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Unformatted text preview: aturity will be: P24 = $1,000/1.0452 = $915.73 Year 24 interest deduction = $1,000 – 915.73 = $84.27 338 c. Previous IRS regulations required a straight-line calculation of interest. The total interest received by the bondholder is: Total interest = $1,000 – 110.71 = $889.29 The annual interest deduction is simply the total interest divided by the maturity of the bond, so the straight-line deduction is: Annual interest deduction = $889.29 / 25 = $35.57 d. 13. a. The company will prefer straight-line methods when allowed because the valuable interest deductions occur earlier in the life of the bond. The coupon bonds have an 8% coupon which matches the 8% required return, so they will sell at par. The number of bonds that must be sold is the amount needed divided by the bond price, so: Number of coupon bonds to sell = $30,000,000 / $1,000 = 30,000 The number of zero coupon bonds to sell would be: Price of zero coupon bonds = $1,000/1.0460 = $95.06 Number of zero coupon bonds to sell = $30,000,000 / $95.06 = 315,589 b. The repayment of the coupon bond will be the par value plus the last coupon payment times the number of bonds issued. So: Coupon bonds repayment = 30,000($1,080) = $32,400,000 The repayment of the zero coupon bond will be the par value times the number of bonds issued, so: Zeroes: repayment = 315,589($1,000) = $315,588,822 Challenge 14. To calculate this, we need to set up an equation with the callable bond equal to a weighted average of the noncallable bonds. We will invest X percent of our money in the first noncallable bond, which means our investment in Bond 3 (the other noncallable bond) will be (1 – X). The equation is: C2 8.25 8.25 X = C1 X + C3(1 – X) = 6.50 X + 12(1 – X) = 6.50 X + 12 – 12 X = 0.68182 339 So, we invest about 68 percent of our money in Bond 1, and about 32 percent in Bond 3. This combination of bonds should have the same value as the callable bond, excluding the value of the call. So: P2 P2 P2 = 0.68182P1 + 0.31819P3 = 0.68182(106.375) + 0.31819(134.96875) = 115.4730 The call value is the difference between this implied bond value and the actual bond price. So, the call value is: Call value = 115.4730 – 103.50 = 11.9730 Assuming $1,000 par value, the call value is $119.73. 15. In general, this is not likely to happen, although it can (and did). The reason that this bond has a negative YTM is that it is a callable U.S. Treasury bond. Market participants know this. Given the high coupon rate of the bond, it is extremely likely to be called, which means the bondholder will not receive all the cash flows promised. A better measure of the return on a callable bond is the yield to call (YTC). The YTC calculation is the basically the same as the YTM calculation, but the number of periods is the number of periods until the call date. If the YTC were calculated on this bond, it would be positive. 340 CHAPTER 16 CAPITAL STRUCTURE: BASIC CONCEPTS
Answers to Concepts Review and Critical Thinking Questions 1. Assumptions of the Modigliani-Miller theory in a world without taxes: 1) Individuals can borrow at the same interest rate at which the firm borrows. Since investors can purchase securities on margin, an individual’s effective interest rate is probably no higher than that for a firm. Therefore, this assumption is reasonable when applying MM’s theory to the real world. If a firm were able to borrow at a rate lower than individuals, the firm’s value would increase through corporate leverage. As MM Proposition I states, this is not the case in a world with no taxes. 2) There are no taxes. In the real world, firms do pay taxes. In the presence of corporate taxes, the value of a firm is positively related to its debt level. Since interest payments are deductible, increasing debt reduces taxes and raises the value of the firm. 3) There are no costs of financial distress. In the real world, costs of financial distress can be substantial. Since stockholders eventually bear these costs, there are incentives for a firm to lower the amount of debt in its capital structure. This topic will be discussed in more detail in later chapters. False. A reduction in leverage will decrease both the risk of the stock and its expected return. Modigliani and Miller state that, in the absence of taxes, these two effects exactly cancel each other out and leave the price of the stock and the overall value of the firm unchanged. False. Modigliani-Miller Proposition II (No Taxes) states that the required return on a firm’s equity is positively related to the firm’s debt-equity ratio [RS = R0 + (B/S)(R0 – RB)]. Therefore, any increase in the amount of debt in a firm’s capital structure will increase the required return on the firm’s equity. Interest payments are tax deductible, where payments to shareholders (dividends) are not tax deductible. Business risk is the equity risk arising from the nature of the firm’s operating activity, and is directly related to the systematic risk of the firm’s assets. Financial risk is th...
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