QuestionJune 1, 2025

Petty Productions Inc. recently issued 30-year 1,000 face value. 12% annual coupon bonds. The market discount rate for this bond is only 7% . What is the current price of this bond? 387.59 597.24 1,000.00 1,620.45

Petty Productions Inc. recently issued 30-year 1,000 face value. 12% annual coupon bonds. The market discount rate for this bond is only 7% . What is the current price of this bond? 387.59 597.24 1,000.00 1,620.45
Petty Productions Inc. recently issued 30-year 1,000 face value. 12% annual coupon bonds. The market discount rate for this bond is only 7% . What is the current price of this bond? 387.59 597.24 1,000.00 1,620.45

Solution
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Answer

\1,620.45 Explanation 1. Identify Bond Cash Flows The bond pays an annual coupon of 12\% on a \1,000 face value, so the annual coupon payment is \120. 2. Calculate Present Value of Coupons Use the formula for the present value of an annuity: **PV = C \times \frac{1 - (1 + r)^{-n}}{r}**, where C = 120, r = 0.07, and n = 30. PV_{\text{coupons}} = 120 \times \frac{1 - (1 + 0.07)^{-30}}{0.07} = 120 \times 12.4093 = \1,489.12 3. Calculate Present Value of Face Value Use the formula for present value: **PV = \frac{FV}{(1 + r)^n}**, where FV = 1000, r = 0.07, and n = 30. PV_{\text{face value}} = \frac{1000}{(1 + 0.07)^{30}} = \frac{1000}{7.612255} = \131.37 4. Sum Present Values Add the present values of the coupons and the face value to find the bond price. Total Price = PV_{\text{coupons}} + PV_{\text{face value}} = 1489.12 + 131.37 = \1,620.49

Explanation

1. Identify Bond Cash Flows<br /> The bond pays an annual coupon of $12\%$ on a $\$1,000$ face value, so the annual coupon payment is $\$120$.<br /><br />2. Calculate Present Value of Coupons<br /> Use the formula for the present value of an annuity: **$PV = C \times \frac{1 - (1 + r)^{-n}}{r}$**, where $C = 120$, $r = 0.07$, and $n = 30$.<br /> $PV_{\text{coupons}} = 120 \times \frac{1 - (1 + 0.07)^{-30}}{0.07} = 120 \times 12.4093 = \$1,489.12$<br /><br />3. Calculate Present Value of Face Value<br /> Use the formula for present value: **$PV = \frac{FV}{(1 + r)^n}$**, where $FV = 1000$, $r = 0.07$, and $n = 30$.<br /> $PV_{\text{face value}} = \frac{1000}{(1 + 0.07)^{30}} = \frac{1000}{7.612255} = \$131.37$<br /><br />4. Sum Present Values<br /> Add the present values of the coupons and the face value to find the bond price.<br /> Total Price = $PV_{\text{coupons}} + PV_{\text{face value}} = 1489.12 + 131.37 = \$1,620.49$
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