Question

Pecos Manufacturing has just issued a 15​-year, 11​% coupon interest​ rate, 1,000​-par bond that pays interest annually. The required return is currently 18​%, and the company is certain it will remain at 18​% until the bond matures in 15 years.

a. Assuming that the required return does remain at 18​% 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.

.

Answer 1

1

Face value	1000
Ytm =	18%
Time (n) =	15
Coupon amount = (1000*11%) =	110
Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n
(110*(1-(1/(1+18%)^15))/18%) + (1000/(1+18%)^15) =643.5895709 So value of bond is $643.59

2.

Face value	1000
Ytm =	18%
Time (n) =	12
Coupon amount = (1000*11%) =	110
Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n
(110*(1-(1/(1+18%)^12))/18%) + (1000/(1+18%)^12) =664.4742598 So value of bond is $664.474

3

Face value	1000
Ytm =	18%
Time (n) =	9
Coupon amount = (1000*11%) =	110
Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n
(110*(1-(1/(1+18%)^9))/18%) + (1000/(1+18%)^9) =698.788472 So value of bond is $698.79

4

Face value	1000
Ytm =	18%
Time (n) =	6
Coupon amount = (1000*11%) =	110
Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n
(110*(1-(1/(1+18%)^6))/18%) + (1000/(1+18%)^6) =755.1678208 So value of bond is $755.17

5

Face value	1000
Ytm =	18%
Time (n) =	3
Coupon amount = (1000*11%) =	110
Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n
(110*(1-(1/(1+18%)^3))/18%) + (1000/(1+18%)^3) =847.8008949 So value of bond is $847.80

6

Face value	1000
Ytm =	18%
Time (n) =	1
Coupon amount = (1000*11%) =	110
Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n
(110*(1-(1/(1+18%)^1))/18%) + (1000/(1+18%)^1) =940.6779661 So value of bond is $940.6779661