Valuing New Bonds

Valuing New Bonds

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.
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.
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
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.

Valuing Stock

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))
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 – 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
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
Mkt Price Formula Inputs WACC
Market Rate Price Proportions Costs Amount
FV New Issue Costs
Compounding periods Adjusted Price
g TOTAL >>
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-E E. Accept projects>>> Yes or No Yes or No Why?:
End of Part 1

Part 2 – 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
2-A Answer A Capital Structure
2-B Answer B Debt
2-C Answer C Equity
End of Part 2
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