Question

The Altoona Company issued a 25-year bond 5 years ago with a face value of $1,000. The bond pays interest semiannually at a 10% annual rate.

1. What is the bond's price today if the interest rate on comparable new issues is 12%? Do not round intermediate calculations. Round PVFA and PVF values in intermediate calculations to four decimal places. Round the answer to the nearest cent.
   $   
2. 
   
3. What is the price today if the interest rate is 8%? Do not round intermediate calculations. Round PVFA and PVF values in intermediate calculations to four decimal places. Round the answer to the nearest cent.
   $   
4. 
   
5. Explain the results of parts (a) and (b) in terms of opportunities available to investors.
   
   The input in the box below will not be graded, but may be reviewed and considered by your instructor.
6. 
   
7. What is the price today if the interest rate is 10%? Round the answer to the nearest cent.
   $   
8. 
   
9. Comment on the answer to part (d).
   The input in the box below will not be graded, but may be reviewed and considered by your instructor.
   

Answer 1

Answer a.

Face Value of Bond = $1,000

Annual Coupon Rate = 10.00%
Semiannual Coupon Rate = 5.00%
Semiannual Coupon = 5.00% * $1,000
Semiannual Coupon = $50

Time to Maturity = 20 years
Semiannual Period = 40

Annual Interest Rate = 12%
Semiannual Interest Rate = 6%

Bond Price = $50 * PVFA (6%, 40) + $1,000 * PVF (6%, 40)
Bond Price = $50 * 15.0463 + $1,000 * 0.0972
Bond Price = $849.52

Answer b.

Annual Interest Rate = 8%
Semiannual Interest Rate = 4%

Bond Price = $50 * PVFA (4%, 40) + $1,000 * PVF (4%, 40)
Bond Price = $50 * 19.7928 + $1,000 * 0.2083
Bond Price = $1,197.94

Answer c.

If interest rate is higher than coupon rate, then bond will trade at discount.
If interest rate is less than coupon rate, then bond will trade at premium.

Answer d.

Annual Interest Rate = 10%
Semiannual Interest Rate = 5%

Bond Price = $50 * PVFA (5%, 40) + $1,000 * PVF (5%, 40)
Bond Price = $50 * 17.1591 + $1,000 * 0.1420
Bond Price = $1,000.00

Answer e.

If interest rate is equal to coupon rate, then bond will trade at par.