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boyakko [2]
3 years ago
15

Calculate the after-tax cost of debt using following bond information. A four year bond has a 7 percent coupon rate and a $1000

face value. If the market value of the bond is $788, assuming that the bond makes annual coupon payments and the tax rate is 35%.
a. 7.16 %
b. 14.32 %
c. 12.12 %
d. 9.31 %
e. 5.01 %
Business
1 answer:
miv72 [106K]3 years ago
3 0

Answer:

d. 9.31 %

Explanation:

in order to solve this question you cannot use the approximate yield to maturity since it will yield an approximation, but not an exact answer:

approximate YTM = {70 + [(1,000 - 788)/4]} / [(1,000 - 788)/2] = 13.76%

after tax cost of debt = 13.76% x 0.65 = 8.94%, but that is not an option

we must determine the exact yield to maturity which is determined by the following formula:

$788 = $70/(1 + i) + $70/(1 + i)² + $70/(1 + i)³ + $1,070/(1 + i)⁴

the simplest way to solve this is by using a financial calculator since the math is complicated. The exact yield to maturity = 14.324%

after tax cost of debt = 14.324% x (1 - tax rate) = 14.324% x 0.65 = 9.31%

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The present value of a deferred perpetuity is $1,938.89.

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The present value of a prospective sum of money or cash flow stream given a specified return rate is known as its present value (PV). The present value of future cash flows is reduced by the discount rate, and the higher coupon rate, the lower the present value of future cash flows. The key to correctly valuing future cash flows, whether they are earnings or debt obligations, is determining the appropriate discount rate. The concept of present value states that a quantity of funds today is worth greater than the same amount in the long term. In other words, money gained in the long term is not as valuable as money received today.

The present value of a deferred perpetuity that pays $141 annually with the first payment occurring at year 5 is $1,938.89. This can be calculated by taking the present value of an ordinary annuity formula, which is PV = A / (1 + r)^n, and adding 5 to n. This gives the equation PV = A / (1 + r)^(n + 5), which can be simplified to PV = A / (1 + r)^n * (1 + r)^5. Thus, the present value is $141 / (1 + 0.06)^10 * (1 + 0.06)^5, which equals $1,938.89.

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