Module 10 (Ch 10) Homework
Module 10 (Ch 10) Homework
Due Sunday by 11:59pm Points 10 Submitting a file upload Available until Apr 5 at 11:59pm
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Create an Excel spreadsheet to organize your answers to the following problem, and submit your Excel file as an
attachment by clicking on the appropriate button on this page.
A firm that is in the 35% tax
acket forecasts that it can retain $4 million of new earnings plans to raise new
capital in the following proportions:
60% from 30-year bonds with a flotation cost of 4% of face value. Their cu
ent bonds are selling at a price
of 91 (91% of face value), have 4 years remaining, have an annual coupon of 7%, and their investment
ank thinks that new bonds will have a 40 basis point (0.40%) higher yield-to-maturity than their cu
ent 4-
year bonds due to their longer term. Any new bonds will be sold at par.
10% from prefe
ed stock with a flotation cost of 5% of face value. The firm cu
ently has an outstanding
issue of $30 face value fixed-rate prefe
ed stock with an annual dividend of $2 per share, and the stock is
cu
ently selling at $27 per share. Any newly issued prefe
ed stock will continue with the $30 par-value,
and will continue with the $2 dividend.
30% from equity. Their common dividend payout ratio is 60%, they paid a dividend of $1.59 per share
yesterday, the dividend is expected to grow to $4.22 in 20 years, and is expected to continue this growth
ate into the foreseeable future. The common stock has a cu
ent market price of $19, and their investment
anker suggests a flotation cost of 7% of market value on new common equity.
Part 1: Calculate the after-tax cost of the new bond financing. ___________
Part 2: Calculate the after-tax cost of the new prefe
ed stock financing. ______
Part 3: Calculate the after-tax cost of retained earnings financing. _______
Part 4: Calculate the after-tax cost of the new common equity financing. ______
Part 5: Calculate the company's WACC using retained earnings as the source of equity. __________
Part 6: Calculate the
eak point in the cost of capital schedule due to running out of retained earnings. __________
Part 7: Calculate the company's WACC after it substitutes the new common stock issue for retained earnings after it runs out
of retained earnings. _________
Part 8: If the bonds had an after tax cost of 5.2% rather than the number you calculated in part #1 above, what would be the
WACC using retained earnings as the source of equity?
Part 9: If you have done the calculations above co
ectly, the after-tax cost of debt for this company is lower than the cost of
equity when using retained earnings as the equity source. Explain why raising capital by bo
owing is less costly than using
your own funds on which you do not have to pay any interest at all.
Part 10: Briefly explain the conceptual difference between the after-tax cost of retained earnings and the after-tax cost of new
common stock.
Fin 310
Study Guide
Chapter 10
The Cost of Capital
Summary of Key Concepts of the Chapte
Determining the Cost of Capital for each Source of Funds. A separate cost of capital must be calculated for each source of funds. Typically these sources will be debt securities (bonds), and equity securities (prefe
ed stock and common stock).
1. The first step in determining the cost of each source is to find the required rate of return using the HP10BII calculator (or Excel) as we have done in previous chapters. Please recall that this required rate of return is the rate that equates the present value of the security under consideration with the cash flows that are expected to be offered to the investor by the security, and this is true for debt securities (bonds) as well and equity securities (prefe
ed stock and common stock). This required rate of return is sometime called the yield on the security.
2. The second step is to adjust the required rate of return for the effects of flotation costs for the security under consideration. This is done very easily by using the net proceeds from the security (from the firm’s perspective) instead of the market price of the security in the calculation of the required rate of return. The net proceeds from the issuance of debt or equity is merely the market price minus the flotation costs. Please note that this second step can really be thought of as a modification of the first step above. In other words, the rate of return that is calculated in the first step above, if calculated using net proceeds rather than the market price of the security, is the calculation that is needed, so the first step and the second step can really be thought of as one step in this sense. Also, please remember that there are two kinds of common equity—retained earnings and new common stock. Please recall from previous chapters that the cost of retained earnings is merely the total yield on the common stock, which is the dividend yield plus the capital gains yield (growth rate) on the stock. But for new common stock, we will have flotation costs, which will decrease the net proceeds from the sale of the stock, which will in turn increase the cost of capital for new common stock.
3. The third step is to adjust the rate of return for the effect of income taxes. In this regard, the first thing to note is that debt securities (bonds) are treated differently from equity securities (stock) with respect to the tax effect. The interest paid on debt securities (bonds) is tax deductible by the corporation, so the effective cost of debt is going to be less than the interest rate paid by the firm. But the dividends paid on equity securities (stock) are not tax deductible, so there is no tax effect to wo
y about. The adjustment for income taxes can be easily made by simply multiplying the required rate of return obtained in step two above by one minus the marginal tax rate (1-T). If we have, for example a company that has a 35% tax rate that plans to issue bonds that will yield 8% (obtained using the net proceeds rather than the market value of the bonds), then the after-tax cost of capital is as follows:
0.08 X (1 – 0.35) = 0.052, or 5.2%
[Please note that the textbook, on page 250, goes through an elaborate method of adjusting for the tax effect of bonds. That method goes beyond the mark, and is not recommended. By using the simpler method above, practically the same result is obtained with far less complication.]
Determining the Overall Cost of Capital. Once the cost of capital for each individual source of funds has been determined, these figures can be combined in order to a
ive at an overall cost of capital for the firm as a whole. This is usually called the Weighted Average Cost of Capital (WACC). This WACC is calculated by simply multiplying each cost of capital by the proportion that that source is of the total funding for the firm, and then adding up these numbers. For example, if a firm is composed of 50% debt, 20% prefe
ed stock, and 30% common equity, and the after-tax cost of capital figures are 6% for debt, 8% for prefe
ed equity, and 11% for common equity, then we would calculate the WACC as follows:
Individual
After-Tax
Cost of Capital
Percentage
of
Total Funds
Product
Debt
6%
50%
3.0%
Prefe
ed Equity
8%
20%
1.6%
Common Equity
11%
30%
3.3%
WACC
7.9%
Determining the Marginal Cost of Capital Schedule. After the overall cost of capital for the firm has been determined, we need to realize that this WACC may increase as more funds are raised. This increase will take place because the firm gets riskier as it raises more funds, and as we know from discussions in prior chapters, risk and returns are positively co
elated. The Marginal Cost of Capital schedule is a graphical representation of this increase.
The vertical axis on the graph is the WACC, and the horizontal axis is the amount of capital raised. The first step on the schedule (on the left side closest to the origin on the graph) will show the WACC using Retained Earnings as the common equity source. But the amount of Retained Earnings is limited in any given year. And if the firm wants to raise more equity funds than what is provided by Retained Earnings, then it must issue new common stock. This decision to issue now common stock will increase the WACC because the cost of new common stock is higher than the cost of Retained Earnings due to the fact that there are flotation costs on the issuance of new stock. So, the second step on the graph (going to the right) will show a WACC slightly higher than the first step on the graph due to the higher WACC caused by the substitution of new common stock for Retained Earnings in the equity portion of the WACC calculation. Thus, if the WACC calculation in the table above represents the WACC using Retained Earnings as the common equity source, and if the existence of flotation costs for new common equity increases the cost equity from 11% to 12% for example, the new WACC calculation (for the second step on the graph) will be as follows:
Individual
After-Tax
Cost of Capital
Percentage
of
Total Funds
Product
Debt
6%
50%
3.0%
Prefe
ed Equity
8%
20%
1.6%
Common Equity (New common equity)
12%
30%
3.6%
WACC
8.2%
Notice that the only difference in the two tables above is the slightly higher cost of common equity in the second table that is caused by the fact that the firm presumably ran out of Retained Earnings and had to issue new common stock which has a higher cost of capital.
The so-called “
eak point” in the marginal cost of capital graph is the point at which the firm’s WACC increases due to the fact that they are using a more expensive source of funding (such as substituting new common equity for Retained Earnings).
End-of-Chapter Problems
1. A company has an outstanding issue of $1,000 face value bonds with a 9.5% annual coupon and 20 years remaining until maturity. The bonds are cu
ently selling at a price of 90 (90% of face value). And investment bank has advised that a new 20-year issue could be sold for a flotation cost of 5% of face value. The company is in the 35% tax
acket.
a. Calculate the investors’ required rate of return today.
1,000