Question

0. Bond pricing and yield to maturity:

   •  Be able to make future value and present value calculations with given values of i and n. For example, what is the future value of $500 saved for two years at a 5% annual interest rate?

   •  How does present value change for larger values of i? How does it change for larger values for n?

   •  What is a debt instrument? What are the three main characteristics of a debt instrument?

   •  What is the bond pricing formula? What does it say about the relationship between a bond’s

     expected price and its future coupon and principal payments?

     •  Be able to calculate a bond price for given F, C, n, and i. For example, what is the predicted

       price of a 2-year bond with a $5,000 face value and $250 coupon payments if market interest

       rates are 5%?

     •  What is a nominal yield? What is a current yield? What is their relationship if a bond is sold

       at a premium or discount? (HW#6)

     •  How do bond prices adjust to higher or lower interest rates? How do bond yields to maturity

       adjust to higher or lower interest rates?

     •  How do bond prices change for short-term versus long-term bonds? Which is predicted to be

       more volatile over time?

   •  What is the predicted relationship between inflation and bond prices?

Answer 1

1) Future Value = Present value * ( 1 + i )ⁿ

= 500 * (1+0.05)²

= 551.25

2) Assuming larger value of i = 10%, Future Value = 500*(1+0.1)² = 605

So, with larger values of i, Future value goes up.

Assuming a larger value of n = 4 , Future Value = 500 * (1+0.05)⁴ = 607.75

So, with larger values of n, Future value goes up.

3) A debt instrument is a paper or electric obligation that enables the issuing party to raise funds by promising to repay a lender in accordance with terms of a contract.

Three main characteristics of debt instrument are as follows:

• It has definite maturity
• Income is fixed because of interest rates mentioned in contract
• Legally binding

4)   Bond pricing formula is as follows :

P = ( $\sum$ CF / (1+i)ⁿ )+ M / (1+i)ⁿ ; C = coupon payment at every period, M = maturity value , n= number of coupon payments.

It says that coupon payments are discounted at every period and added with the discounted maturity value to give the present value of bond.

5) 5000 = 250/ (1+0.05)¹ + 250/(1+0.05)² + M/(1+0.05)²  

= 238.09 + 226.75 + M/(1+0.05)²

or, 4535.16 = M/(1+0.05)²

^or, 5000.01 = M

6) Nominal yield is the coupon rate of a bond or fixed security and this is fixed. Current yield is investment's annual income divided by current price of security.

For discounted bond, Current yield > nominal yield

For premium bond, Current yield > nominal yield