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##### You consider an investment in the following stock.

**Description**

solution

**Question**

1. [20 marks] You consider an investment in the following stock. The stock just paid $8;per share in dividends and is expected to increase its dividends at 10% rate for the;next 4 years. After that the dividend growth rate will decrease to 5% per year. All;dividends are paid at the end of each year. The appropriate risk-adjusted discount rate;is 8% and it is expected to stay constant in the future. You plan to buy this stock and;hold it for 8 years.;(a) [12 marks] What is the price you are willing to pay?;(b) [8 marks] At which price do you expect to sell the stock at the end of year 8?;2. [20 marks] Assume you have a one-year investment horizon and are trying to choose;among three bonds. All have a face value of $1,000 and mature in 10 years. The rst;is a zero-coupon bond, the second has an 8% coupon rate, and the third has a 10%;coupon rate. All coupon payments are annual.;(a) [6 marks] If all three bonds are now priced based on (annualized) 8% yield to;maturity, what are their prices?;(b) [7 marks] If the yields to maturity for all three bonds are 8% a year from now;what would their prices be then? What would the holding period return on each;bond be?;1;(c) [7 marks] Recalculate your answer to part (b) under the assumption that the yield;to maturity on each bond will be 7% a year from now.;3. [20 marks] A 20-year-maturity bond with face value of $1,000 makes semiannual coupon;payments at a coupon rate of 8 percent. Find the bond equivalent yield (i.e., APR);and eective annual yield to maturity of the bond if the bond price is;(a) [4 marks] $950;(b) [4 marks] $1,000;(c) [4 marks] $1,050;(d) [8 marks] Repeat (a), (b), (c) using the same data, but assuming that the bond;makes its coupon payments annually. Why are the yields you compute lower in;this case?;4. [20 marks] Sylvio is turning 60 and plans to retire early at the end of the year. He will;start receiving his pension when he turns 67, i.e., in 7 years. He has some savings and;plans to invest in bonds to guarantee a stream of income for the next 6 years (age 61;through 66). Specically, he aims at starting at $56,000 next year and then each year;receiving $2,000 less than the previous year, ending up with $46,000 when he is 66.;Sylvio can invest in a number of bonds, all of which have face value $1,000, described;as follows;Bond;A;B;C;D;E;F;G;Coupon rate (%);4;2;0;0;0;8;0;Maturity;6 years;6 years;5 years;4 years;3 years;2 years;1 year;Price;$977.19;$872.54;$812.12;$854.80;$895.44;$1,085.67;$968.52;All coupon payments are annual and, therefore, you should use annual compounding;throughout. His current savings are $275,000. In addition to guaranteeing the cash;ow stream described above, Sylvio wants to receive a single payment at the end of;year 3 which he plans to spend on a cruise to celebrate his 30th wedding anniversary.;2;(a) [14 marks] How many units of each bond does Sylvio need to buy or sell?;(b) [6 marks] How much will Sylvio get to spend on the cruise?;5. [20 marks] A pension fund must pay $100M in 15 years. Suppose the fund has $65M;in cash right now. Assume that the term structure is currently at at 3.3%.;(a) [4 marks] What is the PV of funds liabilities? What is the PV of funds liabilities;if the interest rate falls to 2.7%?;(b) [8 marks] The funds manager considers duration-based hedging of interest rate;risk. He can use 10-year bond with annual coupon rate of 2% and 20-year zerocoupon bond for that, both with par values of $1,000. Construct the hedging;portfolio of the two bonds that has the same market value and the same interestrate sensitivity (measured using the duration model) as the pension fund liability.;(c) [8 marks] Suppose that the government introduces a new Early Retirement Program, which allows individuals to retire earlier but with a smaller pension. The;pension fund expects 25% of its clients to take advantage of this program to retire;in 10 years instead of 15 years and with a pension of 80% of the standard level.;What is the new hedging portfolio?

Paper#30341 | Written in 18-Jul-2015

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