Work out bond auction cut off yield instantly with clear inputs, formula shown and shareable results.
In a multiple-price auction the cut-off is the highest yield accepted and the weighted average is what successful bidders paid on average. The gap between them — the tail — measures how thin demand was at the margin.
Auction price
Price = Σ coupon/(1+y)^t + 100/(1+y)^n; tail = cut-off yield - weighted average yield
Figures are estimates based on the inputs given. Bank charges, regulatory minima and market rates change and differ between institutions and jurisdictions. This is not financial advice — confirm with your bank or treasury policy.
Weak demand — bidders were only willing to take the last bonds at a materially higher yield.
Because the cut-off yield exceeds the coupon, so the bond must be discounted to deliver that yield.