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Compute the price of a 5.7 percent coupon bond with fifteen years left to maturi

ID: 2555381 • Letter: C

Question

Compute the price of a 5.7 percent coupon bond with fifteen years left to maturity and a market interest rate of 8.0 percent. (Assume interest payments are semiannual.) (Do not round intermediate calculations and round your final answer to 2 decimal places.)

  

Compute the price of a 5.7 percent coupon bond with fifteen years left to maturity and a market interest rate of 8.0 percent. (Assume interest payments are semiannual.) (Do not round intermediate calculations and round your final answer to 2 decimal places.)

Explanation / Answer

Assuming face value of the bond to be $1,000

When payments are made semiannually, interest rate is divided by 2 and time period is multiplied by 2

Time period n = 15 x 2 = 30 semi annual periods

Interest rate r = 8 / 2 = 4% or 0.04

Semi annual payments

= Principal x Rate x Time / 12 months

= $1,000 x 5.7% x 6 / 12

= $ 28.5

Maturity payment = Face value = $1,000

Present value factor

= 1 / (1 + r) ^ n

So, PV Factor for n = 2 will be

1 / (1.04 ^ 2)

= 1 / 1.0816

= 0.924556

The following table shows the calculations

So, the price of the bond is $801.14

The bond is trading at below its face value. So, it is a discount bond

Calculations A B C = A x B Time Cash flow PV Factor Present value 1 28.5 0.961538 27.40384615 2 28.5 0.924556 26.34985207 3 28.5 0.888996 25.33639622 4 28.5 0.854804 24.36191944 5 28.5 0.821927 23.42492254 6 28.5 0.790315 22.52396398 7 28.5 0.759918 21.65765768 8 28.5 0.73069 20.82467084 9 28.5 0.702587 20.02372196 10 28.5 0.675564 19.25357881 11 28.5 0.649581 18.51305655 12 28.5 0.624597 17.80101591 13 28.5 0.600574 17.11636145 14 28.5 0.577475 16.45803986 15 28.5 0.555265 15.82503833 16 28.5 0.533908 15.21638301 17 28.5 0.513373 14.63113751 18 28.5 0.493628 14.06840145 19 28.5 0.474642 13.52730909 20 28.5 0.456387 13.00702797 21 28.5 0.438834 12.50675766 22 28.5 0.421955 12.02572852 23 28.5 0.405726 11.5632005 24 28.5 0.390121 11.11846202 25 28.5 0.375117 10.69082886 26 28.5 0.360689 10.27964314 27 28.5 0.346817 9.884272249 28 28.5 0.333477 9.504107931 29 28.5 0.320651 9.138565319 30 28.5 0.308319 8.787082037 30 1000 0.308319 308.318668 Price 801.14
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