An investor has two bonds in her portfolio, Bond C and Bond Z. Each bond matures in 4 years, has a face value of $1,000, and has
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Answer:
Ans. The after tax cost of this bond is 2.09%
Explanation:
Hi, first we need to establish the cash flow of the bond, so we can find the after tax cost of the bond. After we find the after tax cash flow of the bond, we must use the IRR function of MS Excel to find the semi-annual cost of this debt, but, all after tax debts should be presented in annual basis. Let me walk you through the process. First, let me show you how it should look.
Face Value 100
price 101,4
years 7 years
Coupon 9%
Coupon 4,5% semi-annually
tax 30%
Per Cash Flow After Tax
0 101,4 101,4
1 -4,5 -3,15
2 -4,5 -3,15
3 -4,5 -3,15
4 -4,5 -3,15
5 -4,5 -3,15
6 -4,5 -3,15
7 -4,5 -3,15
8 -4,5 -3,15
9 -4,5 -3,15
10 -4,5 -3,15
11 -4,5 -3,15
12 -4,5 -3,15
13 -4,5 -3,15
14 -104,5 -73,15
Cost of Debt 1,04% semi-annually
Cost of Debt 2,09% annually
Ok, now, as you can see, there are 14 periods, that is because the coupon is paid semi-annually, the way to find the cash flow (I mean, the bond´s coupon) is:
At the end (period 14), we need to add the face value and the coupon, that is $100+$4.5=$104.5
Now, to find the value of the third column (after-tax cost), we do the following.
Now, consider this, you are receiving 101.4 for every 100 of debt, that means that you are receiving more money than the emission value, and paying interests over 100 instead of 101.4, that is why we have to use the IRR excel function to find out the semi-annual cost of debt. That is, 1.04%.
Now, to make this an effective annual rate, we calculate it like this.
Finally, the after-tax cost of this debt is = 2.09%
Best of luck.