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Worked-example setupScope and assumptions
- Cedar Trail Sensors, its financing packet, counterparties, dates, terms, and amounts are fictional and supplied for instruction.
- The bond is issued on an interest date for $2,000,000 face, matures after four years, bears 6 percent annual stated interest paid semiannually, and has eight equal coupon periods.
- An 8 percent nominal annual market yield with semiannual compounding is supplied by an approved valuation source for this instrument and date; learners do not infer it from the workbook.
- The $25,000 closing invoice is stipulated to qualify as a direct debt issuance cost; the example does not decide whether another fee qualifies.
- The cost-adjusted periodic effective yield is solved from net proceeds and unchanged contractual cash flows.
- Period
- Four years from the fictional January 1, 2028 issue date
- Units
- US dollars and nominal annual rates with semiannual compounding
- Rounding
- Retain full precision in all calculations; display dollars to cents and rates to at least six decimals
Cedar Trail issues one bond, but the financing produces several different amounts. Move from contract cash flows to issue price, net carrying amount, interest expense, and the maturity balance. Keep each amount in its proper place.
Contract map: one instrument, several amounts
Cedar Trail promises eight $60,000 coupon payments and $2,000,000 principal at maturity. Face supplies principal and coupon cash. The approved market yield prices those cash flows. The closing invoice affects net carrying amount, not the holder's contractual receipts.
| Field | Supplied fact | Controlled use |
|---|---|---|
| Face amount | $2,000,000.00 | Maturity principal and coupon base |
| Stated annual rate | 6.00% | Convert to 3.00% each half-year |
| Market annual yield | 8.00% | Convert to 4.00% each half-year for price |
| Coupon periods | 8 | Discounting horizon |
| Qualifying issuance costs | $25,000.00 | Reduce opening net carrying amount |
Price the promised cash flows
coupon cash = $2,000,000 × 6% ÷ 2 = $60,000
coupon present value = $60,000 × [1 − (1.04)^−8] ÷ 0.04
principal present value = $2,000,000 × (1.04)^−8
issue price = $1,865,345.102500992
discount = $2,000,000 − $1,865,345.102500992
= $134,654.897499008
Price is below face because the supplied market yield exceeds the stated coupon rate. That difference is a financing basis layer, not an immediate loss or a freestanding asset.
Bridge price to opening net carrying amount
issue price before costs $1,865,345.10
less: supplied qualifying issuance costs (25,000.00)
opening net carrying amount $1,840,345.10
The unchanged cash flows solve to a 4.195237022474 percent semiannual effective yield on net proceeds. Using 4 percent on the cost-adjusted basis would strand the issuance costs and force an unexplained maturity plug. ASC 835-30-45-1A requires the company to subtract qualifying issuance costs when it presents the related debt. The company does not report those costs as a separate deferred asset.
Effective-interest schedule
| Period | Opening carrying amount | Cash interest | Interest expense | Carrying increase | Ending carrying amount |
|---|---|---|---|---|---|
| 1 | $1,840,345.10 | $60,000.00 | $77,206.84 | $17,206.84 | $1,857,551.94 |
| 2 | 1,857,551.94 | 60,000.00 | 77,928.71 | 17,928.71 | 1,875,480.65 |
| 3 | 1,875,480.65 | 60,000.00 | 78,680.86 | 18,680.86 | 1,894,161.51 |
| 4 | 1,894,161.51 | 60,000.00 | 79,464.56 | 19,464.56 | 1,913,626.07 |
| 5 | 1,913,626.07 | 60,000.00 | 80,281.15 | 20,281.15 | 1,933,907.22 |
| 6 | 1,933,907.22 | 60,000.00 | 81,131.99 | 21,131.99 | 1,955,039.21 |
| 7 | 1,955,039.21 | 60,000.00 | 82,018.53 | 22,018.53 | 1,977,057.74 |
| 8 | 1,977,057.74 | 60,000.00 | 82,942.26 | 22,942.26 | 2,000,000.00 |
The displayed cents do not drive the next row; full-precision balances do. The schedule reaches face through the same effective-yield formula in every period. ASC 835-30-35-2 and 35-3 connect the constant rate on opening carrying amount to the difference between interest expense and contractual interest cash.
Opening and first-interest entries
One transparent detail-account presentation is:
Dr Cash $1,840,345.10
Dr Discount and issuance-cost detail 159,654.90
Cr Bonds payable $2,000,000.00
Dr Interest expense $77,206.84
Cr Cash $60,000.00
Cr Discount and issuance-cost detail 17,206.84
The exact account presentation follows the entity's controlled chart and applicable guidance. The arithmetic model does not qualify costs, choose the market yield, interpret the indenture, or approve disclosure.
Release checks
- The coupon stream and maturity principal trace to the contract map.
- Price equals the present value of those streams at the supplied matched yield.
- Price less qualifying costs equals opening net carrying amount.
- Every row uses opening carrying amount times one solved periodic yield.
- Total carrying increase equals face less opening net carrying amount.
- The final balance reaches face without overwriting the calculated last row.
Cedar Trail's schedule connects one contract to five controlled amounts. They are $2,000,000 face, $1,865,345.10 issue price, $1,840,345.10 opening net carrying amount, $60,000 first-period cash interest, and $77,206.84 first-period interest expense. A different coupon, market yield, term, or qualifying cost changes the numbers but not their separate roles.
Quantitative companions
Choose from 2 ways to work with this calculation.
Verified calculation · debt effective interest analysis
The curriculum loader recomputed this example before it entered the site build. Expand any structured input to inspect the stated facts.
- debt issues
- 1 field
Inspect data
{
"cedar_trail_bond": {
"face_amount": 2000000,
"issuance_costs": 25000,
"market_annual_rate": 0.08,
"payments_per_year": 2,
"stated_annual_rate": 0.06,
"total_periods": 8
}
}Recomputed result
| Measure | Value |
|---|---|
| ending carrying amount | 2,000,000 |
| gross discount | 134,654.8975 |
| issuance costs | 25,000 |
| issue price | 1,865,345.1025 |
| net periodic yield | 0.042 |
| opening net carrying amount | 1,840,345.1025 |
| period 1 carrying amount change | 17,206.8391 |
| period 1 ending carrying amount | 1,857,551.9416 |
| period 1 interest expense | 77,206.8391 |
| periodic cash interest | 60,000 |
| total cash interest | 480,000 |