[g13544055]

Hi guys,
Just a quick question as I am studying this at the minute. Say I purchase a bond for a nominal value of £50,000, on a maturity of 6yrs, with 5% annual interest (non compound just to make it easy). The following year I want to sell this bond on, but interest rates are now 8% say, with the same maturity date. Obviously someone would rather buy a bond at £50,000 with the higher interest rate, so I would have to sell mine for less to attract customers, as they will want the same yield.

Taking the flat yield to be = (coupon rate/market price) x 100%
Coupon rate on my bond = £2500 per annum.

So, 8%= (2500/market price) x 100%
therefore market price = 31250

So after year one I have made 2500 in interest, and can sell my bond at the dearest of 31250, so I'm actually losing money because I spent 50,000, and only getting back 31250+2500=36750. Is that right? Lol.

Would you advise me to hold on to my bond, and wait until it matures, or at least until interest rates fall?

Basically I want to know if I have done this right, and also, do you not get your investment back from a bond until the redemption date? Or is it paid back annually?

Thanks, B.:D

[ArcSine]

Actually, whether you hold or sell, you'll earn an overall return of 5%, either way, assuming you reinvest the sales proceeds at the prevailing market rate. That's probably counterintuitive at first, but follow through a simple illustration:

I'll use a zero-coupon bond, and annual compounding, for simplicity.

I buy a two-year zero which matures at 1,000. The paper is priced to yield 5%, so I pay 907.03. Certainly, by holding to maturity, my annual return is = 5%. So far so good.

Instead, suppose I sell after one year, at which time the market is pricing this bond to yield 8%. With a single cash flow of 1K occurring in one year, I'll be selling for 925.93. By immediately reinvesting the 925.93 for one year at 8%, I'll receive 1,000 at the end of that second year (natch, you could see where this was going).

Either way, I originally parted with 907.03 and then received 1,000 two years later, whether I held the original paper, or sold and reinvested. Thus, I earned a two-year overall return of 5% per year under either scenario.

The same logic and mathematics will hold when you introduce the additional wrinkles in your situation (e.g. interim cash flows represented by the bond's coupon payments).

On a side note, if you sell after one year, you're selling a stream of future cash flows which play out as 2,500 per year for 4 years, and then 52,500 one year later, as the maturity payout. At a market rate of 8%, you'd be selling for 44,011, not 31,250.

By reinvesting that 44,011 at 8% for the remaining 5 years, you'll find that your overall 6-year return comes out to an annual average of exactly 5%.

Hope that helped a bit.

[g13544055]

I see where you are coming from.

I'm only starting with this kind of thing, and it's just as a side interest!

If I sell my bond on to the buyer with the same maturity date, they keep my 5% rate. If they buy my bond for 44,011, they only make a profit of 12,500 (through interest, 5 x 2,500) at the redemption date, plus 5989 ( from the 50,000 maturity pay out, take away the 44,011 they paid for the bond). That makes a total of 18489. However if they had of bought a bond for 50,000 at the 8% rate for 5 years, it would make a profit of 20,000.. so why would they buy mine?

Also, what formula did you use to work out the sell on price?

Thanks.

[g13544055]

I see where you are coming from.

I'm only starting with this kind of thing, and it's just as a side interest!

If I sell my bond on to the buyer with the same maturity date, they keep my 5% rate. If they buy my bond for 44,011, they only make a profit of 12,500 (through interest, 5 x 2,500) at the redemption date, plus 5989 ( from the 50,000 maturity pay out, take away the 44,011 they paid for the bond). That makes a total of 18489. However if they had of bought a bond for 50,000 at the 8% rate for 5 years, it would make a profit of 20,000.. so why would they buy mine?

Also, what formula did you use to work out the sell on price?

Thanks.

[morgaine300]

You're leaving out the fact that the buyer can take the 5989 they didn't pay for yours and stick that into something else earning 8%. If they purchased a 50,000 bond actually paying 8% they have to pay 5989 more for it and tie up that money. If they buy yours, it's available. Yes, they're getting less return on your bond, but they're also tying up less money to get it. That's the entire point of your bond getting discounted.

In a way it's like saying if I stick $10,000 into this thing I'll get a return of $1000. Or if I stick $15,000 in it, I'll get $1500. Wow, $1500 is a greater return -- yeah, and I got to put more in it to get more. That doesn't mean I'm getting a "better" return. I'm getting the same return relative to what I put into it.

The value of something like this is based on the present value of it. That idea can be a little quirky if you're just learning. A present value is basically what you would have to invest today in order to get a certain amount (or amounts) in the future. What they will get in the future is those 2500 interest payments, which is a series of payments, plus they will get the 50,000 back in 5 years.

So the present value of that is whatever amount it would take at the 8% in order to get that particular return. That's where the 44K came from. So the buyer needs 44K to get the return on your bond: the interest payments and the payback of the face value. The buyer will need 50K to get a new 50K bond actually paying 8%. If he gets yours, he still has 6K free. An amount you have now is its own present value, so add that to the 44K present value of your bond, and they both come out to 50K total present value.

Don't know how much sense that is making.

[ArcSine]

If I sell my bond on to the buyer with the same maturity date, they keep my 5% rate. If they buy my bond for 44,011, they only make a profit of 12,500 (through interest, 5 x 2,500) at the redemption date, plus 5989 ( from the 50,000 maturity pay out, take away the 44,011 they paid for the bond). That makes a total of 18489. However if they had of bought a bond for 50,000 at the 8% rate for 5 years, it would make a profit of 20,000..so why would they buy mine?

Also, what formula did you use to work out the sell on price?

Thanks.

You're viewing the problem as a simple comparison of amounts paid vs amounts received. But when dealing with bonds--their pricing under various conditions, how much you could sell for, how much someone would be willing to pay to acquire a bond--you have to also factor in the timing of the cash flows.

What I'd suggest is for you to do a little research into "Present Value" (and its alter ego, "Future Value") in the context of finance and economics. At its basic level it's pretty simple stuff, but you'll need to understand the concept in order to answer the kind of question you asking about.

A little taste of the basic idea can be wrapped inside a simple example: Suppose I offer to sell you a bond which pays a single cash flow: The bond pays its owner $100 one year from today. Assume that you can earn 8% on similar investments at the time. So how much would you pay me for this bond?

You'd be willing to pay $92.59. Why? Because if you invested your 92.59 for one year in any other investment, after one year that investment would give you back 92.59 plus 8% interest on your money, which is 92.59 x 8% = 7.41. Thus in total you'd be getting back 92.59 + 7.41 = 100, one year from now.

Therefore, by paying me 92.59 today for the bond, and receiving the bond's lone cash flow of 100 one year from now, you'd be receiving precisely the same benefit you'd get from investing your 92.59 anywhere else, at 8%, for one year. Or equivalently, by paying me 92.59 for the bond, you're earning exactly 8% on your bond investment.

Now I'll change it up slightly. The bond's single cash flow of 100 happens not one year from today, but two. In that case, you'd only be willing to pay 85.73 for the bond. Your reasoning would correctly go as follows: If you invested 85.73 at 8% for one year, after one year you'd have 85.73 + 8% interest, which is 85.73 + 6.86, for a total of 92.59 after one year. You'd then invest the 92.59 for another year at 8%, which as we've already seen, will give you 100 after one year.

Therefore, paying me 85.73 today for the bond, and receiving 100 from the bond in two years, would exactly replicate the cash flow you'd get from investing your 85.73 anywhere else, at 8%, for two years.

So even though the bond's cash flow of 100 was the same under both scenarios, the price of the bond changed, as it was affected by the timing of that cash flow.

But as I said, spend a little time exploring this concept further, as a proper answer to your original question really depends on a decent understanding of the Present Value concepts. Good News I: The basics aren't difficult at all. Good News II: The basics form the foundation of some pretty powerful and far-reaching concepts, if you choose to pursue them. Best of luck!

[g13544055]

Thanks guys, that's great help. I'm a graduate in pure mathematics, so I'm quite pedantic about everything! Lol. Not to pursue this any further, but I just realised that if I bought that bond for 44K, I would still have 5989 spare (if I was originally going to spend 50k on a bond), and I could invest this at a rate of 8% (if I was willing to tie it up). After five years it would yield a nice return. I think it is all starting to make sense! Lol. Thanks guys.

[ArcSine]

With an academic background in pure mathematics, you'll find the 'applied' topic of bond valuation to be smooth sailing.

For a pretty good jumping off point, Fabozzi's Fixed Income Mathematics gets you up to speed on the basics in no time flat. When you're ready for a more in-depth treatment I think it's hard to beat Martellini, Priaulet, & Priaulet's Fixed Income Securities.

Cheers!

[amdeist]

Hi guys,
Just a quick question as I am studying this at the minute. Say I purchase a bond for a nominal value of £50,000, on a maturity of 6yrs, with 5% annual interest (non compound just to make it easy). The following year I want to sell this bond on, but interest rates are now 8% say, with the same maturity date. Obviously someone would rather buy a bond at £50,000 with the higher interest rate, so I would have to sell mine for less to attract customers, as they will want the same yield.

Taking the flat yield to be = (coupon rate/market price) x 100%
Coupon rate on my bond = £2500 per annum.

So, 8%= (2500/market price) x 100%
therefore market price = 31250

So after year one i have made 2500 in interest, and can sell my bond at the dearest of 31250, so i'm actually losing money because i spent 50,000, and only getting back 31250+2500=36750. Is that right? lol.

Would you advise me to hold on to my bond, and wait until it matures, or at least until interest rates fall?

Basically I want to know if i have done this right, and also, do you not get your investment back from a bond untill the redemption date? or is it paid back annually?

Thanks, B.:D

Bonds have historically been a good investment if you believe the interest rates are going to drop. Bond values are inversely proportional to interest rates. With rates at all time lows, it seems almost like an oxymoron that people would be buying bonds today. Without a doubt, interest rates are going to rise significantly when the recession is over and we start growing again. Economists would have us believe that this is next week, but seeing is believing. When the FED starts raising interst rates to either cool off the economy or prevent inflation, bonds will not be the investment of choice.