FIN 301 Exam 3
Constant Dividend - Zero Growth
If dividends are expected at regular intervals forever, thenthis is a perpetuity, and the present value of expected future dividends can be found using the perpetuity formula P0 = D/R
Espy Hotels has bonds outstanding that mature in 9 years, pay interest semiannually, and have a coupon rate of 5.5 percent. These bonds have a face value of $1,000 and a current market price of $989.28. What is the company's aftertax cost of debt if its tax rate is 22 percent?
N = 18 FV = 1000 PV = -989.28 PMT = 27.5
Werden Drilling offers 5.5 percent coupon bonds with semiannual payments and a yield to maturity of 7 percent. The bonds mature in 10 years. What is the market price per bond if the face value is $1,000?
N = 20 FV = 1000 I/Y = 3.5 PMT = 27.5
Ahmad Couture has bonds outstanding with a face value of $1,000, 11 years to maturity, and a coupon rate of 6 percent paid semiannually. What is the company's pretax cost of debt if the bonds currently sell for $1,067.12?
N = 22 FV = 1000 PMT = 30 PV = -1067.12
Nazarian's has bonds on the market with 13 years to maturity, a YTM of 7.6 percent, and a current price of $901.98. The bonds make semiannual payments and have a face value of $1,000. What is the coupon rate?
N = 26 I/Y = 3.8 PV = -901.98 FV = 1000
Lichtenfeld has a bond issue outstanding that matures in 19 years. The bonds pay interest semiannually. The bonds have a face value of $1,000 and are currently priced at $995.28. The bonds carry a coupon rate of 3.5 percent. What is the aftertax cost of debt if the total tax rate is 22 percent?
N = 38 FV = 1000 PV = -995.28 PMT = 17.5
The 30-year, 5.5 percent bonds issued by Modern Kitchens pay interest semiannually, mature in 4 years, and have a $1,000 face value. Currently, the bonds sell for $1,020.66. What is the yield to maturity?
N = 8 PV = -1020.66 FV = 1000 PMT = 27.5
Why Cost of Capital is Important
- We know that the return earned on assets depends on the risk of those assets. - The return to an investor is the same as the cost to the company. - Our cost of capital provides us with an indication of how the market views the risk of our assets. - Knowing our cost of capital can also help us determine our required return for capital budgeting projects
Announcements & News
- contain both an expected component and a surprise/unexpected component - It is the surprise component that affects a stock's price and therefore its return. - This is very obvious when we watch how stock prices move when an unexpected announcement is made or earnings are different than anticipated
Measuring Systematic Risk
- use beta coefficient A beta of 1 implies the asset has the same systematic risk as the overall market A beta < 1 implies the asset has less systematic risk than the overall market A beta > 1 implies the asset has more systematic risk than the overall market
Mullineaux Corporation has a target capital structure of 46 percent common stock, 5 percent preferred stock, and the balance in debt. Its cost of equity is 15.8 percent, the cost of preferred stock is 8.3 percent, and the aftertax cost of debt is 6.8 percent. What is the WACC given a tax rate of 23 percent?
.46 * .158 + .05 * .083 + .49 * .068 0.07268 + .00415 + 0.03332
In a booming economy, the stock of Pattee Productions is expected to return 17 percent. It is expected to return 9 percent in a normal economy and will decline 18 percent in a recessionary economy. The probability of a recession is 18 percent while the probability of a boom is 22 percent. What is the standard deviation of the returns on this stock?
0.17(.22) + 0.09(.60) - .18(.18) 0.0374 + 0.054 - 0.0324 = 0.05900 (0.17 - 0.059)^2 * 0.22 + (0.09 - 0.059)^2 * 0.60 + (-0.18 - 0.059^2 * 0.18) = (0.11100)^2 * 0.22 + (0.03100)^2 * 0.60 + (0.23900)^2 * 0.18 = (0.01232) * 0.22 + (0.00096) * 0.60 + (0.05712) * 0.18 = square root of 0.01357 = 11.65%
Your portfolio is comprised of 22 percent of Stock X, 32 percent of Stock Y, and 46 percent of Stock Z. Stock X has a beta of 1.04, Stock Y has a beta of .96, and Stock Z has a beta of 1.24. What is the beta of your portfolio?
0.22 * 1.04 + 0.32 * 0.96 + .46 * 1.24 22.88 + 30.72 + 57.04
The rate of return on the common stock of Luna Lights is expected to be 11.5 percent in a boom economy and 4.5 percent in a normal economy. The probability of a boom is 23 percent. What is the standard deviation of the returns on this common stock?
0.23(0.115) + 0.77(0.045) = 0.06110 (0.115 - 0.06110)^2 * 0.23 + (0.045-0.06110)^2 * 0.77 (0.05390)^2 * 0.23 + (-0.01610)^2 * 0.77 (0.00291) * 0.23 + (-0.00026) * 0.77 = square root of 0.00087 = 2.95%
Montez Supply is expected to pay an annual dividend of $.95 per share next year. The market price of the stock is $43.50 and the growth rate is 4.5 percent. What is the cost of equity?
0.95 / 43.50 + 0.045
The stock of Yakir Development has a beta of 1.31. The risk-free rate of return is 1.5 percent and the market rate of return is 8 percent. What is the risk premium on this stock?
1.31 * (0.08-0.015)
Nasafi Lumber paid an annual dividend of $1.37 per share yesterday. Today, the company announced that future dividends will be increasing by 3 percent annually. If you require a return of 14.6 percent, how much are you willing to pay to purchase one share of this stock today?
1.37 * (1+0.03) / (14.6 - 3)
Municipal Securities
Debt of state and local governments - Varying degrees of default risk, rated similar to corporate debt - Interest received is tax-exempt at the federal level
Expected vs Unexpected Returns
Realized returns are generally not equal to expected returns There is the expected component and the unexpected component - At any point in time, the unexpected return can be either positive or negative - Over time, the average of the unexpected component is zero
Beta and the Risk Premium
The risk premium = expected return - risk-free rate. The higher the beta, the greater the risk premium should be
Required Return vs Cost of Capital
The terms required return, appropriate discount rate, and cost of capital essentially mean the same thing If the required return on an investment is 10%, we mean the investment will have a positive NPV only if its return exceeds 10% the firm must earn 10% on the investment to compensate investors for the use of the capital needed to finance the project Furthermore, 10% is the cost of capital associated with the investment Cost of capital associated with an investment depends on the risk
How much are you willing to pay for one share of Govender stock if the company just paid an annual dividend of $1.61, the dividends increase by 4.2 percent annually, and you require a return of 16.4 percent?
1.61 * (1.042) / (16.4-4.2)
Nguyen Corporation's common stock has a beta of 1.38. The risk-free rate is 1.78 percent and the expected return on the market is 14.6 percent. What is the cost of equity?
1.78 + 1.38(14.6-1.78)
The Downtowner has 168,000 shares of common stock outstanding valued at $53 per share along with 13,000 bonds selling for $1,008 each. What weight should be given to the debt when the company computes its weighted average cost of capital?
168000(53) + 13000(1008) 8904000 + 13104000 = 22008000
Financial Policy & Cost of Capital
The particular mixture of debt and equity a firm chooses to employ—its capital structure—is a managerial variable - we will assume the firm has a fixed debt-equity ratio that it maintains - This ratio reflects the firm's target capital structure• Recall, a firm's overall cost of capital will reflect the required return on the firm's assets as a whole - Thus, a firm's cost of capital will reflect both its cost of debt capital and its cost of equity capital
Treasury Securities
Federal government debt that is considered to carry a risk-free rate of return
Rao Investments has 6.5 percent coupon bonds outstanding with a current market price of $548. The yield to maturity is 13.2 percent and the face value is $1,000. Interest is paid annually. How many years is it until these bonds mature?
PV = -548 I/Y = 13.2 FV = 1000 PMT = 65
Bond value
PV of coupons + PV of par PV of annuity + PV of lump sum - As interest rates increase, present values decrease - So, as interest rates increase, bond prices decrease and vice versa
Diversification
Portfolio diversification is the investment in several different asset classes or sectors. Diversification is not just holding a lot of assets if you own 50 Internet stocks, you are not diversified if you own 50 stocks that span 20 different industries, then you are diversified
Using the Dividend Growth Model to find Required Return
R = D1 / P0 + g
Yield or Yield to maturity (I/Y)
internal rate of return required in the market for the bond. Rate required for the present value of all the future cash flows of the bond (face value and coupon payments) to equal the current bond price
Variance
measure of volatility because it measures how much a stock tends to deviate from its mean. The higher the variance, the more wildly the stock fluctuates.Accordingly, the higher the variance, the riskier the stock
Risk return trade off
- low risk = low potential return - high risk = high potential return
Coupon rate
annual coupon divided by face value
Par value (FV)
face value or principal amount, repaid at maturity, stated in values of $100, $1,000, $10,000, $100,000, etc.
Total coupon payments (N)
frequency of coupon payments each year times thenumber of years to bond maturity
YTM vs coupon rate
- If YTM = coupon rate, then par value = bond price - If YTM > coupon rate, then par value > bond price - If YTM < coupon rate, then par value < bond price
Features of Common Stock
- Voting Rights - Proxy voting - Classes of stock: A and B impacting voting rights Other Rights - Share proportionally in declared dividends - Share proportionally in remaining assets during liquidation - Preemptive right: first shot at new stock issue to maintain proportional ownership if desired
Interest rates vs bond values
- When interest rates rise, the present value of the bond's remaining cash flows declines, and the bond is worth less - When interest rates fall, the bond is worth more
Standard deviation
- often used by investors to measure the risk of a stock or a stock portfolio. The basic idea is that the standard deviation is a measure of volatility: the more a stock's returns vary from the stock's average return, the more volatile the stock - measures the dispersion of a dataset relative to its mean. A volatile stock has a high standard deviation, while the deviation of a stable blue-chip stock is usually rather low. As a downside, it calculates all uncertainty as risk, even when it's in the investor's favor—such as above average returns
You recently purchased a stock that is expected to earn 12 percent in a booming economy, 6.5 percent in a normal economy, and lose 1.5 percent in a recessionary economy. The probability of a booming economy is 14 percent while the probability of a normal economy is 65 percent. What is your expected rate of return on this stock?
12 * 14 + 6.5 * 65 + 1.5 * 21 168 + 422.5 - 31.5
Currently, a firm has an EPS of $2.08 and a benchmark PE of 12.7. Earnings are expected to grow by 3.8 percent annually. What is the estimated current stock price?
12.7*2.08
Walker Systems has an issue of preferred stock outstanding with a stated annual dividend of $2.60 that just sold for $23.85 per share. What is the bank's cost of preferred stock?
2.60 / 23.85
Altitude Group is expected to pay an annual dividend next year of $2.71 per share. Dividends are expected to increase by 4.3 percent annually. What is one share of this stock worth at a required rate of return of 13.9 percent?
2.71 / (13.9-4.3)
Florida Groves has a $380,000 bond issue outstanding that is selling at 97.4 percent of face value. The firm also has 2,600 shares of preferred stock valued at $61 per share and 37,500 shares of common stock valued at $19 per share. What weight should be assigned to the common stock when computing the weighted average cost of capital?
380000(0.974) + 2600(61) + 37500(19) 370120 + 158600 + 712500 = 1241220
Murchison preferred stock pays an annual dividend of $4.45. What is the current price of this stock at a discount rate of 12.5 percent?
4.45/0.125
Castillo Corporation common stock is currently priced at $39.75 per share. The company just paid $4.35 per share as its annual dividend. The dividends have been increasing by 7.5 percent annually and are expected to continue doing the same. What is the cost of equity?
4.67625 / 39.75 + 0.075
Theresa's Flower Garden has 650 bonds outstanding that are selling for $1,007 each, 2,100 shares of preferred stock with a market price of $68 per share, and 42,000 shares of common stock valued at $44 per share. What weight should be assigned to the preferred stock when computing the weighted average cost of capital?
650 * 1007 + 2100 * 68 + 42000 * 44 654550 + 142800 + 1848000 = 2645350
Features of Prefered Stock
Dividends - Stated dividend that must be paid before dividends can be paid to common stockholders - Dividends are not a liability of the firm, and preferred dividends can be deferred indefinitely - Most preferred dividends are cumulative: any missed preferred dividends have to be paid before common dividends can be paid Generally does not carry voting rights
Dividend Growth Model
Dividends are expected to grow at a constant percent per period P0 = D1 / (R-g)
The Capital Asset Pricing Model
The capital asset pricing model defines the relationship between risk and return If we know an asset's systematic risk, we can use the CAPM to determine its expected return.• This is true whether we are talking about financial assets or physical assets
T-notes
coupon debt with original maturity between one and ten years
T-bonds
coupon debt with original maturity greater than ten years
Market Price (PV)
current price of the bond in the market
Maturity date
date that bond matures and the par value is paid
T-bills
pure discount bonds with original maturity of one year or less
Coupon (PMT)
stated interest payment (Coupon rate x Par value)
