Yield To Maturity?

Question

i cant remember the correct method for calculating YTM......example:
A bond makes annual interest payments of $75. The bond matures in four years, has a par value of $1,000, and sells for 975.30 (market value). What is the bonds YTM?

now i realise that for example the % to par is 7.5% and the bond is selling at a discount as it is valued at 975.30 so the interest must be higher than 7.5%. So the next stage is to calculate by making to guess's as to what the interest rate is so i would choose 8% and 12%. I would use these figures in the Po= cf/(1+r)^n......... to incorporate the time value of money and so on and so forth. then obviously i would be given to end values for both sets of interest so that i could find the market price of 975.30. But where do i go from here? the percentage that i get is out everytime , i know the figure is 8.25%. I am not using excel for this or a financial calculator......so no answers in this format. if you can help, much appreciated.

Answer 1

The YTM is the IRR of the cash flows so.....

975.3/(1+r)^0=75/(1+r)^1

+75/(1+r)^2+75/(1+r)^3+

1075/(1+r)^4.

I came up with 8.3% when I did it in excel.

Hope this helps.

Answer 2

Yield to maturity or YTM is the yield that equates the future cash inflows of cash with the initial investment.
The formula using your initial data is,
975.3=75(PVIFA)4,r+1000/75(75)(PVIF)4,r
Now since it is 7.5 coupon bond the YTM will remain close to 7.5 so by trial and error you can get the YTM. Here use a compound interest table to figure out Present Value Interest rate of an Annuity and Present value interest factor for 4 years and r%. r% will be close to the coupon rate.
If you refer to 'Financial Management by Van Horn you will find a point form formula which will give directly the approximate YTM.

Answer 3

I guess you haven't been invited to any parties tonight.