Question

1)Trees Inc. has outstanding a fixed coupon, $1,000 par value bond with 10 years remaining until maturity. The bond makes semi-annual coupon payments and the annual coupon rate is 6 percent. If the annual discount rate is 10%, what will be the price of this bond?

2) Horizon Co. just paid a dividend of $3.50.  The dividend is paid on annual basis.  The required annual rate of return is 12 percent.  If the dividend is expected to grow at 2 percent every year, what should be the stock price?

3)A ten-year bond pays 8 percent annual coupon on the semiannual basis.  Also, this bond pays a face value of $1,000.  If similar bonds are currently yielding 12 percent annually, what is the market value of the bond?

Answer 1

Question 1:

C = Semi annual coupon = $1,000 * 6%/2 = $30

n = 10*2 = 20 semi annual compoundings

P = Par value = $1,000

r = discount rate = 10%/2 = 5%

Price of bond = [C*[1 - (1+r)^-n] / r] + [P / (1+r)^n]

= [$30 * [1 - (1+5%)^-20] / 5%] + [$1,000 / (1+5%)^20]

= [$30 * 0.623111 / 0.05] + [$1,000 / 2.65329]

= $373.8663 + $376.8895

= $750.7558

Therefore, price of this bond is $750.76

Question 2:

Current Dividend = D0 = $3.50

g = growth rate = 2%

r = required return = 12%

Expected dividend = D1 = D0*(1+g) = $3.50 * (1+2%) = $3.57

Stock Price = D1 / (r-g)

= $3.57 / (12%-2%)

= $3.57 / 10%

= $35.7

Therefore, Stock price is $35.7

Question 3:

C = Semi annual coupon = $1,000 * 8%/2 = $40

n = 10*2 = 20 semi annual compoundings

P = Par value = $1,000

r = discount rate = 12%/2 = 6%

Price of bond = [C*[1 - (1+r)^-n] / r] + [P / (1+r)^n]

= [$40 * [1 - (1+6%)^-20] / 6%] + [$1,000 / (1+6%)^20]

= [$30 * 0.688195273 / 0.06] + [$1,000 /3.20713547 ]

= $344.097637 + $311.804727

= $655.902364

Therefore, market value of the bond is $655.90