Question

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?

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?

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

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?

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?

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

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?

Answer 1

Price of bond = C x PVIFA (r, n) + F x PVIF (r, n)

F = Face value

C = Coupon amount = F x Coupon rate/Annual coupon frequency

r = Periodic interest rate

n = Number of periods to maturity

1)

F = $ 1,000

C = $ 1,000 x 0.1 = $ 100

r = 12 %

n = 20

Price of bond = $ 100 x PVIFA (12%, 20) + $ 1,000 x PVIF (12%, 20)

                        = $ 100 x 7.4694 + $ 1,000 x 0.1037

                        = $ 746.94 + $ 103.70 = $ 850.64

2)

F = $ 1,000

C = $ 1,000 x 0.1 = $ 100

r = 8 %

n = 20

Price of bond = $ 100 x PVIFA (8 %, 20) + $ 1,000 x PVIF (8 %, 20)

                        = $ 100 x 9.8181 + $ 1,000 x 0.2145

                        = $ 981.81 + $ 214.50 = $ 1,196.31

3)

We concluded that for a constant coupon rate and years to maturity, bond price inversely proportional to the required return.

If required return > Coupon rate; bond price < Par value; Discount bond

If required return < Coupon rate; bond price > Par value; Premium bond

4)

F = $ 1,000

C = $ 1,000 x 0.1 = $ 100

r = 13 %

n = 30

New Price of bond = $ 100 x PVIFA (13 %, 30) + $ 1,000 x PVIF (13 %, 30)

                        = $ 100 x 7.4957 + $ 1,000 x 0.0256

                        = $ 749.57 + $ 25.60 = $ 775.17

5)

F = $ 1,000

C = $ 1,000 x 0.1 = $ 100

r = 13 %

n = 10

New Price of bond = $ 100 x PVIFA (13 %, 10) + $ 1,000 x PVIF (13 %, 10)

                        = $ 100 x 5.4262 + $ 1,000 x 0.2946

                        = $ 5.4262 + $ 29.46 = $ 837.22

6)

It is concluded that par bond can change to discount bond if required return increased than coupon rate and bond price is inversely proportional to years to maturity. Price of bond nearer to maturity is more than the bond with a larger maturity period.

If required return > Coupon rate, bond price < Par value; Discount bond

7)

Expected dividend D₁ = D₀ x (1 + g)

                                        = $ 2 x (1+0.03)

                                        = $ 2 x 1.03 = $ 2.06

As per DDM,

        Price of stock = D₁ / (r – g)

                                 = $ 2.06/ (10 % - 3 %)

                                = $ 2.06/ (0.1 – 0.03)

                                 = $ 2.06/0.07

                                 = $ 29.4285714285714 or $ 29.43

Current price of stock is $ 29.43