The homework problem states:
Debt: Jones Industries borrows $600,000 for 10 years with an annual payment of $100,000. What is the expected interest rate (cost of debt)? my answer is 16.667%

Internal common stock: Jones Industries has a beta of 1.39. The risk-free rate as measured by the rate on short-term US Treasury bill is 3 percent, and the expected return on the overall market is 12 percent. Determine the expected rate of return on Jones’s stock (cost of equity). My answer is 15.51%
Here are the details:

Jones Total Assets $2,000,000
Long- & short-term debt $600,000
Common internal stock equity $400,000
New common stock equity $1,000,000
Total liabilities & equity $2,000,000

Looking for the calculated answer and the formula used. I'm in an online class where the professor doesn't feel that he should take anytime on the phone to explain material to a confused student who is asking for help. Could some please assist. Answers are needed by tomorrow. I think I may have obtained the right answers but need someone to verify that they are right.

Your cost of equity is correct; your cost of debt is not.

The cost of Jones' debt is simply the interest rate that corresponds to the 600,000 loan amount being exactly amortized with 10 annual payments of 100K each.

For example, had Jones borrowed the 600K at (say) 14% with a 10-year payback, their annual payment would be 115,028. If they had instead borrowed at (say) 9%, their annual payment would be 93,492.

Since their annual payment is actually 100K, then right away my examples tell you that the cost of the debt must lie somewhere between 14% and 9%.

To find the actual rate (and hence the cost of the debt), there are multiple approaches. You could use a "present value of an annuity" table; you could set up the "present value of an annuity" formula in a calculator and use trial-and-error iterations to narrow in on the answer; you could set up an amortization schedule in a spreadsheet---with an initial loan amount of 600K and 10 payments of 100K---and then tinker with the interest rate until the loan is exactly paid off following the tenth payment. Without knowing which method you've been given in your book or class, I can't advise on the specifics, but maybe the foregoing will give you enough to take the baton and run with it.

I just want to say thank you for the wonderful explanation and I can most certainly find the solution with one of your approaches. Some times it is a matter of understanding the given information and what formula or approach to take. If your not a professor, which I'm assuming you are not, you should be. Your approach is what I would have expected from my professor to do.

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Originally Posted by ArcSine

Your cost of equity is correct; your cost of debt is not.

The cost of Jones' debt is simply the interest rate that corresponds to the 600,000 loan amount being exactly amortized with 10 annual payments of 100K each.

For example, had Jones borrowed the 600K at (say) 14% with a 10-year payback, their annual payment would be 115,028. If they had instead borrowed at (say) 9%, their annual payment would be 93,492.

Since their annual payment is actually 100K, then right away my examples tell you that the cost of the debt must lie somewhere between 14% and 9%.

To find the actual rate (and hence the cost of the debt), there are multiple approaches. You could use a "present value of an annuity" table; you could set up the "present value of an annuity" formula in a calculator and use trial-and-error iterations to narrow in on the answer; you could set up an amortization schedule in a spreadsheet---with an initial loan amount of 600K and 10 payments of 100K---and then tinker with the interest rate until the loan is exactly paid off following the tenth payment. Without knowing which method you've been given in your book or class, I can't advise on the specifics, but maybe the foregoing will give you enough to take the baton and run with it.

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Glad to hear it helped out a bit, and thanks. Sometimes, it's just a matter of hearing something described a little differently, or accompanied by a different mental picture, to reach that "aha!" moment when the light suddenly clicks on.

Keep hitting the ol' books and you'll get along just fine.