Part A A bond was issued 3 years ago at a coupon rate of 6%. Since then, interes

Question

Part A

A bond was issued 3 years ago at a coupon rate of 6%. Since then, interest rates have declined to 4%. The bond matures 20 years from today. Compute the current market value of this bond.

Part B

A stock paid a dividend of $1.50 yesterday. The stock is expected to grow at a rate of 4% per year indefinitely. Investors require a return of 13% to invest in this stock. Compute its fair market value.

Part C

A stock’s next 3 dividends are as follows: $0.50, 0, $1.00. After that, the stock is expected to grow at a rate of 2% indefinitely. The required return on this stock is 12%. Compute its intrinsic value.

Explanation / Answer

Answer:

Part A: Assume the face value of bond = $1,000

Value of the bond = The present value of the bond's interest payments+Present value of the maturity amount of the bond

Annual Interest amount = $1,000*6% = $60, Remaining period = 17, market Interest rate = 4%

The present value of the bond's interest payments = $60*[{(1+0.04)17-1}/0.04(1+0.04)17] = $729.94

present value of the bond's maturity amount = $1000/(1+.04)17 = $513.37

Current market value of this bond = $729.94+$513.37= $1,243.31

PART-B

As per Gorden's dividend growth model - Fair market value = {$1.50(1+0.04)}/(0.13-0.04) = $1.56/0.09 = $17.33

PART-C

Intrinsic value of stock

= Present value of dividend payment for next three years + Present value of at the intrinsic value of the stock at the end of year 3

= $0.5/(1+0.12) + 0+ $1/(1+0.12)3+ ${(1+ 0.02)/(0.12-0.02)}/(1+0.02)3 = 0.446+0+0.712+9.612 = $10.77

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