Question

1. Five years ago, Natalia Sandino bought a 30-year 6.5%, $1,000 bond. The bond pays interest annually. She wants to sell the bond after receiving the fifth annual dividend. Similar bonds are being issued that pay 7%. What is Natalia’s bond worth today? Round to the nearest cent.

2. Holiday Hotel Corporation has 1,500,000 shares of common stock and 150,000 shares of cumulative preferred stock. The annual dividend on the preferred stock is $4.75 per share. The only dividends paid last year were to preferred stockholders in the amount of $2.50 per share. This year the board of directors decides to distribute $3,750,000 in dividends. You own 50 shares of common stock. What amount will you receive this year? Round to the nearest cent.

Answer 1

1. Present value of bond (Natalia’s bond worth today) = Present value of face value + present value of interest payment

=face value / (1+market interest)^{number of payment} + interest [1 - (1+market interest)^{-number of payment}] / market interest

   = $1000 /(1+0.07)²⁵ + ($1000*6.5%)[1 - (1+0.07)^-25] / 0.07

= $1000 /(1.07)²⁵ + $65[1 - 1/(1.07)²⁵] / 0.07

= $1000 /5.427433 + $65[1 - 1/5.427433] / 0.07

= 184.25 + 757.48

= $941.73

2. Dividend in arrears (for cumulative preferred stock) = [$4.75 - $2.5] * 150000 shares

= $337500

  Total distributable dividend = $3,750,000

less: dividend in arrears = $337500

   less: cumulative preferred stock.current year dividend [$4.75*150000] = $712500

   Dividend to be distributed to common stockholder = $2700000

Common stock dividend on 50 shares = $2700000 / 1500000 shares * 50 shares

= $90