Gargoyle Unlimited Gargoyle Unlimited is planning to issue a zero coupon bond to fund a project that will yield its first positive cash flow in three years. That cash flow will be sufficient to pay off the entire debt issue. The bond's par value will be $1,000, it will mature in 3 years, and it will sell in the market for $727.25. The firm's marginal tax rate is 40 percent. Refer to Gargoyle Unlimited. What is the expected after-tax cost of this debt issue

The answer is 6.72%

Explanation:

Calculating the imputed rate from a discount bond as follows:

( 1 + i  )^n = FV / PV  

( 1 + i )^3 = FV / PV,   here FV= 1000 and PV= 727.25

so putting values in equation we have:

( 1 +i )^3 = 1000 / 727.25  

( 1 + i )^3 = 1.375  

solving for i

( 1 + i) = 1.375^1/3  

( 1 + i ) = 1.112  

i = 0.112 before tax rate

0.112 * (1 - tax rate) = after tax interest rate

0.112 * .60 = 0.0672 = 6.72%

thus the expected after tax cost of this debt issue is 6.72%

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