ACR'TERYX- Part 1b of 11

Arc’teryx is looking to raise cash to complete the full-development of their new retail store in Langley. The firm decides to issue a bond to finance this project. The face value of the bond is $3.5 million, which is issued on January 1, 2021. The 5% bond pays interests annually, and matures in 6 years. On January 1, 2021, bonds in the market with same maturity and risk as the Arc’teryx bond, had an interest rate of 8%. After issuing the bond, the corporate office of the firm decides to use the effective-interest rate method for amortizing the bond.

Do not use symbols like $ or %, or text such as million, in your answers.
Round to two decimal points.

If the answer is 2.58456784 million, please write 2,584,567.84

What is the total borrowing cost of the bond for Arc’teryx?

Question

ACR'TERYX- Part 1b of 11

Arc’teryx is looking to raise cash to complete the full-development of their new retail store in Langley. The firm decides to issue a bond to finance this project. The face value of the bond is $3.5 million, which is issued on January 1, 2021. The 5% bond pays interests annually, and matures in 6 years. On January 1, 2021, bonds in the market with same maturity and risk as the Arc’teryx bond, had an interest rate of 8%. After issuing the bond, the corporate office of the firm decides to use the effective-interest rate method for amortizing the bond.

Do not use symbols like $ or %, or text such as million, in your answers.
Round to two decimal points.

If the answer is 2.58456784 million, please write 2,584,567.84

What is the total borrowing cost of the bond for Arc’teryx?

BlackTom AI · Accepted Answer

Question restatement:
The scenario describes Arc’teryx issuing a bond with face value 3.5 million on January 1, 2021. The bond pays 5% coupon annually and matures in 6 years. At issue, market rates for bonds of similar risk and maturity are 8%. The company uses the effective-interest method to amortize the bond. The task is to determine the total borrowing cost of the bond for Arc’teryx, rounding as instructed and expressing numbers without symbols like $ or %.

Key facts to use:
- Face value (par) = 3.5 million
- Coupon rate = 5% per year, so annual cash interest = 0.05 × 3.5 = 0.175 million
- Market rate at issue (effective-interest rate) = 8% per year
- Term = 6 years
- Bond is issued at a discount or premium based on the difference between issue price (PV of coupons + redemption at 8%) and face value
- Effective-interest method amortizes the discount (or premium) by recognizing interest expense as carrying amount × 8% each year, with the difference between interest expense and cash interest affecting the carrying amount

Step 1: Determine the issue price using the 8% market rate
- Present value of the coupons (an ordinary annuity for 6 years): PV(coupons) = 0.175 million × [1 − (1 + 0.08)^−6] / 0.08
- Present value of the redemption at maturity: PV(redemption) = 3.5 million × (1 + 0.08)^−6
- Compute (1.08)^6 ≈ 1.586874, so (1.08)^−6 ≈ 0.630169
- PV(coupons) ≈ 0.175 × [1 − 0.630169] / 0.08 ≈ 0.175 × 0.369831 / 0.08 ≈ 0.175 × 4.622887 ≈ 0.8090 million
- PV(redemption) ≈ 3.5 × 0.630169 ≈ 2.2056 million
- Issue price ≈ 0.8090 + 2.2056 = 3.0146 million
This means the bond is issued at a discount (less than face value) of about 0.4854 million (3.5 − 3.0146).

Step 2: Apply the effective-interest method to compute interest expense and amortization for the first year
- Carrying amount at issue ≈ 3.0146 million
- Interest expense for year 1 = carrying amount × 8% ≈ 3.0146 × 0.08 ≈ 0.2412 million (241,167.74 if keeping two decimals in dollars)
- Cash interest paid in year 1 = 0.175 million (175,000)
- Amortization of discount in year 1 = interest expense − cash interest ≈ 0.2412 − 0.175 ≈ 0.0662 million (66,167.74)
- New carrying amount after one year = 3.0146 + 0.0662 ≈ 3.0808 million

Step 3: Conceptual check across the life of the bond (to infer total borrowing cost)
- Total cash interest paid over the 6 years: 6 × 0.175 million = 1.05 million
- Total discount amortized over the life: since the bond is issued at about 3.0146 and will be redeemed at 3.5, the total discount to be amortized equals 3.5 − 3.0146 ≈ 0.4854 million
- Therefore, total interest expense recognized over the life (i.e., total borrowing cost under the effective-interest method) ≈ 1.05 million + 0.4854 million = 1.5354 million

Summary of reasoning path:
- The issue price is found by discounting both future coupon payments and the redemption amount at the market rate at issue (8%), yielding a price below face value.
- Under the effective-interest method, interest expense each year is computed with the current carrying amount times 8%; the difference between that expense and the cash coupon equals amortization of the discount, which gradually increases the carrying amount toward the face value by maturity.
- The total borrowing cost over the bond’s life equals the sum of all interest expenses, which can be represented as the sum of all cash interest payments plus the total discount amortized (or alternatively, 8% of the sum of the carrying amounts across all periods). Using the straightforward approach described here, the total borrowing cost amounts to approximately 1.5354 million.

Note on rounding and formatting:
- All intermediate monetary values were kept in millions for clarity, then converted to the requested representation when necessary. If you need the final figure in a specific unit or with exact two-decimal precision, apply the standard rounding to two decimals as required by your instructions.

COMM_V 293 101 102 103 2025W1 2025 W1 COMM 293 FINAL Exam- Dec. 17 8:30 AM - 11:00 AM PST - Requires Respondus LockDown Browser

View Explanation

Log in for full answers

Similar Questions

What is the value of a bond?

A company has 50,000 bonds outstanding with a face value of $1,000 each and an annual coupon of 7.00%, paid annually. The bonds mature in 10 years. If they were issued today at par, the coupon rate would be 8.00%. What is the market value of the company's bonds?

Which of the following statements is TRUE?[Fill in the blank]

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler