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Unformatted text preview: Answers to EndofChapter Problems B41 Chapter 6: How to Value Bonds and Stocks 6.2. The price of any bond is the PV of the interest payment, plus the PV of the par value. Notice this problem assumes semiannual coupon. The price of the bond at each YTM will be: a. P = $40({1 [1/(1 + 0.04)] 40 } / 0.04) + $1,000[1 / (1 + 0.04) 40 ] P = $1,000.00 When the YTM and the coupon rate are equal, the bond will sell at par. b. P = $40({1 [1/(1 + 0.05)] 40 } / 0.05) + $1,000[1 /1 + 0.05 40 ] P = $828.41 When the YTM is greater than the coupon rate, the bond will sell at a discount. c. P = $40({1 [1/(1 + 0.03)] 40 } / 0.03) + $1,000[1 /1 + 0.03 40 ] P = $1,231.15 When the YTM is less than the coupon rate, the bond will sell at a premium. We would like to introduce shorthand notation here. Rather than write (or type, as the case may be) the entire equation for the PV of an annuity , it is common to abbreviate the equations as: t r ! = ({1 [1/(1 + r)] t } / r ) which stands for Present Value Interest Factor of an Annuity This abbreviation is short hand notation for the equations in which the interest rate and the number of periods are substituted into the equation and solved. We will use this shorthand notation in the remainder of the solutions key. 6.4. Here we are finding the YTM of semiannual coupon bonds for various maturity lengths. The bond price equation is: P = C t r ! + $1,000/1+r t Miller Corporation bond: P = $40 26 03 . ! + $1,000/1+0.03 26 = $1,178.77 P 1 = $40 24 03 . ! + $1,000/1+0.03 24 = $1,169.36 P 3 = $40 20 03 . ! + $1,000/1+0.03 20 = $1,148.77 P 8 = $40 10 03 . ! + $1,000/1+0.03 10 = $1,085.30 P 12 = $40 2 03 . ! + $1,000/1+0.03 2 = $1,019.13 P 13 = $1,000 Modigliani Company bond: Answers to EndofChapter Problems B42 P = $30 26 04 . ! + $1,000/1+0.04 26 = $840.17 P 1 = $30 24 04 . ! + $1,000/1+0.04 24 = $847.53 P 3 = $30 20 04 . ! + $1,000/1+0.04 20 = $864.10 P 8 = $30 10 04 . ! + $1,000/1+0.04 10 = $918.89 P 12 = $30 2 04 . ! + $1,000/1+0.04 24 = $981.14 P 13 = $1,000 All else held equal, the premium over par value for a premium bond declines as maturity approaches, and the discount from par value for a discount bond declines as maturity approaches. This is called pull to par. In both cases, the largest percentage price changes occur at the shortest maturity lengths. Also, notice that the price of each bond when no time is left to maturity is the par value, even though the purchaser would receive the par value plus the coupon payment immediately. This is because we calculate the clean price of the bond. 6.6 The price of any bond (or financial instrument) is the PV of the future cash flows. Even though Bond M makes different coupons payments, to find the price of the bond, we just find the PV of the cash flows. The PV of the cash flows for Bond M is: P M = $1,200 16 05 ....
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 Spring '08
 Wood

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