# Can I use zero rates bootstrapped from a swap curve to price a bond?

Say that some corporation has a long position in a fixed rate bond. To turn this into a float-rate asset, they take a fixed paying position in a fixed/float swap. If we are given the par swap curve, we can bootstrap the par swap rates to discount the swap cash flows at the zero coupon rates.

My question: Are we allowed to use these same zero coupon rates to discount the bond as well, or would we need to have the yield curve to calculate zero coupon rates based on the bond yield curve?

So say we have the following bond (B):
principal = 100
coupon = 6% (annual)
maturity = 3 years

And the following float receiving swap (S):
notional principle = 100
fixed rate = 6% (annual)
float = LIBOR (annual)
contract length = 3 years

If we have the following par swap curve:
1 year - 9.00%
2 year - 9.10%
3 year - 9.20%

Then we get the following bootstrapped swap zero rates:
1 year - 9.0000%
2 year - 9.1046%
3 year - 9.2126%

We can use these to value the swap S:
value S = PV(float) - PV(fixed)
To calculate the PV(fixed), we discount the cash flows with the appropriate zero coupon rates.

Now my question in this example: Are we allowed to value the bond B with the swap curve zero coupon rates as well, or are we only allowed to use this for swap valuation?

Thanks!