Question

1. Compute the market price (V_b) of the following $1,000 par value bonds with 10-year maturity: (15)

1. 8% coupon (interest rate) paid semi-annually? Assume the yield to maturity of 12%.
2. 6% coupon (interest rate) paid semi-annually? Assume the yield to maturity of 12%.
3. 8% coupon (interest rate) paid semi-annually? Assume the yield to maturity of 6%.

Based on your answers, comment on the relationship (what happens to one variable when the other goes up/down) of (a) price with yield to maturity and (b) price with coupon rate. (5)

Answer 1

i) We are given the following information:

Maturity in years	n	10
Coupon rate		8%
Semi annual frequency	frequency	2
par value	FV	1000
Discount rate	r	12.00%

Price is calculated as follows:

ii) We are given the following information:

Maturity in years	n	10
Coupon rate		6%
Semi annual frequency	frequency	2
par value	FV	1000
Discount rate	r	12.00%

iii)

We are given the following information:

Maturity in years	n	10
Coupon rate		8%
Semi annual frequency	frequency	2
par value	FV	1000
Discount rate	r	6.00%

(a) Relationship of price with yield to maturity

As YTM goes on increasing, the price goes on decreasing and vice versa. We can see this by comparaing (i) and (iii) both have 8% coupon but one has 12% YTM and other has 6% YTM, the price is higher for 6% YTM. Therefore the   relationship between YTM and price is inverse.

Further, when YTM<coupon rate, Price>par value, and when YTM>coupon rate, price<par value

(b)Relationship of price with coupon rate

As Coupon goes on increasing, the price goes on increasing and vice versa. We can see this by comparaing (i) and (ii) both have 12% YTM but one has 8% coupon and the other has 6% coupon, the price is higher for 8% coupon. Therefore the relationship between coupon and price is direct.