Question

Lance Whittingham IV specializes in buying deep discount bonds. These represent bonds that are trading at well below par value. He has his eye on a bond issued by the Leisure Time Corporation. The $1,000 par value bond pays 8 percent annual interest and has 17 years remaining to maturity. The current yield to maturity on similar bonds is 13 percent.

a. What is the current price of the bonds? Use Appendix B and Appendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods. (Do not round intermediate calculations. Round your final answer to 2 decimal places. Assume interest payments are annual.)
  

  
b. By what percent will the price of the bonds increase between now and maturity? (Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.)
  

Answer 1

(1)-Current Price of the Bond

The Current 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 = $80 [$1000 x 8%]

Annual Yield to Maturity = 13%

Maturity Period = 17 Years

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

= $80[PVIFA 13%, 17 Years] + $1,000[PVIF 13%, 17 Years]

= [$80 x 6.729] + [$1,000 x 0.125]

= $538.32 + $125.00

= $663.32

“The Current Price of the Bond = $663.32”

(2)- Percentage increase in the price between now and maturity

Percentage increase in price = [Par Value – Price of the Bond) / Price of the Bond] x 100

= [($1,000 – $663.32) / $663.32] x 100

= [$336.68 / $663.32] x 100

= 50.76%

“Price increases by 50.76%”

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.