In: Economics
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?
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:
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