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Robert Campbell and Carol Morris are senior vice-presidents of the Mutual of Chicago Insurance Company. They...

  1. Robert Campbell and Carol Morris are senior vice-presidents of the Mutual of Chicago Insurance Company. They are co-directors of the company’s pension fund management division. A major new client has requested that Mutual of Chicago present an investment seminar to illustrate the stock valuation process. As a result, Campbell and Morris have asked you to analyze the Bon Temps Company, an employment agency that supplies word processor operators and computer programmers to businesses with temporarily heavy workloads. You are to answer the following questions.
  1. What is the value of a 1-year, $1,000 par value bond with a 8% annual coupon if its required rate of return is 12%? What is the value of a similar 10-year bond?

Solutions

Expert Solution

Value of a 1-Year Bond

The Price of the is the Present Value of the Coupon Payments plus the Present Value of the face Value

Face Value of the bond = $1,000

Annual Coupon Amount = $80 [$1,000 x 8%]

Annual Yield to Maturity = 12%

Maturity Period = 1 Year

Price of the Bond = Present Value of the Coupon Payments + Present Value of the face Value

= $80[PVIFA 12%, 1 Year] + $1,000[PVIF 12%, 1 Years]

= [$80 x 0.89286] + [$1,000 x 0.89286]

= $71.43 + $892.86

= $964.29

“Value of a 1-Year Bond = $964.29”

Value of a 10-Year Bond

The Price of the is the Present Value of the Coupon Payments plus the Present Value of the face Value

Face Value of the bond = $1,000

Annual Coupon Amount = $80 [$1,000 x 8%]

Annual Yield to Maturity = 12%

Maturity Period = 10 Year

Price of the Bond = Present Value of the Coupon Payments + Present Value of the face Value

= $80[PVIFA 12%, 10 Year] + $1,000[PVIF 12%, 10 Years]

= [$80 x 5.65022] + [$1,000 x .32197]

= $452.02 + $321.97

= $773.99

“Value of a 10-Year Bond = $773.99”

NOTE

-The formula for calculating the Present Value Annuity Inflow Factor (PVIFA) is [{1 - (1 / (1 + r)n} / r], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.  

--The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)n], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.    


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