PV of bond's cash flow face, something, discount, interest, payments

busprof

I have a question about the wording of a lesson I looked @ that doesn't seem to make sense to me. I wonder if I'm missing something them. The details of the problem itself don't really matter, but the problem is:

Bond pays coupon interest payments of 70 euros (7% of its face value) at the end of each year and will also pay the full face value of 1,000 euros at maturity in five years. Assuming a discount rate of 8%, whats the present value of the bond’s promised cash flow?

My issue is that at the end of the problem, the lesson says:

"So with a YIELD TO MATURITY of 8%, the bond's present value is 960 euros."

My question is, why are they referring to the discount rate as the YTM, when YTM means the rate of return anticipated on a bond if it is held until the maturity date, taking into account the current market price, par value, coupon interest rate and time to maturity?

Isn't the 8% just the rate we used to discount the future cash flow of the bond, which is very different from the YTM of this particular bond?! Am I missing something?

Mechanic

I'm trying to understand what you're saying. Isn't a bonds present value always less than par because of discounting? I don't understand why you are making this contingent on the fact that the required rate is 8%, while the coupon is 7%.

Thanks for your help.

Micholien

P.S. It seems that the YTM is equal to the discount rate at which the present value of all future payments would equal the present price of the bond. In other words, if you use a discount rate that does not result in the PV of all future payments being equal to the present price, then the YTM is not equal to the discount rate. Am I missing something here?

JRossSter

Oh wait I think I get what you're saying: You mean that if the required of return is 8% then then the price of the bond will drop to ensure that the YTM will equal 8%. Is that what you mean?

kasinkei

Chuckrox8 Wrote:
-------------------------------------------------------
> xwowsersx Wrote:
> --------------------------------------------------
> -----
> > Oh wait I think I get what you're saying: You
> mean
> > that if the required of return is 8% then then
> the
> > price of the bond will drop to ensure that the
> YTM
> > will equal 8%. Is that what you mean?
>
> You need to look at the basic relationship of
> coupon rates and yield to maturity.
>
> Coupon Rate>Current Yield>Yield To Maturity
> (Premium Bond)
> Coupon Rate=Current Yield=Yield To Maturity
> (Par)
> Coupon Rate<Current Yield<Yield To Maturity
> (Discount Bond)
>
> If you're are given that the coupon rate is 7% and
> the YTM is 8% you should know right off the bat
> that you are looking at a discount bond.


Chuckrox8, thanks for responding. I appreciate it. You're saying that, as an example, if a bond has a coupon rate of 7% and the YTM is 8% then its a discount bond. In this scenario the price of the bond is below par, making the coupon rate lower than the actual current yield. I think I understand this.

My only issue was how, in the original problem, was the example using the term "discount rate?"

Are you saying when it uses a "discount rate" of 8%, the question is simply saying that in our example we are dealing with a bond with a YTM of 8%, which in turn is the discount rate that we must apply in order to obtain the present value of this bond's cash flow?

rkapoor

Yes, the discount rate is the yield to maturity.

Bluetick1010

I know I'm being really slow and annoying today. But I think I finally get it. I'm complicating this too much. Is the following accurate:

In this example, the question simply asserts that this bond will have a YTM of 8%. This is also the discount rate because, conceptually, the yield to maturity (YTM) is the discount rate which returns the market price of the bond.

?

smartpants

Bingo. To go a step further, the discount rate/ytm is actually an internal rate of return which makes the pv of your bond cash flows equal to par.

JGovender

Right! You mean that's the flip-side or other logical angle of what you stated before. It's the IRR that will net the PV to par. Thank you so much again, sir. I sincerely appreciate your help on this.