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

Face value – 6,000.

Coupon rate – 5% or $ 300.

Price - $ 5,000.

T – 10 years.

> YTM = C + (F-P)/n

                   (F+P)/2

>             300 + (6000-5000)/10

                    (6000+5000)/2

                = 7.27%.

2. With the changes, Coupon for first 4 years remains $300 and becomes $120 for year 5. Face value also changes to $ 5,250. Putting these values in the formula below in excel and equating PV to $5,000, return works out to 6.25%.

It is less than YTM since the price and coupon on the bond has fallen sharply.

                300/(1+r) + 300/(1+r)^2 + …. + 120/(1+r)^5 + 5,250F/(1+r)^5.

	6.25%
1	2	3	4	5	5	Total PV
300	300	300	300	120	5,250
282	266	250	235	89	3,878	5,000

3. Using the same formula till year 4 and using F = 5,100, the return works out to 6.45%.

Since return is better in this case, he would have been better selling in Year 4.

	6.45%
1	2	3	4	4	Total PV
300	300	300	300	5,100
282	265	249	234	3,971	5,000