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Bond value and time—Constant required returns Pecos Manufacturing has just issued a 15​-year, 14​% coupon interest​ rate, $1,000​-par bond that pays interest annually. The required return is currently 13​%, and the company is certain it will remain at 13​% until the bond matures in 15 years. a.  Assuming that the required return does remain at 13​% until​ maturity, find the value of the bond with​ (1) 15 ​years, (2) 12​ years, (3) 9​ years, (4) 6​ years, (5) 3​ years, (6) 1 year to maturity.b.  All else remaining the​ same, when the required return differs from the coupon interest rate and is assumed to be constant to​ maturity, what happens to the bond value as time moves toward​ maturity?

Question
Bond value and time—Constant required returns
 
Pecos Manufacturing has just issued a 15​-year, 14​% coupon interest​ rate, $1,000​-par bond that pays interest annually. The required return is currently 13​%, and the company is certain it will remain at 13​% until the bond matures in 15 years.
 
a.  Assuming that the required return does remain at 13​% until​ maturity, find the value of the bond with​ (1) 15 ​years, (2) 12​ years, (3) 9​ years, (4) 6​ years, (5) 3​ years, (6) 1 year to maturity.
b.  All else remaining the​ same, when the required return differs from the coupon interest rate and is assumed to be constant to​ maturity, what happens to the bond value as time moves toward​ maturity?
check_circleAnswer
Step 1

a.

Calculation of Value of Bond if the maturity period is 15 years, 12 years, 9 years, 6 years, 3 years and 1 year:

The value of bond if the maturity period is 15 years is $1,064.62, 12 years is $1,059.18, 9 years is $1,051.32, 6 years is $1,039.98, 3 years is $1,023.61 and 1 year is $1,008.85.

Excel Spreadsheet:

А
В
1 Face Value
2 Coupon Rate
3 Yield to Maturity
4 Coupon Payment
S1,000
14%
13%
S140
5
Maturity Period Bond Price
6
15
$1,064.62
$1,059.18
$1,051.32
12
10
6
$1,039.98
11
3
$1,023.61
$1,008.85
12
1
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Image Transcriptionclose

А В 1 Face Value 2 Coupon Rate 3 Yield to Maturity 4 Coupon Payment S1,000 14% 13% S140 5 Maturity Period Bond Price 6 15 $1,064.62 $1,059.18 $1,051.32 12 10 6 $1,039.98 11 3 $1,023.61 $1,008.85 12 1

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Step 2

Excel Workings:

...
А
В
1 Face Value
2 Coupon Rate
3 Yield to Maturity 0.13
4 Coupon Payment=B1*B2
1000
0.14
5
6 Maturity Period
Bond Price
|=PV(B3,A7,-B4,-B1)
|=PV(B3,A8,-B4,-B1)
|=PV(B3.A9,-B4,-B1)
|=PV(B3,A10,-B4,-B1)
|=PV(B3,A11,-B4,-B1)
| -PVВЗ,А12,-В4,-B1)
7 15
8 12
9 9
10 6
11 3
12 1
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Image Transcriptionclose

А В 1 Face Value 2 Coupon Rate 3 Yield to Maturity 0.13 4 Coupon Payment=B1*B2 1000 0.14 5 6 Maturity Period Bond Price |=PV(B3,A7,-B4,-B1) |=PV(B3,A8,-B4,-B1) |=PV(B3.A9,-B4,-B1) |=PV(B3,A10,-B4,-B1) |=PV(B3,A11,-B4,-B1) | -PVВЗ,А12,-В4,-B1) 7 15 8 12 9 9 10 6 11 3 12 1

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