Pricing Bonds and Shares14 Aug 2024 12:23
It’s raining so, as promised, my understanding of how to calculate bond prices for existing issues when interest rates change. The same concept can be used to price shares based on on future cash generation.
Assume you have a bond, duration 5yrs, coupon £10pa and maturity value £100. The coupon is the cash paid out each year.
What is its price? Now you don’t need to this for a new bond, as it will probably be issued at £ 100 to reflect a prevailing interest rate of 10%, but let’s do the calculation from the future cash flows to demonstrate the maths by discounting the future coupon and maturity value by the coupon rate (which becomes the discount rate).
You do this by dividing the coupons and maturity value by (1 + discount rate/100) which is in this example (1 + 10/100) which in turn equals 1.1 - once for the first year, twice for the second year and so on. Thus:
For year 1 divide £10 by 1.1 once to give £ 9.09
For year 2 divide £10 by 1.1 twice to give £8.26
For year 3 divide £10 by 1.1 thrice to give £ 7.51
For year 4 divide £10 by 1.1 four times give £ 6.83
For year 5 divide £10 by 1.1 five times to give £ 6.21
For year 5 also divide the maturity value of £100 by 1.1 five times to give £62.09
Add all these discounted values together you get £100 exactly - the calculated bond price from future cash flows. It is interesting to note that this price is made of several numbers, each of which is associated with a future cash flow. So the £7.51 discounted value is associated with the £10 coupon of year 3 - £7.51 compounding by multiplying by 1.1 three times is £ 10.
So to get the bond price if the prevailing interest rates rise to 15%, you discount the existing coupons and maturity value as above by 15%, giving a sequence of numbers of:£8.70;£7.56;£6.58;£5.72;£4.97;£49.72 which, if added together, gives the calculated reduced bond price of £83.24.
If the prevailing interest rate falls to 5%, the bond price would increase to £121.65.
The same basic concept is used to value shares by Buffett and most brokers . But there are difference in that you don’t actually have a duration or a defined figure for cash flows and a defined maturity value. You need to estimate these yourself to get an idea of what the SP should be. And a company has a book value now that must, too, be added.
All my understanding - DYOR.