Question

There is a bond that pays $100 per year interest, with a $1,000 par value. It matures in 15 years. The market required yield to maturity on a comparable bond is 12%.

1. What is the value of the bond?
2. How does the value change if the yield to maturity on a comparable bond increase to 15%? What if it decreases to 8%.
3. Explain the above questions (part b) with the concepts of interest rate risk, premium bonds and discount bonds.
4. Recalculate the answer in b, with the assumption that the bond matures in 5 years (instead of 15 years).
5. Explain the above questions (part d) with the concepts of interest rate risk, premium bonds and discount bonds.

Clearly show which EQUATIONS could be used to solve the problem mathematically

Indicate the detailed steps on how to use FINANCIAL CALCULATOR or Equations from the Textbook to solve the problems.

Answer 1

Q. 1). If yield to maturity is 12 % :-

Value of bond = Present value of interest on bond + Present value of principal on bond.

= 100 * Cumulative present value factors for 15 years at 12 % + 1000 / (1.12)¹⁵

= 100 * 6.81 (using present value factor table) + 1000 / 5.4736

= 681 + 183 (approx).

= $ 864 (approx).

Q. 2). If yield to maturity is 15 % :-

Value of bond = Present value of interest on bond + Present value of principal on bond.

= 100 * Cumulative present value factors for 15 years at 15 % + 1000 / (1.15)¹⁵

= 100 * 5.85 (using present value factor table) + 1000 / 8.137

= 585 + 123 (approx).

= $ 708 (approx).

Q. 3). If yield to maturity is 8 % :-

Value of bond = Present value of interest on bond + Present value of principal on bond.

= 100 * Cumulative present value factors for 15 years at 8 % + 1000 / (1.08)¹⁵

= 100 * 8.56 (using present value factor table) + 1000 / 3.172

= 856 + 315 (approx).

= $ 1171 (approx).

Conclusion :-

Q. 1). If yield to maturity is 12 %, Value of bond	$ 864
Q. 2). If yield to maturity is 15 %, Value of bond	$ 708
Q. 3). If yield to maturity is 8 %, Value of bond	$ 1171