Redemption Yield of treasury stock

Kemik

Kemik

Kemik

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Hey,

I'm doing some revision for a securities markets module and the same question comes up on each exam but I cannot find the equation in my notes. I've googled and asked over at TSR but no one seems to be able to help.

I know the equation for the redemption yield of treasury stock if I have dates and a purchase price but I don't so I'm a bit stuck.

Calculate the approximate redemption yield on 4% Treasury Stock maturing in 5 years time, when the current market price is 80
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My fantastic lecturer doesn't use email (he's old school) and doesn't put the past exam paper answers in the library, just the questions.

Is it safe to assume that the purchase price is 100 so the coupon would be 4 for each year? In which case I'm gonna take a guess and use the dividend pricing model to get a 5% return. Is the approximate redemption yield 5%? Edit: with a purchase price of 100 it would give a capital gain of 5% bringing the total to 10%. This is all assuming a purchase of 100.

Any help? Thanks guys.
 
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To solve it, you need to equate price to present value of all future payments (coupons + face value, discounted).

You'd have:

80 = 100/(1+i)^5 + 4/(1+i) + 4/(1+i)^2 + 4/(1+i)^3 + 4/(1+i)^4 + 4/(1+i)^5.

i is your yield to maturity (i.e. redemption yield). It's tough to solve that though (which is why the question asks for an approximation).
 
Without a financial calculator you need to use trial and error to get the right answer, using the following equation;

B = Cn/(1+R)^1 + Cn/(1+R)^2 + ..... + Cn + P/(1+R)^n


Where

B is the bond price

Cn is the gross coupon (if you are working out the Gross Redemtion Yield or the Internal Rate of Return)

So, the bond pays £4 per year as the flat yield is based on the par value of £100, the bond price is £80 and you need to find 'R'. So plug in some values and work from there, unless you have a financial calcuator in which case you can just work it out.
 
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So I have to take a guess at the redemption yield and keep trying till it gets close to 80? Stupid question. If he hadn't put "maturing in five years" I could have just used a perpetuity and done 4/80.

Thanks guys.
 
Indeed, the fact that N is specified makes it all the more difficult and so you can't write it in general form.

There may be an online calculator that can do this for you?
 
N9ne said:
Indeed, the fact that N is specified makes it all the more difficult and so you can't write it in general form.

There may be an online calculator that can do this for you?
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Probably. It's just the question will have different figures in the exam. Financial calculators aren't allowed either :(
 
That's not an appropriate question for an exam then unless you have a few different bonds to compare and you're assuming the expectations theory holds, but that's a whole different question.
 
10 Mark question too. I've emailed him but it'll probably take days for him to reply. Luckily the exam isn't until a week Monday. Until then I'll ask around with some friends to see what they think of the question.
 
If I saw that in an exam, I'd look to find a discount rate that'd give a zero NPV for all cash flows - from purchase to redemption.

Your cash flow at t(0) is the purchase price of 80. Cash flows from t(1) to t(5) are the coupon of 4. Also at t(5) is the redemption of the bond at 100.

The procedure is called linear interpolation - you pick an IRR that gives you a negative NPV. Choose another that gives you a positive NPV (the closer together these IRRs are, the more accurate your answer). You then know that between these two IRRs, there is a solution to your equation i.e. plotting these numbers on a graph, the solution is the point at which a line through the two coordinates crosses the x-axis. If you have some annuity tabes to hand it's a quick exercise to calculate the NPV of the coupon payments without faffing around with powers on the calculator. Jotting some numbers down and using 5% (where NPV = 15.7) and 10% (where NPV = -2.7) as my 'potential' IRRs, I got 9.3% as an overall answer.
 
My exam is tomorrow. I received a reply to my email on friday

Sorry for the delay in replying to your enquiry about redemption yield. The purchase price is the current market price. In the formula as I used it market value is the purchase price. The future value is the redemption value of £100.

**lecturer name removed**

-----Original Message-----
From: Harrison, Sean
Sent: 04 May 2008 19:42
To:
Subject: RE: Any problems!

Hello,

I've been looking at the past papers from previous years and have found a small question I'm having difficulty with.

"Calculate the approximate redemption yield on 4% Treasury Stock maturing in 5 years time, when the current market price is 80."

I'm a bit confused. I cannot use the redemption yield formulas I've found in books unless I have the purchase price as well as the market price. Can you confirm what formula I'd need to answer this question please?

My guess is either 5% (4/80) or if I set a purchase price of 100 (I remember reading somewhere that bonds come usually priced at 100) then the capital gains element would increase this to 10%.

Thanks,

Sean Harrison
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That doesn't really help with a formula! It just confirms my assumptions about the redemption amount. I've got two equations, the one from above that you guys gave (as an annuity) verse the following

Yield on income
cpn/market price *100

Yield on capital gain/loss
(discount/years) / market price *100

Add the two above together
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The annuity formula gives me between 12% and 13% while the formula above gives 10%.
 
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