# Mid-Term Exam Practice Set and Solutions.

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2 Question 3 (5 points): On January 10, you sold short one round lot (i.e., 100 shares) of Netscape stock at \$14 per share. On March 10, a quarterly dividend of \$2 per share was paid by Netscape. On April 10, you covered the short sale by buying the stock at a price of \$9 per share. Assume that you paid 50 cents per share in commissions for each transaction. What is the value of your account on April 10? Explain briefly. Question 4 (5 points): Consider a bond with a 10% coupon rate and with yield to maturity equal to 8%. If the bond s yield to maturity remains constant, then in one year will the bond price be higher, lower, or unchanged? Why? Question 5 (15 points): We are in A large forest product manufacturer has outstanding two Baa-rated, \$150 million par amount, intermediate-term debt issues: 10.10% Notes Floating-Rate Notes Maturity Issue date Callable (beginning on) Callable at Sinking fund None None Current coupon 10.10% 9.9% Coupon changes Fixed Every 6 months Rate adjusts to - 6-month T-bill rate + 1% Range since issued %-8.3% Current price 73 3/8 97 Current yield 13.77% 10.3% Yield to maturity 15.87% - Price range since issue Given the data above: (a) What is the minimum coupon rate (of interest) at which the firm could sell a fixed-rate issue at par due in Assume the same indenture provisions as the 10.10% notes and disregard any tax considerations. (b) Give two reasons why the floating-rate notes are not selling at par. (c) Is the risk of call high, moderate, or low for the fixed-rate issue? Why? (d) Does it make sense to compute the yield to maturity for the floating-rate note? Why or why not?

3 Question 6 (20 points): The current yield curve for default-free-zero-coupon bonds is as follows: Maturity (years) YTM % 2 11% 3 12% (a) What are the implied one-year forward rates? (b) Assume that the (pure) expectations hypothesis of the term structure is correct. If market expectations are accurate, what will the pure yield curve, that is, the yields to maturity on one- and two-year zero-coupon bonds, be next year? (c) If you purchase a two-year zero-coupon bond now, what is the expected total rate of return over the next year? What if you purchased a three-year zero coupon bond? Ignore taxes. (Hint: compute the current and expected future prices). (d) What should be the current price of a three-year maturity bond with a 12% coupon rate paid annually? If you purchased it at that price, what would your total expected rate of return be over the next year (coupon plus price change)? Ignore taxes. Bonus question (5 points). Using the above data and assuming a decline in interest rates is anticipated, identify and justify which issue would be most appropriate for an actively managed bond portfolio where total return is the primary objective.

5 Question 3 (5 points): On January 10, you sold short one round lot (i.e., 100 shares) of Netscape stock at \$14 per share. On March 10, a quarterly dividend of \$2 per share was paid by Netscape. On April 10, you covered the short sale by buying the stock at a price of \$9 per share. Assume that you paid 50 cents per share in commissions for each transaction. What is the value of your account on April 10? Explain briefly. Solution: Account balance (without considering interest rate in the period): January 10: Short sell of 100 shares.\$1,400 January 10: Transaction cost on the short sale....(\$ 50) March 10: Dividend payment (\$ 200) March 10: Transaction cost on dividend payment.(\$ 50) April 10: Purchase of 100 shares.(\$ 900) April 10: transaction cost on the stock purchase.(\$ 50) April 10: Net Account Value \$150 Question 4: Consider a bond with a 10% coupon rate and with yield to maturity equal to 8%. If the bond s yield to maturity remains constant, then in one year will the bond price be higher, lower, or unchanged? Why? Answer: The bond price will be lower. As time passes, the bond price, which now must be above par value, will approach par. Question 5: We are in A large forest product manufacturer has outstanding two Baa-rated, \$150 million par amount, intermediate-term debt issues: 10.10% Notes Floating-Rate Notes Maturity Issue date Callable (beginning on) Callable at Sinking fund None None

6 Current coupon 10.10% 9.9% Coupon changes Fixed Every 6 months Rate adjusts to - 6-month T-bill rate + 1% Range since issued %-8.3% Current price 73 3/8 97 Current yield 13.77% 10.3% Yield to maturity 15.87% - Price range since issue Given the data above: (a) What is the minimum coupon rate (of interest) at which the firm could sell a fixed-rate issue at par due in 2003? Assume the same indenture provisions as the 10.10% notes and disregard any tax considerations. (b) Give two reasons why the floating-rate notes are not selling at par. (c) Is the risk of call high, moderate, or low for the fixed-rate issue? Why? (d) Does it make sense to compute the yield to maturity for the floating-rate note? Why or why not? Answer. (a) The minimum coupon rate would be 15.87% -- that is, the yield to maturity of the current outstanding Fixed Rate Issue. (b) Floating Rate Notes may not sell at par for any of the following reasons: The yield spread between 6-month Treasury bills and other money market instruments of comparable maturity could be wider than when the bond was issued; The credit standing of Georgia-Pacific may have eroded relative to Treasury securities, which have no credit risk. Therefore, the 1% premium (over T-bills) would become insufficient to sustain the issue at par; The coupon increases are implemented with a lag, that is, once every six months. During a period of rising interest rates, even this brief lag will be reflected in the security price. (c) The risk of call is low. Intermediate-term interest rates would have to decline by more than a third (15.87% to 10.10%) by June 15, 1999 to make call of the Fixed Rate Issue attractive. (d) The concept makes little sense for floating-rate notes. The yield to maturity incorporates the return from a fixed stream of coupon interest payments and the accretion (i.e., the accumulation) of depreciation between the present price of the bond and its par value to be received at maturity. Because the Floating Rate Note consists of a variable stream of interest payments to maturity, the effective maturity for comparative purposes with other debt securities is closer to next coupon reset date than the final maturity date. Therefore, yield-tomaturity is an indeterminable calculation for a Floating Rate Note, whereas yield-torecoupon date is a more meaningful measure of total return.

7 Question 5: The current yield curve for default-free-zero-coupon bonds is as follows: Maturity (years) YTM % 2 11% 3 12% (a) What are the implied one-year forward rates? (b) Assume that the pure expectations hypothesis of the term structure is correct. If market expectations are accurate, what will the pure yield curve, that is, the yields to maturity on one- and two-year zero coupon bonds, be next year? (e) If you purchase a two-year zero-coupon bond now, what is the expected total rate of return over the next year? What if you purchased a three-year zero coupon bond? Ignore taxes. (Hint: compute the current and expected future prices). (d) What should be the current price of a three-year maturity bond with a 12% coupon rate paid annually? If you purchased it at that price, what would your total expected rate of return be over the next year (coupon plus price change)? Ignore taxes. Answer: (a) we obtain forward rates from the following table: Maturity (years) YTM Price Forward Rate 1 10% \$ N-A (short rate = 10%) 2 11% \$ % [( /1.10) 1] 3 12% \$ % [( / ) 1] (b) If the expectations hypothesis holds, then forward rates = expected future short rates. We obtain next year s prices and yields by discounting each zero s face value at the forward rates for next year that we derived in item (a): Maturity (years) Price YTM 1 \$ [= 1000/1.1201] 12.01% 2 \$ [= 1000/( x )] 13.02% Note that this year s upward sloping yield curve implies, according to the expectations hypothesis, a shift upward in next year s curve.

8 (c) The 2-year zero will be a 1-year zero next year, and will therefore sell at (\$1000/1.1201) = \$ Similarly, the current 3-year zero will be a 2-year zero and will sell for \$ The expected total rates of returns are: 2-year bond = 9\$892.78/\$811.62) 1 = 10% 3-year bond = (\$782.93/\$711.78) 1 = 10% (d) The current price of the bond should equal the value of each payment times appropriate discount factor (i.e., the present value of \$1 to be received at the maturity of that payment). The present value schedule can be taken directly from the prices of zero-coupon bonds calculated above, such that Current price = \$120 x ( ) + \$120 x ( ) +\$1,120 x ( ) = \$ \$ \$ = \$1, Similarly, the expected prices of zeros in 1 year can be used to calculate the expected bond value at that time: Expected price 1 year from now = \$120 x ( ) + \$1,120 x ( ) = \$ \$ = \$ Total expected rate of return = [\$120 + (\$ \$1,003.68)]/\$1,003.68] = (\$120 - \$19.64)/\$1, = 10% Bonus question. Using the above data and assuming a decline in interest rates is anticipated, identify and justify which issue would be most appropriate for an actively managed bond portfolio where total return is the primary objective. Answer. The Fixed Rate Issue has the most appeal for an actively managed bond portfolio since a change in interest rates downward from present levels could produce a substantial gain in the principal value, in addition to the coupon interest. By contrast, Floating Rate Notes lack significant capital gain or loss because the changing coupon interest tends to stabilize principal values. Hence, the opportunity to maximize total return based on a forecast of declining interest rates is less than in the case of Fixed Rate Obligations.

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