Too Young, Incorporated, has a bond outstanding with a coupon rate of 6.2 percent and semiannual payments. The bond currently sells for $943 and matures in 19 years. The par value is $1,000. What is the company's pretax cost of debt?

Question

BlackTom AI · Accepted Answer

First, restating the problem helps set the stage: a bond with a semiannual coupon of 6.2% annual on a $1,000 par pays 31 every six months, it has 19 years to maturity (38 semiannual periods), and it’s currently priced at $943. We’re asked for the pretax cost of debt, which is the bond’s yield to maturity (annualized).

Option A: 6.81%. If the semiannual yield were 3.405% (since 6.81% annual nominal would split to two equal semiannual payments), the present value of coupons and par repayment would need to equal 943. Computing roughly, the factor (1+i)^-38 with i≈0.03405 gives a v^38 around 0.28–0.29, and the annuity present value term would likely produce a price near or above 943 but not as precisely as the calculation below. In short, 6.81% is slightly high for a price of 943 with a 6.2% coupon, making this option less likely than the correct figure.

Option B: 7.24%. A higher yield than 6.74% would push the price well below 943 for a 6.2% coupon, given the same 38 periods remaining. If i per half-year were around 3.62%, the present value of the coupons (31 times an annuity factor around 20–22) plus the redemption PV would typically fall short of 943. Therefore this option overstates the cost of debt for this bond.

Option C: 6.74%. This corresponds to a semiannual yield of about 3.37% (since 6.74% nominal annual divided into two periods). Checking PV: v = 1/(1+0.0337) ≈ 0.9679. v^38 ≈ 0.28. Annuity factor (1 - v^38)/i ≈ (1 - 0.28)/0.0337 ≈ 0.72/0.0337 ≈ 21.3. Then PV of coupons ≈ 31 × 21.3 ≈ 660.3, plus PV of par ≈ 1000 × 0.28 ≈ 280, totaling ≈ 940–943. This aligns well with the given price, making 6.74% the correct estimate of the pretax cost of debt.

Option D: 7.00%. If the nominal annual yield is 7.00%, the semiannual yield is 3.50%. With i = 0.035, v^38 ≈ (1/1.035)^38 ≈ e^{38 ln(1/1.035)} ≈ e^{-38×0.0344} ≈ e^{-1.307} ≈ 0.271. Annuity factor ≈ (1 - 0.271)/0.035 ≈ 0.729/0.035 ≈ 20.83. PV of coupons ≈ 31 × 20.83 ≈ 645.7. PV of par ≈ 271. The total ≈ 917, which is notably below 943, indicating this yield is too high given the price, so this option is not consistent with the data.

Option E: 3.31%. This would be extraordinarily low for a 19-year bond’s pretax cost of debt with a 6.2% coupon and a price under par; the semiannual yield would be about 1.655%. The PV factors would produce a price well above par, not 943, making this option clearly implausible for the given price and coupon.

In summary, among the provided choices, option C (6.74%) yields a present value closest to the actual price of 943 when using the bond’s semiannual coupon structure and 38 periods remaining. The other options produce either prices noticeably above or below 943 when applied to the same cash-flow schedule, indicating their inaccuracy in this scenario.

Too Young, Incorporated, has a bond outstanding with a coupon rate of 6.2 percent and semiannual payments. The bond currently sells for $943 and matures in 19 years. The par value is $1,000. What is the company's pretax cost of debt?单项选择题

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