Mr. Simpson buys a $1000 bond paying bond interest at j2= 6.5% and redeemable at par...

Mr. Simpson buys a $1000 bond paying bond interest at j2= 6.5% and redeemable at par in 20 years. He desires a yield rate of j4= 7%. (a) How much did he pay for the bond? (b) After exactly 5 years he sells the bond. Interest rates have dropped and the bond is sold to a buyer to yield at j1 = 5%. Find sale price. (other answer here is not correct)

Solutions

Expert Solution

(a)-The Market Price of the Bond

The Market Price of the Bond 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 = $65 [$1,000 x 6.50%]

Annual Yield to Maturity = 7%

Maturity Period = 20 Years

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

= $65[PVIFA 7%, 20 Years] + $1,000[PVIF 7%, 20 Years]

= [$65 x 10.59401] + [$1,000 x 0.25842]

= $688.61 + $258.42

= $947.03 per Bond

“The Price of the Bond will be $947.03”

(b)-The Selling price of the Bond after 5 years if the yield dropped to 5%

Face Value of the bond = $1,000

Annual Coupon Amount = $65 [$1,000 x 6.50%]

Annual Yield to Maturity = 5%%

Maturity Period = 15 Years [20 Years – 5 Years]

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

= $65[PVIFA 5%, 15 Years] + $1,000[PVIF 5%, 50 Years]

= [$65 x 10.37966] + [$1,000 x 0.48102]

= $674.67 + $481.02

= $1,155.69

“The Selling Price of the Bond will be $1,155.69”

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.

jeff jeffy answered 9 months ago

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