How to calculate YTM on non zero-coupon bonds?

Question

Without a financial calcultor, or computer. Does anyone know the formula, really need for the exam. Wasn't given by the lecturer. Thank you.
The zero coupon YTM is par value divided by the present value price as far as I know.
If you know any good websites that give exmples with explanations, that would be really helpful, thank you.
Maria.

ok I havean example two year 7%coupon bond with face vlue of 1000 and current price of 1034.3
the answer my teacher gave me is 5.15% for YTM
using the formula from the internet I get a negative value close to the value of 5.15% what am or could I be doing wrong? please help!!!!!!!!!!!!!!!!

thank you so much for replying Ranto this is the question from past exam paper:
A 10-year bond trading at par with a 5% coupon will change in price by
what percentage if the yield-to-maturity changes to 6%? (Round the
proportional change in price to the nearest tenth of a percent and assume a
face value of $100.)
A. Fall by 7.4%
B. Fall by 5.0%
C. Increase by 2.4%
D. Increase by 7.7%
E. Price will not change
F. Increase by 1%
the answer to this is apparently A) fall by 7.4%

24. What is the yield-to-maturity of a two-year 8% fixed-coupon bond? (Round
the yield to the nearest hundredth of a percent.)
A. 8.00%
B. 8.57%
C. 9.79%
D. 10%
E. 9.00%
F. 9.29%

The solution is C. How????

Answer 1

The yield of a zero coupon bond is NOT the par value divided by the price. The formula for the PV of a zero coupon bond is:

PV = Par/(1+Y/M)^N

where Par is the par value (we usually use 100), Y is the yield, M is the number of compounding periods per year, and N is the number of periods until you get the payment. In the case where you have the price, Y is the only unknown. You can use algebra to find the YTM. You get:

(1+Y/M)^N = Par/PV

Y = (Par/PV)^(1/N) - 1

For coupon bearing bonds, you can find the PV by getting the present value of each cash flow and adding them up. If there are a lot of coupons being paid, then you can use the annuity formula for finding the present value of the coupon payments and then add the PV of the final principal payment.

However, there is no formula that exists for algebraically finding the yield of a coupon bearing bond with five or more coupons (this is a mathematical theorem proved by N Abel -- who proved that there is no general solution for polynomials of degree five or greater). The way that we usually find the yield is to guess. Based on how far off we are, we guess again. We keep doing this until we find an answer that is close to being right.

Your professor will not ask you to find the yield of a coupon bearing bond. He may give you the yield & ask you to find the price.

Let's look at your example & show how to find the price if you are given the yield.

Bonds have a coupon payment -- so this bond will pay 3.5% every six months (7% per year paid twice a year is 3.5 per half year). That means $35 every six months. At the end of two years, you also get your principal back -- so you get $1035. The annual yield is 5.15% -- so for each half year, we get 5.15%/2. The PV of each cash flow is:

1. 35/(1+5.15%/2)^1 = 34.12137
2. 35/(1+5.15%/2)^2 = 33.26481
3. 35/(1+5.15%/2)^3 = 32.42974
4. 1035/(1+5.15%/2)^4 = 934.9196

Add these four numbers together and you get 1034.735.


Notice that this is actually a little higher than the price you gave. If we want more precision, we need to bring down the price by using a slightly lower yield. We could guess at this (in a smart way) to get a better estimate of the yield.

If you do things right, it should take about five or six guesses to find the yield that gives the right answer to the penny. As I said, it is impossible to find the exact answer.

Answer 2

Zero Coupon Bond Price Calculator

Answer 3

Zero Coupon Bond Formula

Answer 4

maybe help