Subjects finance

Current Yield E9A23D

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1. **State the problem:** We need to find the current yield of Well Foods bonds. 2. **Given data:** - Face value $F = 1000$ - Coupon rate $c = 9\% = 0.09$ - Yield to maturity (YTM) = 8\% (not directly needed for current yield) - Time to maturity = 5 years (not needed for current yield) 3. **Formula for current yield:** $$\text{Current Yield} = \frac{\text{Annual Coupon Payment}}{\text{Current Market Price}}$$ 4. **Calculate annual coupon payment:** $$\text{Annual Coupon Payment} = c \times F = 0.09 \times 1000 = 90$$ 5. **Calculate current market price:** Since the bond's yield to maturity is 8\%, which is less than the coupon rate, the bond price will be above face value. However, for current yield, we need the current price. Price $P$ can be approximated by the present value of coupons and face value discounted at YTM: $$P = \sum_{t=1}^5 \frac{90}{(1+0.08)^t} + \frac{1000}{(1+0.08)^5}$$ Calculate each term: $$\frac{90}{1.08} = 83.33$$ $$\frac{90}{1.08^2} = 77.16$$ $$\frac{90}{1.08^3} = 71.44$$ $$\frac{90}{1.08^4} = 66.15$$ $$\frac{90}{1.08^5} = 61.25$$ Sum of coupons present value: $$83.33 + 77.16 + 71.44 + 66.15 + 61.25 = 359.33$$ Present value of face value: $$\frac{1000}{1.08^5} = 680.58$$ Total price: $$P = 359.33 + 680.58 = 1039.91$$ 6. **Calculate current yield:** $$\text{Current Yield} = \frac{90}{1039.91} = 0.0865 = 8.65\%$$ **Final answer:** The current yield of the bond is approximately **8.65\%**.