) (1 + i)

Rf is the real risk-free rate and I is the inflation rate

The left side of this equation is the amount per dollar invested that the investor would have after two years if he invested in two-year securities. The right side shows the amount he can expect to have after two years if he invests in one-year obligations. Competition is assumed to make the left side equal to the right side.

The theory is easily generalized to cover any number of maturity classes. And however many maturity classes there may be, the theory always explains the existence of longer-term rates in terms of expected future shorter-term rates.

The expectations theory of interest rates provides the theoretical basis for the use of the yield curve as an analytical tool by economic and financial analysts. For example, an upward-sloping yield curve is explained as an indication that the market expects rising short-term rates in the future. Since rising rates normally occur during economic expansions, an upward-sloping yield curve is a sign that the market expects continued expansion in the ...

#### Solution Summary

In great detail with all the computations, the answers to the questions are fully explained.