Question

Which of the following investments has greater value today (you must show your work in calculating the values)?

a) 200 shares of Numbers, Inc. common stock. Numbers will pay its first dividend 5 years from today in the amount of $4 per share. Over the next 3 years (years 6, 7, and 8), the dividend will grow by 20% per year, after which the growth rate would be a constant rate of 3%, forever. The appropriate discount rate for Number’s stock is 10.5%.

b) 10 bonds of Letters Corp. Each bond makes semiannual coupon payments of $35, has a face value of $1000, has 8 years remaining to maturity, and is priced to reflect an annual YTM of 7.2%.

Answer 1

Value of shares is equal to the present value all future dividends

= 4/(1.105)⁵ + 4(1.2)(1.105)⁶ + 4(1.2)²/(1.105)⁷+4(1.2)³/(1.105)⁸ + 4(1.2)³(1.03)/(10.5%-3%)*(1.105)⁷

= $53.743

Value of 200 shares today = $53.743*200 = $10,748.6

Value of bond is equal to the present value of interest payments as well as principal amount

= 35*PVAF(3.6%, 16 periods) + 1,000*PVF(3.6%, 16 periods)

= 35*12.003 +1,000*0.5679

= $988.03

Value of 10 bonds = $9880.3

Hence, value of a)shares is greater