Adjusting Bond Valuation for New Issue Fees | |||

You learned how to value a basic bond in Chapter 8 | |||

The difference here is that the company is considering a issue of new bonds. | |||

There are costs involved in issuing bonds | |||

You will need to adjust the price of the new issue by subtracting the issuing fees. | |||

Example | |||

A firm can sell a 20-year, $1000 par value, 9% bond for $980. A flotation cost of 2% of the face value would be required in addition to the discount of $20. | |||

Compute the rate of this bond. Note: The $20 discount has already been added. The discount is what brought the price down from $1000 to $980. | |||

Debt | |||

NPER | 20 | <<The period of the bond is 20 years | |

Coupon Price | 1000 | <<The standard Coupon Price of bonds is always $1000 | |

Coupon Rate | 9.0% | <<The Coupon Rate is the initial rate at which the bond was sold | |

PMT | 90 | <<You calculate the PMT by multiplying the coupon price by the coupon rate | |

Mkt Price | 960 | <<The market price of the bond is $980 less the flotation fee $980 – (2% * 1000) | |

Market Rate | ? | <<You are being asked to compute the new RATE | |

FV | 1000 | <<The FV of all bonds is same as the Coupon Price – because you get back your initial investment at the end | |

Compounding periods | 1 | <<Standard compounding is yearly (1 compounding period per year) | |

Compute RATE | 9.4524% | =RATE(E15,E18,-E19,E21) or =RATE( 20, 90, -960, 1000) | |

The same problem with monthly compounding | |||

Debt | |||

NPER | 20 | ||

Coupon Price | 1000 | ||

Coupon Rate | 9.0% | ||

PMT | 90 | ||

Mkt Price | 960 | ||

Market Rate | ? | ||

FV | 1000 | ||

Compounding periods | 12 | ||

RATE= | 9.4457% | =RATE(E29*12,E32/12,-E33,E35)*12 | |

Note: I had to go to 4 decimal spaces for you to see the difference the compounding made | |||

This is why it is very importand for you to include several decimal spaces when calculating financial problems. |

Stocks | Valuing Common Stocks – Examples and Practice | |||||

Preferred Stocks | The Constant (Gordon) Growth Model: Cost of Stock (RATE) = (D1 / P ) + g | |||||

You should know that most companies do not issue preferred stock. | Note: This method ONLY works for stock with dividends that are expected to grow at a constant rate | |||||

However, you still need to learn how to value it. | The firm’s common stock is currently selling for $40 per share. The dividend | |||||

The good part is that it is very easy to calculate. | expected to be paid at the end of the coming year is $5.07. Its dividend payments have been | |||||

Because preferred stock receives a fixed periodic dividend – it is calculated like a perpetuity | growing at a constant rate for the last five years. Five years ago, the dividend was $3.45. It is | |||||

expected that to sell, a new common stock issue must be underpriced at $1 per share and the firm <<<<<<< | Note: Just like the new issue of bonds, when a problem | |||||

Cost/RATE = Dividend / Price | must pay $1 per share in flotation costs. | gives you costs for a new issue of stock, you will need | ||||

Price = Dividend / RATE | Calculate the cost (RATE) of the new issue of preferred stock | to subtract the cost from the price of the stock. | ||||

Common Stock | Common Stock | Computing Growth Rate | ||||

The value of a share of stock is equal to the PV of all future cash flows (dividends) | Price | $40 | NPER | 5 | Computing the Gordon Growth Model Equation for Yield/Cost/Rate of Stock | |

Shareholders can earn capital gains if they sell their stock for more than the purchase price but, | D1 | $5.07 | RATE | ? | Cost of Stock = (D1 / P ) + g | |

what the stockholder really pays for is the right to all future dividends | g | 8% | PV | -3.45 | (5.07 / 38) + 8% = | 21.34% |

Stock valuation equations measure stock value at a point in time based on expected risk and return. | Cost/share | $2 | PMT | 0 | Note: You were given the expected dividend (D1) in this problem. | |

The textbook mentions several methods for valuing stock – you need to be aware of all of the various methods | Adj. Price | $38 | FV | 5.07 | The expected or future dividend is used in the formula. | |

However, in the assignments and exams, we will concentrate on the most widely used approach, The Constant-Growth Model | CPT ? | 8.00% | Always read the problem carefully to determine if it gives you the | |||

and the Capital Asset Pricing Model (CAPM) | expected or the current dividend. If you are given the current | |||||

You can use excel to calculate both models, however there are no excel formulas that do it automatically, so you have to enter the exact equations. | dividend, it will need to be adjusted. (See note below) | |||||

The constant-growth model is also called the Gordon Growth Model | ||||||

Calculating the Price of the Stock | Calculating the RATE of the stock | The Gordon Growth Model: Current Price of Stock = D1 / (r – g) | ||||

P0 = D1 / (rs – g) | rs = (D1 / P0) + g | The Bradshaw Company’s most recent dividend was $6.75. The historical dividend payment | ||||

Expected dividend divided by (rate – growth rate) | Expected dividend divided by price plus the growth rate | by the company shows a constant growth rate of 5% per year. | ||||

If the required rate of return is 8%, what is the price of the stock. | ||||||

In most of the constant-growth model problems, you are not given the growth rate of the dividends – you must calculate that yourself | ||||||

So, before you can work the Gordon Growth Model – you need to calculate the growth rate with the excel RATE formula | Common Stock | Computing the Gordon Growth Model Equation for Value/Price of Stock | ||||

Once you get the growth rate calculated, you can then work the equation | Price | ? | Price of Stock = D1 / (r – g) | |||

One other thing to be aware of is the dividend you are given in the problem | D1 | 6.75 * (1 + g) | = 6.75 * (1 + 5%) / ( 8% – 5%) | |||

The gordon growth model uses the Expected Dividend (D1), so if the problem gives you the expected or future dividend then you are good to go | Cost of Stock | 8.00% | = 7.0875 / (3%) | |||

However, if the problem gives you the current dividend (D0), then you will need to multiply that by (1 + g) to get the expected dividend (D1) | growth rate | 5.00% | 236.25 | |||

Note: You were given the current dividend (D0) in this problem, since you need the expected dividend in the formula, | ||||||

The Capital Asset Pricing Model for valuing stock quantifies the relationship between risk and return | you will needed to multiply the 6.75 by (1 + g) to convert the D0 to D1. | |||||

When a question gives you the beta of a share of common stock, this is a signal that you will need to use the CAPM equation | ||||||

Rs = RF + (b * (rm – RF)) Note: The extra parenthesis in this equation are for Excel | The Capital Asset Pricing Model (CAPM) Rs = RF + (b * (rm – RF)) or kp = krf + (km – krf) x b | |||||

They tell Excel to calculate the Market Risk Premium (rm-RF) first, then multiply by beta, then add the RF | Note: This method is used to calculate the required rate of return of an investment given its degree of risk. | |||||

Note the part of the formula in the parenthesis: (rm – RF), this is called the Market Risk Premium | Note: The two formulas are the same, just stated a little different. When entering the formula in excel, you will need to add the extra parenthesis so excel knows which | |||||

The Market Risk Premium (rm – RF) is different from the Market Return (rm) | order to compute the components. | |||||

The reason I am pointing this out is because sometimes a problem will give you the Market Risk Premium | Assume the risk-free rate is 5%, the expected rate of return on the market is 15%, and the beta of your firm is 1.2. | |||||

instead of the Return on Market (rm). | Given these conditions, what is the required rate of return on your company’s stock? | |||||

When this happens, you need to know that there is no need to subtract the risk free rate from the market return | ||||||

because this part of the equation has already been calculated for you. | Computing the CAPM | |||||

Required Rate of Return: Rs = RF + (b * (rm – RF)) | ||||||

= 5% + (1.2 * ( 15% – 5%)) <<<Enter this equation into excel, it will do the rest! | ||||||

= 5% + (1.2 * (10%) | ||||||

= 5% + 12% | ||||||

= 17% | ||||||

Valuing Stocks – Your Turn – Please complete the problem below. | ||||||

A firm has common stock with a market price of $100 per share and an expected dividend of $5.61 per share at the end of the coming year. | ||||||

A new issue of stock is expected to be sold for $98, with $2 per share representing the underpricing necessary in the competitive market. | ||||||

Flotation costs are expected to total $1 per share. Five years ago, the dividend was $4.00. Calculate the cost of the stock. | ||||||

Computing Growth Rate | Common Stock | Gordon Growth Rate Formula | ||||

NPER (N) | Expected Dividend | Cost of Stock = (D1 / P ) + g | ||||

RATE (I/Y) | Market Price | |||||

PV | Fees for new issue | |||||

PMT | Adjusted Price | 12.78% | ||||

FV | Growth Rate | 7.00% | ||||

Compute RATE | 7.00% | |||||

Note: Cost, Yield, Rate all mean the same thing when computing stock. | ||||||

You are either going to be asked to compute the cost (RATE), or compute the price. (Cost and price are two different things.) | ||||||

Assume the risk-free rate is 8%, a market return of 12%, and a beta of 1.5. | ||||||

Given these conditions, what is the rate of return on this investment? | ||||||

CAPM Inputs | CAPM Formula | |||||

rF | Rs = RF + (b * (rm – RF)) | |||||

rM | ||||||

Beta | ||||||

14.00% | ||||||

Note: Any time a problem mentions a beta, you know to use the CAPM equation instead of the Gordon Growth Model. | ||||||

*The calculations for Preferred Stock are so simple, than I don’t feel you need an example and a practice problem for that. |

PART 1 A – COMPUTING A WEIGHTED AVERAGE COST OF CAPITAL (WACC) | |||||||

A firm has determined its optimal capital structure, which is composed of the following sources and target market value proportions: | |||||||

Source of Capital | Target Market | ||||||

Proportions | |||||||

Long-term debt | 60% | ||||||

Preferred stock | 5% | ||||||

Common stock equity | 35% | ||||||

Debt: The firm can sell a 15 year bond, compounded monthly, with a $1000 par value and 6.8% coupon rate for $1254. A flotation cost of 1.15% of the | |||||||

face value would also be required. | |||||||

Preferred Stock: The firm has determined that it can issue preferred stock at $125 per share par value. The preferred stock wil pay a $6.75 per share | |||||||

annual dividend. The cost of issuing and selling the preferred will be $3.28 per share. | |||||||

Common Stock: The firm’s common stock is currently selling for $23.75per share. The firm will be paying a dividend of $5.25 at the end of the year. | |||||||

Its dividend payments have been growing at a constant rate for the last five years. Five years ago, the dividend was $3.25. For a new issue | |||||||

of common stock to sell, it has been determined that the new issue would need to be underpriced at $1.50 per share and that the firm must | |||||||

pay $1.20per share in flotation costs. | |||||||

The firm’s marginal tax rate is 21%, plus 4% for state and local taxes. (ISTR = 25%) | |||||||

To determine the firm’s WACC, please complete the following steps, entering your formulas in the blue cells: | |||||||

1A-A | A. Calculate the rate for the bond, notice is has monthly compounding. | ||||||

1A-B | B. Calculate the after-tax cost of the bond. | ||||||

1A-C | C. Calculate the cost of the new issue of preferred stock. | ||||||

1A-D | D. Calculate the growth rate of the common stock dividends. | ||||||

1A-E | E. Calculate the cost of the new common stock issue. | ||||||

1A-F | F. Finally, calculate the firm’s weighted average cost of capital assuming the firm has exhausted all retained earnings. | ||||||

Standard formats for your calculations: | |||||||

Common Stock | Preferred Stock Inputs | ||||||

Debt | Growth Rate | Price | |||||

NPER | NPER | New Issue Costs | |||||

Coupon Price | PV | Adjusted Price | |||||

Coupon Rate | FV | Dividend | |||||

PMT | RATE = | ||||||

Mkt Price | Formula Inputs | WACC | |||||

Market Rate | Price | Proportions | Costs | Amount | |||

FV | New Issue Costs | ||||||

Compounding periods | Adjusted Price | ||||||

RATE= | D1 | ||||||

g | TOTAL >> | ||||||

PART 1 B- CAPITAL BUDGETING | |||||||

The same firm as in Part 1 is considering the investment of two independent projects, X and Y, which are described below. Please do not assume anything. Use the | |||||||

firm’s WACC which you just calculated to evaluate the projects. | |||||||

Cost of Capital>> | |||||||

Year | PROJECT X | PROJECT Y | A. Calculate Payback Period for both projects | For the Payback Period Calculation | |||

Cash Inflows | B. Calculate NPV for both projects | Cash End of Year Balances | |||||

Initial Investment | ($11,050,000) | ($11,250,000) | 0 | C. Calculate PI for both projects | PROJECT X | PROJECT Y | Year |

1 | $3,500,000 | $5,500,000 | 1 | D. Calculate IRR for both projects | 1 | ||

2 | $3,500,000 | $5,800,000 | 2 | E. Which project should the firm accept? Why? | 2 | ||

3 | $5,800,000 | $2,900,000 | 3 | 3 | |||

4 | $5,800,000 | $1,950,000 | 4 | 4 | |||

Please enter your formulas in the blue cells: | |||||||

1B-A | A. Payback | ||||||

1B-B | B. NPV | ||||||

1B-C | C. IRR | ||||||

1B-D | D. MIRR | ||||||

1B-E | E. Accept projects>>> | Yes or No | Yes or No | Why?: | |||

End of Part 1 | |||||||

PART 2 – COMPUTING WACC WITH CAPM | ||

This problem has NO relation to the problem in Part 1 | ||

The current risk-free rate is 5.51% and the market is expected to return 7.55% per year. The company’s beta is 1.57. The company expects to pay 4.9% for its debt. | ||

the target capital structure for the company is 35% equity and 65% debt. The marginal tax rate is 21% plus 4% for state and local taxes (ISTR = 25%). | ||

CAPM Inputs | ||

A. What is the after-tax cost of debt? | rF | |

B. What is the cost of equity? | rM | |

C. Calculate the WACC. | Beta | |

Cost/Debt | ||

ISTR | ||

2-A | Answer A | Capital Structure |

2-B | Answer B | Debt |

2-C | Answer C | Equity |

WACC | ||

Total>> | ||

End of Part 2 |

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