chapter 8 9 solutions.doc

Suggested solutions for a set of select exercise questions - Chapter 8 questionsYield to maturity: Elders Ltd has 4-year bonds outstanding that pay a coupon rate of 6.6 per cent semi-annually. If these bonds are currently selling at $914.89, what is the yield to maturity that an investor can expect to earn on these bonds? What is the effective annual yield?Solution:Years to maturity =4 hence n = 4x2=8Coupon rate = C = 6.6%Current market rate = i Semiannual coupon payments = $1,000 x (0.066/2) = $33Present value of bond = PB = $914.8901238 $33$33$33$33$1,000To solve for the YTM, a trial-and-error approach has to be used. Since this is a discount bond, the market rate should be higher than 6.6 per cent (3.3 per cent per 6 months).Try i = 8% or i/2 = 4%.Try a higher rate, i = 9%, i/2 = 4.5%.Try a higher rate, i = 9.2%, i/2 = 4.6%.8.24Realised yield: Kevin Phan bought 10-year bonds issued by Harvey Norman 5 years ago for $936.05. The bonds make semiannual coupon payments at a rate of 8.4 per cent. If the current price of the bond is $1,048.77, what is the yield that Kevin would earn by selling the bonds today?Solution:Purchase price of bond = $936.05Years investment held = 5 Hence n= 5x2=10Coupon rate = C = 8.4%Frequency of payment = m = 2Annual coupon = $1,000 x (0.084/2) = $42Realised yield = i Selling price of bond = PB = $1,048.77To calculate the realised return, either the trial-and-error approach or the financial calculator can be used. Since the price has increased, market rates must have decreased. So, the realised return is going to be greater than the bonds coupon. Try rates higher than the coupon rate.Try i = 11%, or i/2 = 5.5%.Try a lower rate, i = 10.85% or i/2 = 5.4%.8.27Showtime Ltd has issued 8-year bonds with a coupon of 6.375 per cent and semiannual coupon payments. The markets required rate of return on such bonds is 7.65 per cent. a.What is the market price of these bonds?b.Now assume that the above bond is callable after 5 years at an 8.5 per cent premium on the face value. What is the expected return on this bond?Solution:a.Years to maturity = 8 Hence n= 8x2=16Coupon rate = C = 6.375%Semiannual coupon = $1,000 x (0.06375/2) = $31.875Current market rate = 7.65% Hence i=7.65/2=3.825%Present value of bond = PB012316 $31.875$31.875$31.875 $31.875$1,000The company can sell these bonds at $924.75. b.Assume purchase price of bond = market price from part (a) = $924.75Years investment held = 5 hence n= 5x2=10Coupon rate = C = 6.375%Semiannual coupon = $1,000 x (0.06375/2) = $31.875Frequency of payment = m = 2Realised yield = i Call price of bond = PB = 1085 = $1000x(1.085)To calculate the realised return, either the trial-and-error approach or the financial calculator can be used. Since the call price is higher than the market price, the realised rate must be higher than current market rates. Try rates higher than the current YTM.Try i = 9%, or i/2 = 4.5%.Try a higher rate, i = 9.6% or i/2 = 4.8%.8.30Wattyl Group Ltd has 18-year bonds outstanding. These bonds, which pay semiannual coupons, have a coupon rate of 9.735 per cent and a yield to maturity of 7.95 per cent.a.Calculate the bonds current price.b.If the bonds can be called after 5 more years at a premium of 13.5 per cent over par value, what is the investors realised yield?c.If you bought the bond today, what is your expected rate of return? Explain.Solution:a.Years to maturity = 15 hence n = 15x2=30Coupon rate = C = 9.735%Semiannual coupon = $1,000 x (0.09735/2) = $48.675Current market rate = i = 7.95%Present value of bond = PB012330$48.675 $48.675 $48.675 $48.675 $1,000The bonds current price is at $1169.34. ProcedureKey OperationDisplayEnter cash flow data1000 FV1000=FV1000.0036 N36=N36.003.975I/Y3.975= I/Y3.97548.675 PMT48.675 =PMT48.675Calculate PVCOMP PVPV=-1169.34b.Purchase price of bond = $1169.34 from part aYears investment held = 5 hence n = 5x2=10Coupon rate = C = 9.735%Semiannual coupon = $1,000 x (0.09735/2) = $48.675Frequency of payment = m = 2Realised yield = i Call price of bond = FV = $1000 x 1.135 = 1135To calculate the realised return, either the trial-and-error approach or the financial calculator can be used. Since the call price is lower than the current price, the realised yield to call will be lower than the current market rate. So, try rates lower than the current YTM rate.Try i = 7.8%, or i/2 = 3.9%.Try a higher rate, i = 7.84 or i/2 = 3.92%.The realised rate of return is approximately 7.99 per cent. Using a financial calculator provides an exact yield of 7.9876 per cent. ProcedureKey OperationDisplayEnter cash flow data1135 FV1135=FV1135.0010 N10=N10.00-1169.34PV-1169.34= PV-1169.3448.675 PMT48.675 =PMT48.675Calculate I/YCOMP I/YI/Y =-3.91706 The effective annual yield can be calculated as:c. If we purchased the bond today then the expected return on the bond will be the annualised YTM of 8.108 per cent, if the bond is not called and is held until maturity in 18 years. If the bond is however, called in 5 years we realise a yield to call of 7.9876 per cent.The effective annual yield can be calculated as:Chapter 99.15Constant growth: Your required rate of return is 23 per cent. Gnangara Ltd has just paid a dividend of $3.12 and expects to grow at a constant rate of 5 per cent. What is the expected price of the share 3 years from now?Solution:R = 23%; D0 = $3.12; g = 5%9.26Gerald Neut owns shares in Patina Ltd. Currently, the market price of the share is $36.34. The company expects to grow at a constant rate of 6 per cent for the foreseeable future. Its last dividend was worth $3.25. Geralds required rate of return for such shares is 16 per cent. He wants to find out whether he should sell his shares or add to his holdings.a. What is the value of this share?b.Based on your answer to part a, should Gerald buy additional shares in Patina Ltd? Why or why not?Solution:a. b. No, he should not buy more shares. This share is overpriced with the share selling at a higher price in the market than what it is worth. Gerald should sell his shares.9.28Zarapharm is a fast-growing drug company. The company forecasts that in the next 3 years, its growth rates will be 30 per cent, 28 per cent, and 24 per cent, respectively. Last week it declared a dividend of $1.67. After 3 years the company expects a more stable growth rate of 8 per cent for the next several years. Your required rate of return is 14 per cent.a.Calculate the dividends for th