The price of Snyder preferred stock prior to the payment of today s dividend is 1000 assuming a yield rate of 10% convertible quarterly. 0.

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1 Chapter 7 1. The preferred stock of Koenig Industries pays a quarterly dividend of 8. The next dividend will be paid in 3 months. Using the dividend discount method and an annual effective yield rate of 1%, calculate the price of Koenig preferred stock. Pr ice PV (4) (4) 1 i Pr ice Div i 4. Snyder Pretzel Company has issued preferred stock that pays a quarterly dividend of D. The next dividend will be paid later today. The price of Snyder preferred stock prior to the payment of today s dividend is 1000 assuming a yield rate of 10% convertible quarterly. Determine D. Pr ice PV Div a (4) i Pr ice PV 1000 Div Div 4.39 October 30, 013

2 3. Jenna buys the common stock of Morton Manufacturing for 5000 per share. Morton s stock pays a quarterly dividend of 140 per share. The dividend is expected to remain level and continue forever. The next dividend is payable in three months. Calculate the expected annual effective yield on Morton s stock. 1 Note: The present value of a perpetuity= ( m) i m 1 Pr ice PV (4) i 4 i 4 (4) 0.08 (4) 4 i % i 4 October 30, 013

3 4. Thompson Corporation pays annual dividends. They will pay a dividend of 3 in one year on earnings of 5 for the year. Thompson s earnings are expected increase at a rate of 6% per year with 60% of earnings paid as dividends. Calculate theoretical price of the common stock to yield 10%. 3 Pr ice PV 0.6(5) v 0.6(1.06)(5) v 0.6(1.06) (5) v (5) v v 1.06 v... FirstTerm NextTermAfterLast Now remember that the sum of a geometric series= 1 Ratio 1 0 PV 0.6(5) v 11.06v 1 v PV 0.6(5) The preferred stock of Gick Guttering Company pays annual dividends. The next dividend of 10 will be paid in one year. Each subsequent dividend thereafter will be larger than the previous dividend. The preferred stock is purchased to yield 10% annually. Calculate the price of preferred stock. To do this problem, you must split the dividend payments into two perpetuities: one perpetuity with a payment of 8 every year, and one perpetuity that pays in the first year, 4 in the second year, 6 in the third year and so on such that each payment increases by each year. 8 Perpetuity #1: PV 8a 0.1 Perpetuity #: PV Adding each PV together we get: PV1PV 300 October 30, 013

4 6. The preferred stock of Crosby Chocolate Factory pays an annual dividend of 5. The next dividend will be paid in 5 months. The stock is purchased to yield 8%. Calculate the price of the stock. If payments started today, we could use 5 a but because 0.08 the dividend isn t paid for another 5 months we need to discount the price by 5 months /1 7. The preferred stock of Banu LTD pays a quarterly dividend with the next dividend payable in 3 months. The quarterly dividends are 1 each quarter for the next year, each quarter for the second year, 3 each quarter for the 3 rd year, etc. The stock is purchased to yield 8% compounded monthly. Calculate the theoretical price for Banu LTD preferred stock. We need to use the Increasing Perpetuity Immediate formule. 1 i.08 where i and i 1 i 4 Ia (4) (4) 1 (4) i (4) Ia October 30, 013

5 Chapter 8 Use the following spot yield curve for Problems 8-1: Time Spot Rate ½ 1.0% 1 1.5% 1 ½.0%.5% ½ 3.0% 3 4.0% 3 ½ 5.0% 4 6.0% 8. Calculate the price of a year bond with a par value of 10,000. The bond matures for par and has a coupon rate of 6% convertible semi-annually Coupons 300 Use spot rates for each period of time P 300(1.01) Calculate the present value of a four year annuity due with annual payments of Use spot rates for each period of time October 30, 013

6 10. Two years from today, Rinat will receive 100,000. Three years from today, Rinat will receive 00,000. How much will Rinat have four years from today? We need to use forward rates which can be found from spot rates. 1 r 1 f,4 1 r4 (1.05) 1 f, f, r 1 f 1 r , f ,4 3,4 (1 f ) Now use the forward rates to find the accumulated value at the end of 4 years.,4 3,4 FV f f FV Calculate the accumulated value of a 3 year annuity immediate with annual payments of First find the forward rates, Then find the accumulated value. (1,3) (,3) 3 1 r f(1,3) r r (,3) 1 r 1.05 AV f f 1000 AV 1000* * AV f October 30, 013

7 1. A four year bond matures for 5000 and has annual coupons of 15. The price of the bond is calculated using the spot yield curve. Determine the annual yield rate on the bond. First, let s find the present value using spot rates PV 3 4 (1 r1 ) (1 r ) (1 r3 ) (1 r4 ) (1. 15) (1.05) (1.04) (1.06) Then use your calculator to find the interest rate, PV PMT 15 N 4 FV 5000 CPT I / Y You are given the following yield curve: Term (t) Spot Rate Calculate the 1 year deferred 3 year forward rate f (1,4). (1 r ) (1.07) f(1,4) (1 r1 ) (1.06) (1 ) (1.07) f(1,3) (1.06) 7.603% 4 1/ October 30, 013

8 14. You are given the following two bonds: Term Annual Coupon Maturity Value Price Calculate the year spot interest rate r r % r (1 r ) (1 r ) r r 5% October 30, 013

9 15. You are given the following spot yield curve: r t t 1 4.0% 3.5% r r 4 The present value of a four year annuity due of 100 is The price of a 4 year bond with a maturity value of 000 and annual coupons of 50 is Calculate the three year deferred one year forward interest rate. First, we will need to use the given information to find the spot rates for year 3 and year 4 and then we can use them to find the forward interest rate r1 (1 r ) (1 r3 ) (1 r3 ) 1.04 (1.035) 1000 r / r1 (1 r) (1 r3) (1 r4) (1 r4 ) 1.04 (1.035) ( ) 050 r / f 4 4 (1 r4 ) (1.045) (3,4) (1 r3 ) ( ) % October 30, 013

10 Answers % , , , % % % % October 30, 013