Question

On May 1, 2024, Cullumber Corp. issued $905,000 of 5-year, 5% bonds at $866,401. This price resulted in an effective interest rate of 6% on the bonds. The bonds pay interest semi-annually on May 1. Cullumber's year end is April 30. Date May 1, 2024 Interest Payment Interest Expense Discount Amortization Bond Carrying A Nov. 1, 2024 May 1, 2025 Nov. 1, 2025 May 1,2026 Nov. 1, 2026 May 1, 2027 Nov. 1, 2027 May 1, 2028 Nov. 1, 2028 May 1,2029

Answer 1

To calculate the present value of a bond, we need to discount the future cash flows using the appropriate discount rate. In this case, we have a 5-year, 5% coupon bond that pays interest semi-annually. By calculating the present value of each interest payment and the principal repayment at maturity, we can determine the total present value of the bond. In this case, the present value of the bond is $864,485 when the discount rate is 6%.

Step-by-step explanation:

To calculate the present value of a bond, we need to discount the future cash flows using the appropriate discount rate. In this case, we have a 5-year bond that pays semi-annual interest of 5% on May 1 each year. The bond was issued at a price of $866,401, which resulted in an effective interest rate of 6%. To calculate the present value of the bond, we need to calculate the present value of each interest payment and the principal repayment at maturity.

To calculate the present value of each interest payment, we can use the formula PV = C/((1+r/n)^(n*t)), where PV is the present value, C is the coupon payment, r is the interest rate, n is the number of compounding periods per year, and t is the number of years until the payment is received.

Since the bond pays interest semi-annually, there will be 10 interest payments in total (5 years * 2 payments per year). Let's calculate the present value of the interest payments:

1. Nov. 1, 2024: PV = $905,000 * 0.05 / ((1+0.06/2)^(2*0.5)) = $22,625
2. May 1, 2025: PV = $905,000 * 0.05 / ((1+0.06/2)^(2*1)) = $21,370
3. Nov. 1, 2025: PV = $905,000 * 0.05 / ((1+0.06/2)^(2*1.5)) = $20,144
4. May 1, 2026: PV = $905,000 * 0.05 / ((1+0.06/2)^(2*2)) = $18,946
5. Nov. 1, 2026: PV = $905,000 * 0.05 / ((1+0.06/2)^(2*2.5)) = $17,776
6. May 1, 2027: PV = $905,000 * 0.05 / ((1+0.06/2)^(2*3)) = $16,633
7. Nov. 1, 2027: PV = $905,000 * 0.05 / ((1+0.06/2)^(2*3.5)) = $15,517
8. May 1, 2028: PV = $905,000 * 0.05 / ((1+0.06/2)^(2*4)) = $14,426
9. Nov. 1, 2028: PV = $905,000 * 0.05 / ((1+0.06/2)^(2*4.5)) = $13,360
10. May 1, 2029: PV = $905,000 * 0.05 / ((1+0.06/2)^(2*5)) = $12,318

To calculate the present value of the principal repayment at maturity, we can use the same formula with the principal amount and the number of years to maturity in place of the coupon payment and the number of years until the payment is received. Since the bond will mature in 5 years, the present value of the principal repayment is:

Principal Repayment: PV = $905,000 / ((1+0.06/2)^(2*5)) = $705,640

To calculate the total present value of the bond, we sum the present values of the interest payments and the principal repayment:

Total PV = $22,625 + $21,370 + $20,144 + $18,946 + $17,776 + $16,633 + $15,517 + $14,426 + $13,360 + $12,318 + $705,640 = $864,485

Therefore, the present value of the bond is $864,485 when the discount rate is 6%.