(Cost of debt) AlterU has the option to issue 15-year bonds at $1,180 with a flotation cost of 7%, tax rate of 34%, and a coupon rate of 6% (paid annually). What is AlterU firm’s cost of debt prior to tax?

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BlackTom AI · Accepted Answer

We start by identifying the key numbers: the bond is issued at 1,180, with flotation costs of 7%, a 15-year maturity, annual coupon of 6% on par value, and a corporate tax rate (which will be relevant for after-tax cost but not for the pre-tax calculation). The question asks for the firm’s cost of debt prior to tax, i.e., the yield to maturity on the debt using the net proceeds from the issue.

First, determine the net proceeds to the firm. If flotation costs are 7% of the issue price, net proceeds = 1,180 × (1 − 0.07) = 1,180 × 0.93 = 1,097.40 per bond. This is the cash the firm actually receives per bond sold.

Next, identify the cash flows the firm will pay to investors. The coupon is 6% annually, so on a face value of 1,000, the annual coupon is 60. At maturity after 15 years, the firm will repay 1,000.

Now solve for the yield to maturity (pre-tax cost of debt) that equates net proceeds to the present value of remaining cash flows:
- Price (net proceeds) = 1,097.40
- Coupon = 60 per year for 15 years
- Redemption = 1,000 at year 15
- Yield to maturity i satisfies: 60 × a-angle-15-i + 1,000 × v^15-i = 1,097.40, where a-angle-15-i is the present value of an annuity for 15 periods and v is 1/(1+i).

Test option values to see which aligns with 1,097.40. If i ≈ 5.06% (0.0506):
- (1 + 0.0506)^15 ≈ 2.097, so v^15 ≈ 0.477.
- a-angle-15-0.0506 ≈ (1 − 0.477)/0.0506 ≈ 0.523/0.0506 ≈ 10.34.
- PV of coupons ≈ 60 × 10.34 ≈ 620.4.
- PV of redemption ≈ 1,000 × 0.477 ≈ 477.
- Total PV ≈ 620.4 + 477 ≈ 1,097.4, which exactly matches net proceeds.
Thus, the pre-tax cost of debt is about 5.06%.

Now evaluate the other options:
- 5.88%: At a higher yield, the PV of coupons plus redemption would be lower than the net proceeds (1,097.4). Since the computed PV with 5.06% already matches, a 5.88% result would underprice the bond in present value terms, giving a PV significantly below 1,097.4, which is inconsistent with the given net proceeds.
- 5.24%: This value is closer to 5.06% but still would yield a present value a bit different from 1,097.4. You can check by computing a-angle-15-0.0524 and v^15 for redemption; the PV would not align exactly with 1,097.40, so this would be incorrect for the given net proceeds.
- 4.34%: A much lower yield would push the PV well above 1,097.4, meaning the bond would have net proceeds higher than 1,097.4 if priced at that yield, which contradicts the stated net proceeds after flotation costs.

In summary, only the yield of about 5.06% produces a present value that matches the net proceeds of 1,097.40 when discounting the 60 annual coupons for 15 years plus 1,000 at the end. The other options fail to reproduce that equivalence when you run the cash flows through the standard YTM formula.

MSB-250-300-002 Topic 9 Quiz

(Cost of debt) AlterU has the option to issue 15-year bonds at $1,180 with a flotation cost of 7%, tax rate of 34%, and a coupon rate of 6% (paid annually). What is AlterU firm’s cost of debt prior to tax?

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