1. **Problem Statement:** Calculate the initial balance sheet liability and the liability one year after issuance for All Talentz LLC's 10 million Naira bonds with a 7% coupon rate, 4-year maturity, when the market rate is 7.25%. 2. **Formula Used:** The bond price (initial liability) is the present value of future cash flows, which include annual coupon payments and the principal repayment at maturity, discounted at the market rate. The bond price formula is: $$P = \sum_{t=1}^n \frac{C}{(1+r)^t} + \frac{F}{(1+r)^n}$$ where: - $P$ = price of the bond - $C$ = annual coupon payment = $F \times \text{coupon rate}$ - $F$ = face value = 10,000,000 - $r$ = market interest rate per period = 7.25% = 0.0725 - $n$ = number of periods = 4 3. **Calculate Coupon Payment:** $$C = 10,000,000 \times 0.07 = 700,000$$ 4. **Calculate Present Value of Coupons:** $$PV_{coupons} = 700,000 \times \left(\frac{1 - (1 + 0.0725)^{-4}}{0.0725}\right)$$ Calculate: $$1 + 0.0725 = 1.0725$$ $$1.0725^{-4} = \frac{1}{1.0725^4} \approx \frac{1}{1.331} = 0.751$$ So: $$PV_{coupons} = 700,000 \times \frac{1 - 0.751}{0.0725} = 700,000 \times \frac{0.249}{0.0725} \approx 700,000 \times 3.434 = 2,403,800$$ 5. **Calculate Present Value of Principal:** $$PV_{principal} = \frac{10,000,000}{1.0725^4} = 10,000,000 \times 0.751 = 7,510,000$$ 6. **Calculate Initial Liability (Bond Price):** $$P = PV_{coupons} + PV_{principal} = 2,403,800 + 7,510,000 = 9,913,800$$ 7. **Calculate Liability One Year After Issue:** After one year, the bond has 3 years remaining. The carrying amount increases by amortizing the discount using the effective interest method. - Interest expense for year 1: $$Interest = P \times r = 9,913,800 \times 0.0725 = 718,750$$ - Coupon payment: $$700,000$$ - Amortization of discount: $$718,750 - 700,000 = 18,750$$ - New carrying amount: $$9,913,800 + 18,750 = 9,932,550$$ **Final answers:** - Initial liability: approximately $9,913,800$ - Liability one year after issue: approximately $9,932,550$