Question

1. What is the relationship between the price of a bond and its YTM?

2. Explain why some bonds sell at a premium over par value while other bonds sell at a discount. What do you know about the relationship between the coupon rate and the YTM for premium bonds? What about for discount bonds? For bonds selling at par value?

3. What is the relationship between the current yield and YTM for premium bonds? For discount bonds? For bonds selling at par value?

4. The Back Street Girls Corporation has two different bonds currently outstanding. Bond M has a face value of GH¢20,000 and matures in 20 years. The bond makes no payments for the first six years, then pays GH¢1,000 every six months over the subsequent eight years, and finally pays GH¢1,750 every six months over the last six years. Bond N also has a face value of GH¢20,000 and a maturity of 20 years; it makes no coupon payments over the life of the bond. If the required return on both these bonds is 14 percent compounded semiannually, what is the current price of Bond M? Of Bond N?

Answer 1

a) There is an inverse relation between  price of the bond and its YTM. Higher the price lower the return and the lower the price the higher the return on the bond.

b) When bonds are issued some of them trade at a price which is above thre face value of the bond, these are premium bonds. Wheras some trade below the face valuw. These are discount bonds.The reason is because the YTM of premium bonds is lower than the coupon rate on these bonds. Thus investors have to pay a premium to get a higher coupon rate than what is available in the market. And vice - versa for discount bonds.

Premium bonds YTM=lower than Coupon rate

Discount bonds YTM=Higher than Coupon rate

Par bonds YTM=Same as Coupon rate

c) For premium bonds YTM is less than current yeild, whereas for discount bonds YTM is higher than current yeild. Par bonds have YTM and current yeild as same

d) for this question the following formula can be used to calculate price of each bond:

Bond Price = ∑(Couponn / (1+YTM)^n )+ P / (1+YTM)^n

Here YTM is 14% or 7% semiannual. Coupon(n) is coupon payments, P is the face value payment, n is the period

Sum all the values for each period to get the current price of the bond

Apply this formula to get the