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# ch5 - Chapter 5 How to Value Bonds and Stocks 5.1 The...

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Chapter 5: How to Value Bonds and Stocks 5.1 The present value of any pure discount bond is its face value discounted back to the present. a. PV = F / (1+r) 10 = \$1,000 / (1.05) 10 = \$613.91 b. PV = \$1,000 / (1.10) 10 = \$385.54 c. PV = \$1,000 / (1.15) 10 = \$247.19 5.2 First, find the amount of the semiannual coupon payment. Semiannual Coupon Payment = Annual Coupon Payment / 2 = (0.08 × \$1,000) / 2 = \$40 a. Since the stated annual interest rate is compounded semiannually, simply divide this rate by two in order to calculate the semiannual interest rate. Semiannual Interest Rate = 0.08 / 2 = 0.04 The bond has 40 coupon payments (=20 years × 2 payments per year). Apply the annuity formula to calculate the PV of the 40 coupon payments. In addition, the \$1,000 payment at maturity must be discounted back 40 periods. P = C A T r + F / (1+r) 40 = \$40 A 40 0.04 + \$1,000 / (1.04) 40 = \$1,000 The price of the bond is \$1,000. Notice that whenever the coupon rate and the market rate are the same, the bond is priced at par. That is, its market value is equal to its face value. b. Semiannual Interest Rate = 0.10 / 2 = 0.05 P = \$40 A 40 0.05 + \$1,000 / (1.05) 40 = \$828.41 The price of the bond is \$828.41. Notice that whenever the coupon rate is below the market rate, the bond is priced below par. c. Semiannual Interest Rate = 0.06 / 2 = 0.03 P = \$40 A 40 0.03 + \$1,000 / (1.03) 40 = \$1,231.15 The price of the bond is \$1,231.15. Notice that whenever the coupon rate is above the market rate, the bond is priced above par. B-75

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5.3 Since the payments occur semiannually, discount them at the semiannual interest rate. Convert the effective annual yield (EAY) to a semiannual interest rate. Semiannual Interest Rate = (1+EAY) 1 / T – 1 = (1.12) 1/2 – 1 = 0.0583 a. Calculate the semiannual coupon payment. Semiannual Coupon Payment = Annual Coupon Payment / 2 = (0.08 × \$1,000) / 2 = \$40 Apply the annuity formula to calculate the PV of the 40 coupon payments (=20 years × 2 payments per year). In addition, the \$1,000 payment at maturity must be discounted back 40 periods. The appropriate discount rate is the semiannual interest rate. P = C A T r + F / (1+r) 40 = \$40 A 40 0.0583 + \$1,000 / (1.0583) 40 = \$718.65 The price of the bond is \$718.65 . b. Calculate the semiannual coupon payment. Semiannual Coupon Payment = (0.10 × \$1,000) / 2 = \$50 Apply the annuity formula to calculate the PV of the 30 coupon payments (=15 years × 2 payments per year). In addition, the \$1,000 payment at maturity must be discounted back 30 periods. The appropriate discount rate is the semiannual interest rate. P = \$50 A 30 0.0583 + \$1,000 / (1.0583) 30 = \$883.64 The price of the bond is \$883.64. 5.4 First, calculate the semiannual interest rate. Semiannual Interest Rate = (1+EAY) 1 / T – 1 = (1.10) 1 / 2 – 1 = 0.04881 Next, find the semiannual coupon payment. Semiannual Coupon Payment = (0.08 × \$1,000) / 2 = \$40 B-76
The bond has 40 payments (=20 years × 2 payments per year). Apply the annuity formula to find the PV of the coupon payments. In addition, discount the \$1,000 payment at maturity back 40 periods. The appropriate discount rate is the semiannual interest rate. P = C A T r + F / (1+r) 40 = \$40 A 40 0.04881 + \$1,000 / (1.04881) 40 = \$846.33 The price of the bond is \$846.33. 5.5 First, calculate the semiannual interest rate.

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