Question

Suppose that a Detroit municipal bond was bought at issue for $5,000. Its maturity was ten years, the face value was $6,000 and the coupon rate was 5%. a) What was the initial yield to maturity? b) Suppose that in year 5 the coupon was cut to 2% and the face value was cut by $5,250 due to bankruptcy. What annual return did the bond holder experience? Is it greater than or less than the yield ot maturity? Why? c) If the bond holder could have sold in year four at a price of $5,100 (after receiving the year 4 coupon) would s/he have been better off than waiting until year 5 and experiencing the bankruptcy (as described in part b))? Explain.

Answer 1

a. Initial yeild to maturity can be calculated as follows:

Face value= $6000. Coupon rate= 5% per annum

Coupon value per annum = 5/100 * 6000= $300 per annum

Coupon value for 10 years = 10* 300= $3000

Initial yeild to maturity = isuue price + coupon value for 10 years= $8000

b. If the coupon rate falls to 2% on face value = $5250 from year five, Coupon value from year 5 to 10= 2% of 5250 = $105 per annum which translates to $630 (105*6) for the six years (year 5,6,7,8,9,10).

Coupon rate for the first four years = 300 *4 = $1200.

Hence, at the end of ten years, net yeild to maturity= initial isuue price + coupon value for years 1 to 4 + coupon value for years 5 to 10 = 5000 + 1200 + 630 = $6830.

To calculate annual return in this case we use the following calculations:

rate of return (annual) = [{(6830 - 5000)/ 5000} * 100] / number of years = 3.66%

This rate of return is lower than the initial cuopon rate (3.66% < 5%) because of reduced coupon rate and reduced face value owing to bankruptcy.

c. Yes, the person would have been better off by selling his bond in the fourth year instead of waiting. This is because year 5 saw a coupon rate cut and a lower face value yeilding a rate of return lower in year five than the previous four years. The net (combined) annual rate of return, hence, would have been less than the initial 5%