<p> Exam II: Review II Chapter 6: 1. The real risk-free rate is 4 percent. Inflation is expected to be 4 percent this year, 6 percent next year, and then 5 percent thereafter. The maturity risk premium is estimated to be 0.06 X (t-1)%, where t = number of years to maturity. What is the yield on a 7-year Treasury note? Treasury securities do not have DRP or LP r = r* + IP + MRP + DRP + LP. r = r* + IP + MRP r* = 0.04. IP = [0.04 + 0.06 + (5)(0.05)]/7 = 0.05 MRP = 0.0006(6) = 0.0036. rT7 = 0.04 + 0.05 + 0.0036 = 0.0936 = 9.36%.</p><p>2. Due to a recession, expected inflation this year is only 4 percent. However, the inflation rate in year 2 and thereafter is expected to be constant at some level 4 percent. Assume that the expectations theory holds and the real risk-free rate is r* = 3%. If the yield on 3-year treasury bonds equals the 1-year yield plus 3 percent, what inflation rate is expected after year 1? Basic relevant equations: rt = r* + IPt + DRPt + MRPt + IPt. But here IPt is the only premium, so rt = r* + IPt. IPt = Avg. inflation = (I1 + I2 + . . .)/N. We know that I1 = IP1 = 4% and r* = 3%. Therefore, rT1 = 3% + 4% = 7%. rT3 = rT1 + 3% = 7% + 3% = 10%. But, rT3 = r* + IP3 = 3% + IP3 = 10%, so IP3 = 10% – 3% = 7%. We also know that It = Constant after t = 1. We can set up this table: r* I Avg. I = IPt r = r* + IPt IP3= 7 = (4% + 2IP)/3 21 = 4 + 2IP 2IP = 17 IP = 8.5%</p><p>3. An investor in Treasury securities expects inflation to be 3.5 percent in Year 1, 4.2 percent in Year 2, and 4.6 percent each year thereafter. Assume that the real risk-free rate is 3.75 percent, and that this rate will remain constant. Three-year Treasury securities yield 8.25 percent, while 5-year Treasury securities yield 8.80 percent. What is the difference in the maturity risk premiums (MRPs) on the two securities (MRP5 – MRP3)?</p><p>First, calculate the inflation premiums for the next three and five years, respectively. They are: IP3 = (3.5% + 4.2% + 4.6%)/3 = 4.1% IP5 = (3.5% + 4.2% + 4.6% + 4.6% + 4.6%)/5 = 4.3%. The real risk-free rate (r*) is given as 3.75%. Since the default and liquidity premiums are zero on Treasury bonds, we can now solve for the maturity risk premium. 8.25% = 3.75% + 4.1% + MRP3 MRP3 = 0.4%. 8.8% = 3.75% + 4.3% + MRP5, MRP5 = 0.75%. Thus, MRP5 – MRP3 = 0.75% – 0.40% = 0.35%.</p><p>4. The real risk-free rate of interest is 4 percent. Inflation is expected to be 5 percent this coming year, jump to 6 percent next year, and increase to 7 percent the following year. According to the pure expectations theory, what should be the interest rate on 3-year, risk-free securities today? A. 4% B. 6% C. 12% D. 10% r = r* + IP + MRP + DRP + LP. r = 4 + [(5+6+7)/3] r = 10%</p><p>Chapter 7: YTM = the rate of return earned on a bond if it is held to maturity Current yield = provides information regarding the amount of cash income that will be generated in a given year, but does not provide an accurate measure of the total expected return. </p><p>1. A 10 percent semiannual coupon bond matures in 8 years. The bond has a face value of $1,000 and a current yield of 9.21 percent. What are the bond’s price and YTM? The problem asks you to solve for the YTM and Price, given the following facts: N = 8 X 2 = 16, PMT = 100/2 = 50, and FV = 1000. In order to solve for I/YR we need PV. However, you are also given that the current yield is equal to 9.21%. Given this information, we can find PV (Price). Current yield = Annual interest/Current price 0.0921 = $100/PV PV = $100/0.0921 = $1085.78 Now, solve for the YTM with a financial calculator: N = 16, PV = -$1085.78, PMT = 50, and FV = 1000. Solve for I/YR = YTM = 4.2402%. However, this is a periodic rate so the nominal YTM = 4.2502%(2) = 8.5004%.</p><p>2. A semiannual coupon bond that matures in 9 years sells for $1,060. It has a face value of $1,000 and a YTM of 10.9356 percent. What is its current yield? The problem asks you to solve for the current yield, given the following facts: N = 18, I/YR = 10.9356 /2 = 5.4678, PV = -1060, and FV = 1000. In order to solve for the current yield we need to find PMT. With a financial calculator, we find PMT = $60.00. However, because the bond is a semiannual coupon bond this amount needs to be multiplied by 2 to obtain the annual interest payment: $60.00(2) = $120.00. Finally, find the current yield as follows: Current yield = Annual interest/Current price = $120/$1,060 = 11.32%.</p><p>3. The Pennington Corporation issued a new series of bonds on January 1, 1982. The bonds were sold at par ($1,000), had a 14 percent coupon, and matured in 30 years, on December 31, 2011. Coupon payments are made semiannually (on June 20 and December 31). a. What was the YTM on January 1, 1982? b. What was the price of the bonds on January 1, 1987, 5 years later, assuming that interest rates had fallen to 12 percent? c. Find the current yield, capital gains yield, and total return on January 1, 1987, given the price as determined in part b. d. On July 1, 2005, 6.5 years before maturity, Pennington’s bonds sold for $916.42. What was the YTM, the current yield, the capital gains yield, and the total return at that time? a. Since the bonds were sold at par, the YTM = coupon rate of 14% b. N = 50 (years left till maturity), I/Y = 6, PMT = 70, FV = 1,000, PV = -$1,157.6186 c. Current yield = Annual Coupon/PV = $140/$1,157.6186 = 0.1209 = 12.09% Capital Gains yield = Total yield – Current yield = 12% - 12.09% = -0.09% Total return = 12% d. N = 13, PV = -916.72, PMT = 70, FV = 1000, I/Y = 8.0670%(2) = 16.1140% = YTM = Total return Current yield = $140/$916.42 = 15.28% Capital gains yield = 16.1140% - 15.28% = 0.8340%</p><p>4. Halley Enterprises’ bonds currently sell for $875. They have a eight-year maturity, an annual coupon of $80, and a par value of $1,000. What is their yield to maturity and their current yield? YTM: N = 8, PV = -875, PMT = 80, FV = 1000, I/Y = 10.3751 Current yield = Annual Coupon/PV = 80/875 = 0.0914 = 9.14%</p><p>5. The Henderson Company’s Bonds currently sell for $1,350. They pay a $110 annual coupon and have a 15-year maturity, but they can be called in 5 years at $1,220. What is their YTM and their YTC, and which is “more relevant” in the sense that investors should expect to earn it? YTM: N = 15, PV = -1,350, PMT = 110, FV = 1000, I/Y = 7.1264 YTC: N = 5, PV = -1,350, PMT = 110, FV = 1,220, I/Y = 6.4553 6. Hartwell Corporation bonds have a 30-year maturity, an 9% semiannual coupon, and a face value of $1,000, the going interest rate is 7%, based on semiannual compounding. What is the bond’s price? N = 60, PV = -1,249.4473, PMT = 45, FV = 1000, I/Y = 3.50</p><p>7. Hooper printing Inc. has bonds outstanding with 9 years to maturity. The bonds have an 8 percent annual coupon rate and were issued 1 year ago at their par value of $1,000, but due to changes in interest rates, the bond’s market price has fallen to $901.40. The capital gains yield last year was -9.86 percent. a. What is the YTM? b. For the coming year, what is the expected current yield and the expected capital gains yield? 7. a. Solving for YTM: N = 9, PV = -901.40, PMT = 80, FV = 1000 I/YR = YTM = 9.6911%. b. The current yield is defined as the annual coupon payment divided by the current price. CY = $80/$901.40 = 8.875%. Expected capital gains yield can be found as the difference between YTM and the current yield. CGY = YTM – CY = 9.691% – 8.875% = 0.816%.</p>