Calculating bonds' YTM with PVIFA. Solution is in place, but cannot understand.

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PKirby

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Please, help with understanding the following.

Question:
Titan Mining Corporation has 9 million shares of equity outstanding and 1,200,000 8.5 per cent semi-annual bonds outstanding, par value £100 each. The equity currently sells for £34 per share and has a beta of 1.20, and the bonds have 15 years to maturity and sell for 93 per cent of par. The market risk premium is 10 per cent, T-bills are yielding 5 per cent, and Titan Mining's tax rate is 28 per cent.
If Titan Mining is evaluating a new investment project that has the same risk as the firm's typical project, what rate should the firm use to discount the project's cash flows?

Solution:

Step 1. Find the cost of equality using the CAPM:
RE = 0.05 + 1.20(0.10) = 0.17

Step 2. The cost of debt is the YTM of the bonds. Therefore:
P0= £93 = £4.25(PVIFAR%,30) + £100(PVIFR%,30)
R = 4.69%
YTM = 4.69% × 2 = 9.38%

Step 3. Find the after-taxcost of debt is:

[FONT=&quot]RD= (1 – .28)(.0938) = .0675 or 6.75%

[/FONT]Step 4. Calculate the WACC:

[FONT=&quot]WACC =.1700(.7328) + .0675 (.2672) = .1426 or 14.26%

[/FONT]
Problem: I cannot understand Step 2. Where does £93 come from? Where does £4.25 come from? How did they calculate the entire equation with PVIFA? Please help and let me know if you have any questions!


 
PKirby said:
Please, help with understanding the following.

Question:
Titan Mining Corporation has 9 million shares of equity outstanding and 1,200,000 8.5 per cent semi-annual bonds outstanding, par value £100 each. The equity currently sells for £34 per share and has a beta of 1.20, and the bonds have 15 years to maturity and sell for 93 per cent of par. The market risk premium is 10 per cent, T-bills are yielding 5 per cent, and Titan Mining's tax rate is 28 per cent.
If Titan Mining is evaluating a new investment project that has the same risk as the firm's typical project, what rate should the firm use to discount the project's cash flows?

Solution:

Step 1. Find the cost of equality using the CAPM:
RE = 0.05 + 1.20(0.10) = 0.17

Step 2. The cost of debt is the YTM of the bonds. Therefore:
P0= £93 = £4.25(PVIFAR%,30) + £100(PVIFR%,30)
R = 4.69%
YTM = 4.69% × 2 = 9.38%

Step 3. Find the after-taxcost of debt is:

RD= (1 – .28)(.0938) = .0675 or 6.75%

Step 4. Calculate the WACC:

WACC =.1700(.7328) + .0675 (.2672) = .1426 or 14.26%


Problem: I cannot understand Step 2. Where does £93 come from? Where does £4.25 come from? How did they calculate the entire equation with PVIFA? Please help and let me know if you have any questions!
Click to expand...

From reading carefully!!!
 
Last edited by a moderator:
[FONT=&quot]I found these 2 calculators, giving the same answer of 0.0938:[/FONT]
[FONT=&quot]http://www.moneychimp.com/calculator/popup/calculator.htm?mode=calc_bondytm[/FONT]
[FONT=&quot]http://www.investopedia.com/calculator/aoytm.aspx[/FONT]
[FONT=&quot]This is the formula that does not rely on PVIFs:[/FONT]
[FONT=&quot]http://financetrain.com/yield-to-maturity-ytm-approximation-formula/[/FONT]
[FONT=&quot]I use the formula to get the number, but it still gives me 0.0929. What could I be doing wrong?[/FONT]
 
PKirby said:
Please, help with understanding the following.

Question:
Titan Mining Corporation has 9 million shares of equity outstanding and 1,200,000 8.5 per cent semi-annual bonds outstanding, par value £100 each. The equity currently sells for £34 per share and has a beta of 1.20, and the bonds have 15 years to maturity and sell for 93 per cent of par. The market risk premium is 10 per cent, T-bills are yielding 5 per cent, and Titan Mining's tax rate is 28 per cent.
If Titan Mining is evaluating a new investment project that has the same risk as the firm's typical project, what rate should the firm use to discount the project's cash flows?

Solution:

Step 1. Find the cost of equality using the CAPM:
RE = 0.05 + 1.20(0.10) = 0.17

Step 2. The cost of debt is the YTM of the bonds. Therefore:
P0= £93 = £4.25(PVIFAR%,30) + £100(PVIFR%,30)
R = 4.69%
YTM = 4.69% × 2 = 9.38%

Step 3. Find the after-taxcost of debt is:

RD= (1 – .28)(.0938) = .0675 or 6.75%

Step 4. Calculate the WACC:

WACC =.1700(.7328) + .0675 (.2672) = .1426 or 14.26%


Problem: I cannot understand Step 2. Where does £93 come from? Where does £4.25 come from? How did they calculate the entire equation with PVIFA? Please help and let me know if you have any questions!
Click to expand...
Saying it a slightly different way: The 93 is the 93% of 100 or the current value of one bond ["... par value £100 each ... sell for 93 per cent of par ...] so you pay £93 now, get £4.25 every six months for 15 years [8.5% of £100 paid semi-annually] and, at the end of 15 years get £100. What is your rate of return? The answer to that is not straight forward and requires some sort of iterative solution [Newtons method or whatever].

EDIT: Sure wish fixing a misteak like that would serve as a "GET OUT OF CORNER FREE" ticket. Oh well, easy come, easy go.
 
Last edited:
Denis said:
Say Ishuda buys those bonds.
Purchase price = 1200000 * .93 = 1,116,000.
This means Ishuda is lending Titan 1,116,000;
this loan will be repaid by Titan this way:
30 semiannual payments of 1,200,000 * .0425 = 51,000;
a final pay't of 1,200,000 at same time as final semiannual pay't.

Question: do you understand that?
Click to expand...
No, I wouldn't buy them. I can generally do better than that.
 
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