Question

1. What should the current market price be for a bond with a $1,000 face value, a 10% coupon rate paid annually, a required rate of return of 12%, and 20 years until maturity?

2. What should the current market price be for a bond with a $1,000 face value, a 10% coupon rate paid annually, a required rate of return of 8%, and 20 years until maturity?

3. What generalizations about bond prices can you make given your answers to #1 and #2?

4. A bond has a market price of $1,000, a $1,000 face value, a 10% coupon rate paid annually, a required rate of return of 10%, and 30 years until maturity. If the required rate of return immediately increased to 13%, what is the new market price of the bond?

5. A bond has a market price of $1,000, a $1,000 face value, a 10% coupon rate paid annually, a required rate of return of 10%, and 10 years until maturity. If the required rate of return immediately increased to 13%, what is the new market price of the bond?

6. What generalizations about bond prices can you make given your answers to #4 and #5?

7. The CFO of Brady Corp. announces that the firm plans to grow its annual dividend at a rate of 3% forever. The company just paid its annual dividend (Do) of $2.00 per share. If the required rate of return on Brady’s stock is 10%, what should the current price of the stock be?

8. Page 253: ST1

9. Page 253: ST2

10. Page 254: #2b, c

Answer 1

Answer : Calculation of Current market Price when market rate is 12%

Current Market Price = (Coupon * PVAF @ 10% for 20 years) + (Face vaue * PVF@ 10% for 20th year)

Coupon = 1000 * 10% =100

Face Value = 1000

Value of Bond = (100 * PVAF @ 12% for 20 years) + (1000 * PVF@ 12% for 20th year)

= (100 * 7.46944362384) + (1000 * 0.10366676504)

= 746.944362384 + 103.66676504

= 850.61

Calculation of Current market Price when market rate is 8%

Current Market Price = (Coupon * PVAF @ 8% for 20 years) + (Face vaue * PVF@ 8% for 20th year)

Coupon = 1000 * 10% =100

Face Value = 1000

Value of Bond = (100 * PVAF @ 8% for 20 years) + (1000 * PVF@ 8% for 20th year)

= (100 * 9.81814740671) + (1000 * 0.21454820735)

= 981.814740671 + 214.54820735

= 1196.36

Generalization : If the market Rate is more than Coupon rate , Bond will trade at discount . But if the market Rate is less than coupon Rate ,Bond will trade at Premium.

2.) Calculation of New Market Price if maturity is 30 years :

Old Market Price will be $1000 (As the copupon Rate and market rate is same )

New Market Price =

Current Market Price = (Coupon * PVAF @ 13% for 30 years) + (Face vaue * PVF@ 13% for 30th year)

Coupon = 1000 * 10% =100

Face Value = 1000

Value of Bond = (100 * PVAF @ 13% for 30 years) + (1000 * PVF@ 13% for 30th year)

= (100 * 7.4956534384) + (1000 * 0.02556505284)

= 749.56534384 + 25.56505284

= 775.13

Calculation of New Market Price if maturity is 10 years :

Old Market Price will be $1000 (As the copupon Rate and market rate is same )

New Market Price = = (Coupon * PVAF @ 13% for 10 years) + (Face vaue * PVF@ 13% for 10th year)

Coupon = 1000 * 10% =100

Face Value = 1000

Value of Bond = (100 * PVAF @ 13% for 10 years) + (1000 * PVF@ 13% for 10th year)

= (100 * 5.42624347582) + (1000 * 0.2945883481)

= 542.624347582 + 294.5883481

= 837.21

Generalization : If the maturity period is reduced the market Price will Increase.

3) Current Stock Price = [Expected Dividend / (Required Rate of return - Growth rate)]

= [(2 * 1.03) / (0.10 - 0.03)]

= 2.06 / 0.07

= 29.42857 or 29.43