Question

In: Economics

Bond pricing and yield to maturity:  Be able to make future value and present value...

  1. 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?

Solutions

Expert Solution

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 = ( 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


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