Three year annual coupon bond FV=1000, coupon=5.5%
Spot rates:Y1=5.2% Y2=5.5% Y3=5.7%
value of bond:
a)995.06
b)937.66
c)1000
Answer is A. You discount each coupon by the spot rate that corresponds to that cash flow, you do not multiply the rates, you raise the corresponding rate to the Nth power
Also conceptually, you can knock out C automatically as the rate for the 3rd cash flow is 5.7 and that is the largest cash flow by far. That is a rate greater than the coupon so you can fairly assume it will not be greater than or equal to 1000.
PV =55/(1.052)^1 + 55/(1.055)^2 + (1000+55)/(1.057)^3
PV = 53.66 + 49.41 + 893.36
PV = 996.44
Thus Option A i’ll go for.
Thanks. So when do you multiply the rates ? When forward rates are given ?
Yessir
Also when spot rates are given.
As in when you have to use combo of spot and forward?
That’s one possibility.
Another is that they simply give you the spot rate for each cash flow, as in your original example.
Why would you muliply spot rates? I am getting confused, can you please give an example?
My mistake; I misread your question. Sorry about that.
The only time you compound (multiply) rates is when you’re given spot and forward rates.
No problem. Thanks.
When u r asked to find 1yr forward rate 1 yr from now and the 1st &2nd yr spot rates r given then u use-
(1+s2)^2=(1+s1)(1+fy1y1).
When need to value a bond @ present, then usually spot rates , s1, s2… these r given, maybe z-spreads r also given which needs to be added to the spot rates for discounting all cash flows.
There would not be _z-spread s _; there’s a single z-spread which is added to all spot rates.
Sorry for writing ‘spreads’, I didn’t mean z spread is a variable. Z spread is a constant term and spot rates r variables
lol… nearly got confused there…