fixed income

what is probable change in price of 30year, semi-annual 6.5% coupon , $1000 par value Bond, yeild 8%, when the nominal risk free rate changes from 5% to 4%.

If I’m not mistaken, if the risk-free rate moves downward 1%, the other rates on the economy must do the same. So in this example the bond yield should decrease to 7% and the price would rise. Just calculate the PV of the bond cash flows and then calculate the %change in the price.

The discount rate (nominal rate) = risk free rate + inflation premium + risk premium. thus, assume 8% = rfr(5%) + ip(1%) + rp(2%). Now, if risk free rate (rfr) decreases from 5% to 4%, then the equation changes to:

7% = rfr(4%) + ip(1%) + rp(2%)

Using this new YTM to discount the bond will increase the price as Harrogath rightly stated, then you can subtract the Old PV from the New PV from ( New Pv - Old Pv ) to get the price differential, and the change in Yield will be negative {(7% / 8%)-1} = -12.5%

why are looking at the effects on bond price of any changes in nominal RFR? You should be looking at changes in yields and its effect on bond prices as this would lead to duration and convexity.