The Maryland Department of Transportation has issued 25-year bonds that make sem
ID: 2725919 • Letter: T
Question
The Maryland Department of Transportation has issued 25-year bonds that make semiannual coupon payments at a rate of 10.225 percent. The current market rate for similar securities is 10.8 percent. Assume that the face value of the bond is $1,000.
(a)
What is the current market value of one of these bonds? (Round intermediate calculations to 2 decimal places, e.g. 1.25 and final answer to 2 decimal places, e.g. 15.25.)
(b)
What will be the bond’s price if rates in the market (i) decrease to 8.80 percent or (ii) increase to 11.8 percent? (Round intermediate calculations to 2 decimal places, e.g. 1.25 and final answers to 2 decimal places, e.g. 15.25.)
(c)
Suppose the bond were to mature in 12 years. What will be the bond’s price if rates in the market (i) decrease to 8.80 percent or (ii) increase to 11.8 percent? (Round intermediate calculations to 2 decimal places, e.g. 1.25 and final answers to 2 decimal places, e.g. 15.25.)
Explanation / Answer
Answer:(a) Current market value=$51.125*PVIFA(5.4%,50)+$1000*PVIF(5.4%,50)
=878.4911+72.1
=$950.59
Answer:(b) (i) Decrease to 8.80 percent:
Bond Price=$51.125*PVIFA(4.4%,50)+$1000*PVIF(4.4%,50)
=$1026.99+$116.1
=$1143.09
(ii) Increase to 11.8 percent:
Bond Price=$51.125*PVIFA(5.9%,50)+$1000*PVIF(5.9%,50)
=$817.21+$56.9
=$874.11
Answer:(c)
(i) Decrease to 8.80 percent:
Bond Price=$51.125*PVIFA(4.4%,24)+$1000*PVIF(4.4%,24)
=$748.53+$355.8
=$1104.33
(ii) Increase to 11.8 percent:
Bond Price=$51.125*PVIFA(5.9%,24)+$1000*PVIF(5.9%,24)
=$647.61+$252.6
=$900.21
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