Question

Part A

Seven years ago you’ve purchased a corporate bond for $960 paying an annual coupon rate of 9%. At that time the YTM was 10% and there were 10 years left to maturity. Today, the YTM on your bond is 8%.

Will the price of this bond be lower or higher than its face value? Why?

Calculate the current price of this bond.

Part B

YMCA Company’s preferred stock pays a dividend of $12 per year. If the stock sells for $90 and the next dividend will be paid in one year, what return would you require for investing in this company?

Answer 1

Part A

Price of the bond and yield have inverse relationship. Here, as the YTM has gone down, the price of the bond would increase. Since, the YTM of 8% is less than the coupon rate, the price of the bond would be higher than the face value. The reason being as this bond is paying 9% coupon as compared to the interest rate available in market at 8%, the demand of the bond is higher and hence, the price

To calculate the current price of the bond:

YTM = 8%, Year to Maturity = 3 years (10-7), Face Value = 960 and Coupon = 9%

Price = (9%*960)/(1+8%) + (9%*960)/(1+8%)^2 + (9%*960)/(1+8%)^3 + 960 / (1+8%)^3 =

Price = 86.4 / 1.08 + 86.4 / 1.1664 + 86.4 / 1.259712 + 960 / 1.259712

Price = 80 + 74.07407 + 68.58711 + 762.079 = 984.7401

Part B:

Using Dividend Discount Model

Price of share = Dividend (1 + growth) / (rate of return - growth rate)

Considering, it's a preferred stock and hence, dividend are usually constant

Hence, 90 = 12 / (rate of return)

Rate of return = 12 / 90 = 13.33%