Problem 8.29 The Maryland Department of Transportation has issued 25-year bonds
ID: 2802696 • Letter: P
Question
Problem 8.29 The Maryland Department of Transportation has issued 25-year bonds that make semiannual coupon payments at a rate of 9.575 percent. The current market rate for similar securities is 11.7 percent. Assume that the face value of the bond is $1,000 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.) Current market value What will be the bond's price if rates in the market (0) decrease to 9.70 percent or () increase to 12.7 percent? (Round intermediate calculations to 2 decimal places, e.g. 1.25 and final answers to 2 decimal places, e.g. 15.25.) Bond's price () Decrease to 9.70 percent (ii) Increase to 12.7 percent How do the interest rate changes affect premium bonds and discount bonds? Bonds, in general, in price when interest rates go up. When interest rates decrease, bond prices Suppose the bond were to mature in 12 years. What will be the bond's price if rates in the market (i) decrease to 9.70 percent final answers to 2 decimal places, e.g. 15.2S.) or (i) increase to 12.7 percent? (Round intermediate calculations to 2 decimal places, e.g. 1.25 and (i) Bond's price if rate decrease to 9.70 percent () Bond's price if rate increase to 12.7 percent s the Point Potential Policy set by your By accessing this Question Assistance, you will learn while you earn points based on instructor Question Attempts: o of 3 used SAVE FOR LATER Earn Maximum Points available only if you answer this question correctly in two attempts or lessExplanation / Answer
Answer to A
value of bond
interest*PVAF at 4.25% for 3o semiannual period + face value*PVF at 4.25% at 30th semi annual period
47.875*16.097 + 1000*.05827
828.91
interest
1000*(9.575%/2)
47.875
face value
1000
PVAF at 5.85% for 50 semiannual period
1.716916
PVF at 5.85% at 50th semiannual period
0.058272
PVAF at 5.85% for 50 semiannual period
1-(1+r)^-n / r
1-(1.0585)^-50 / .0585
1.716916
PVF at 5.85% at 50th semiannual period
1/(1+r)^n
1/(1.0585)^50
0.058272
Answer to B
if interest rate decreases to 9.7%
value of bond
interest*PVAF at 4.25% for 3o semiannual period + face value*PVF at 4.25% at 30th semi annual period
47.875*18.6873 + 1000*.05827
952.92
interest
1000*(9.575%/2)
47.875
face value
1000
PVAF at 4.85% for 50 semiannual period
1.716916
PVF at 4.85% at 50th semiannual period
0.093665
PVAF at 4.85% for 50 semiannual period
1-(1+r)^-n / r
1-(1.0485)^-50 / .0485
18.6873
PVF at 4.85% at 50th semiannual period
1/(1+r)^n
1/(1.0485)^50
0.093665
Answer to B
if interest rate increases to 12.7%
value of bond
interest*PVAF at 4.25% for 3o semiannual period + face value*PVF at 4.25% at 30th semi annual period
47.875*15.02301 + 1000*.04603
765.26
interest
1000*(9.575%/2)
47.875
face value
1000
PVAF at 6.35% for 50 semiannual period
0
PVF at 6.35% at 50th semiannual period
0.046039
PVAF at 6.35% for 50 semiannual period
1-(1+r)^-n / r
1-(1.0635)^-50 / .0635
15.02301
PVF at 6.35% at 50th semiannual period
1/(1+r)^n
1/(1.0635)^50
0.046039
C-
1-
decrease
2-
Increases
d-
If maturity is of 12 Years
Answer to B
if interest rate decreases to 9.7%
value of bond
interest*PVAF at 4.25% for 24 semiannual period + face value*PVF at 4.25% at 24th semi annual period
47.875*14.0022 + 1000*.3208
991.16
interest
1000*(9.575%/2)
47.875
face value
1000
PVAF at 4.85% for 24 semiannual period
14.0022
PVF at 4.85% at 24th semiannual period
0.320891
PVAF at 4.85% for 24 semiannual period
1-(1+r)^-n / r
1-(1.0485)^-24 / .0485
14.0022
PVF at 4.85% at 24th semiannual period
1/(1+r)^n
1/(1.0485)^24
0.320891
Answer to B
if interest rate increases to 12.7%
value of bond
interest*PVAF at 4.25% for 24 semiannual period + face value*PVF at 4.25% at 24th semi annual period
47.875*12.1544 + 1000*.2281
809.99
interest
1000*(9.575%/2)
47.875
face value
1000
PVAF at 6.35% for 24 semiannual period
0
PVF at 6.35% at 24th semiannual period
0.228192
PVAF at 6.35% for 24 semiannual period
1-(1+r)^-n / r
1-(1.0635)^-24 / .0635
12.15446
PVF at 6.35% at 24th semiannual period
1/(1+r)^n
1/(1.0635)^24
0.228192
Answer to A
value of bond
interest*PVAF at 4.25% for 3o semiannual period + face value*PVF at 4.25% at 30th semi annual period
47.875*16.097 + 1000*.05827
828.91
interest
1000*(9.575%/2)
47.875
face value
1000
PVAF at 5.85% for 50 semiannual period
1.716916
PVF at 5.85% at 50th semiannual period
0.058272
PVAF at 5.85% for 50 semiannual period
1-(1+r)^-n / r
1-(1.0585)^-50 / .0585
1.716916
PVF at 5.85% at 50th semiannual period
1/(1+r)^n
1/(1.0585)^50
0.058272
Answer to B
if interest rate decreases to 9.7%
value of bond
interest*PVAF at 4.25% for 3o semiannual period + face value*PVF at 4.25% at 30th semi annual period
47.875*18.6873 + 1000*.05827
952.92
interest
1000*(9.575%/2)
47.875
face value
1000
PVAF at 4.85% for 50 semiannual period
1.716916
PVF at 4.85% at 50th semiannual period
0.093665
PVAF at 4.85% for 50 semiannual period
1-(1+r)^-n / r
1-(1.0485)^-50 / .0485
18.6873
PVF at 4.85% at 50th semiannual period
1/(1+r)^n
1/(1.0485)^50
0.093665
Answer to B
if interest rate increases to 12.7%
value of bond
interest*PVAF at 4.25% for 3o semiannual period + face value*PVF at 4.25% at 30th semi annual period
47.875*15.02301 + 1000*.04603
765.26
interest
1000*(9.575%/2)
47.875
face value
1000
PVAF at 6.35% for 50 semiannual period
0
PVF at 6.35% at 50th semiannual period
0.046039
PVAF at 6.35% for 50 semiannual period
1-(1+r)^-n / r
1-(1.0635)^-50 / .0635
15.02301
PVF at 6.35% at 50th semiannual period
1/(1+r)^n
1/(1.0635)^50
0.046039
C-
1-
decrease
2-
Increases
d-
If maturity is of 12 Years
Answer to B
if interest rate decreases to 9.7%
value of bond
interest*PVAF at 4.25% for 24 semiannual period + face value*PVF at 4.25% at 24th semi annual period
47.875*14.0022 + 1000*.3208
991.16
interest
1000*(9.575%/2)
47.875
face value
1000
PVAF at 4.85% for 24 semiannual period
14.0022
PVF at 4.85% at 24th semiannual period
0.320891
PVAF at 4.85% for 24 semiannual period
1-(1+r)^-n / r
1-(1.0485)^-24 / .0485
14.0022
PVF at 4.85% at 24th semiannual period
1/(1+r)^n
1/(1.0485)^24
0.320891
Answer to B
if interest rate increases to 12.7%
value of bond
interest*PVAF at 4.25% for 24 semiannual period + face value*PVF at 4.25% at 24th semi annual period
47.875*12.1544 + 1000*.2281
809.99
interest
1000*(9.575%/2)
47.875
face value
1000
PVAF at 6.35% for 24 semiannual period
0
PVF at 6.35% at 24th semiannual period
0.228192
PVAF at 6.35% for 24 semiannual period
1-(1+r)^-n / r
1-(1.0635)^-24 / .0635
12.15446
PVF at 6.35% at 24th semiannual period
1/(1+r)^n
1/(1.0635)^24
0.228192