Finance Exam 2
Key Features of a Bond
Par value - face amount of the bond, which is paid at maturity (assume $1,000). Coupon interest rate - stated interest rate (generally fixed) paid by the issuer. Multiply by par value to get dollar payment of interest. Maturity date - years until the bond must be repaid. Issue date - when the bond was issued. Yield to maturity - rate of return earned on a bond held until maturity (also called the "promised yield").
For a given time period - the higher the interest rate, the smaller the present value What is the present value of $500 received in 5 years if the interest rate is 10%? 15%?
Rate = 10%: N = 5; I/Y = 10; FV = 500 PMT=0 CPT PV = -310.46 Rate = 15%; N = 5; I/Y = 15; FV = 500 PMT=0 CPT PV = -248.59
What is the effect of compounding?
Simple interest = 10 + 200(10)(.055) = 120.00 Compounding added $447,069.84 to the value of the investment
The historical record for the period 1926-2016 supports which one of the following statements.
Small-company stocks have lost as much as 50 percent and gained as much as 100 percent in a single year.
A 12-year, $1,000 face value bond pays a 9% semiannual coupon. The bond has a nominal yield to maturity of 7.5%, and it can be called in 4 years at a call price of $1,045. What is the bond's nominal yield to call?
Step 1: Find the price of the semiannual bond today using the YTM and other information given: N = 12x2 = 24; I/YR = 7.5/2 = 3.75; PMT = 45 (1,000x.09/2); FV = 1000; and then solve for PV = -$1,117.3362. Step 2: Given the bond's price, calculate the yield to call by entering the following data as inputs: N = 4x2 = 8; PV = -1117.3362; PMT = 45; FV = 1045; and then solve for I/YR = r/2 = 3.3073% per 6 months (SEMI) but then find ANN: r = 3.3073% x2 = 6.6146% ≈ 6.61%.
Dividend Growth Model Example
Suppose JB, Inc., just paid a dividend of $2.50 per share. It is expected to increase its dividend by 5% per year. If the market requires a return of 15% on assets of this risk, how much should the stock be selling for? P0 = 2.50(1+.05) / (.15 - .05) = $26.25
Effective (or equivalent) annual rate (EAR)
The annual rate of interest actually being earned, accounting for compounding. EAR for 10% semiannual investment: EAR = ( 1 + APR / M )M - 1 = ( 1 + 0.10 / 2 )2 - 1 = 10.25% Should be indifferent between receiving 10.25% annual interest and receiving 10% interest, compounded semiannually
A 10-year, 10% semiannual coupon bond selling for $1,135.90 can be called in 4 years for $1,050, what is its yield to call?
The bond's yield to maturity can be determined to be 8%. Solving for the YTC is identical to solving for YTM, except the time to call is used for N and the call premium is FV. N=8 BC Semiannual (4x2) I/YR=X=3.568 PV=-1135.90 PMT=50 FV=1050 3.568% represents the periodic semiannual yield to call. YTCNOM = rNOM = 3.568% x 2 = 7.137% is the rate that a broker would quote.
Primary versus Secondary
The capital markets consist of primary markets and secondary markets: -Newly formed (issued) securities are bought or sold in primary markets. -Secondary markets allow investors to sell securities that they hold or buy existing securities.
Future Value and Compounding
The effect of compounding is small for a small number of periods, but increases as the number of periods increases.
Why is either PV or FV a negative number and the other a positive number when inputting into a calculator to find the interest rate?
The signs are different because one is a cash flow in and the other is cash flow out.
Which one of the following is a correct formula?
Total dollar return = Dividend income + Capital gain
Dollar returns
Total dollar return = income from investment + capital gain (loss) due to change in price Ex: You bought a bond for $950 one year ago. You have received two coupons of $30 each. You can sell the bond for $975 today. What is your total dollar return? Income = 30 + 30 = 60 Capital gain = 975 - 950 = 25 Total dollar return = 60 + 25 = $85
You own 1,200 shares of Western Feed Mills stock valued at $46.80 per share. What is the dividend yield if your annual dividend income is $1,644?
Total value = 1,200 X $46.80 = $56,160 Dividend yield = $1,644 / $56,160 = 2.93%
The rate of return on which type of security is normally used as the risk-free rate of return?
Treasury bills
Which one of the following categories of securities had the lowest average risk premium for the period 1926-2016?
US Treasure bills
Which one of the following statements is a correct reflection of the US financial markets for the period 1926-2016?
US Treasury bills had an annual return in excess of 10 percent in three or more years
You bought a stock for $35, and you received dividends of $1.25. The stock is now selling for $40.
What is your dollar return? Dollar return = 1.25 + (40 - 35) = $6.25 What is your percentage return? Dividend yield = 1.25 / 35 = 3.57% Capital gains yield = (40 - 35) / 35 = 14.29% Total percentage return = 3.57 + 14.29 = 17.86%
What is an annuity?
a constant cash flow that occurs at regular intervals for a fixed period of time.
The discount rate is also
an opportunity cost, since it captures the returns that an individual would have made on the next best opportunity.
The average compound return earned per year over a multiyear period is called the ___________ average return.
geometric
To convince investors to accept greater volatility, you must:
increase the risk premium
An initial public offering (IPO)
is where a company issues stock in the public market for the first time. -"Going public" enables a company's owners to raise capital from a wide variety of outside investors. Once issued, the stock trades in the secondary market. -Public companies are subject to additional regulations and reporting requirements.
For the period 1926-2016, US Treasury bills always:
provided a positive annual rate of return.
Determinants of interest rates
r = r* + IP + MRP + DRP + LP r = required return on a debt security r* = real risk-free rate of interest IP = inflation premium MRP = maturity risk premium DRP = default risk premium LP = liquidity premium
"Nominal" vs. "Real" rates
r = represents any nominal rate r* = represents the "real" risk-free rate of interest. Like a T-bill rate, if there was no inflation. Typically ranges from 1% to 4% per year. rRF = represents the rate of interest on Treasury securities = r* + inflation
Assume that last year T-bills returned 2.8 percent while your investment in large company stocks earned an average of 7.6 percent. Which one of the following terms refers to the difference between these two rates of return?
risk premium
Different approaches for estimating the intrinsic value of a common stock
•Dividend growth model •Corporate value model •Using the multiples of comparable firms
Intrinsic Value and Stock Price
•Outside investors, corporate insiders, and analysts use a variety of approaches to estimate a stock's intrinsic value (P0). •In equilibrium we assume that a stock's price equals its intrinsic value: -Outsiders estimate intrinsic value to help determine which stocks are attractive to buy and/or sell. -Stocks with a price below (above) its intrinsic value are undervalued (overvalued).
Comments on standard deviation
•Standard deviation (σi) measures total, or stand-alone, risk. •The larger σi is, the lower the probability that actual returns will be closer to expected returns. •Larger σi is associated with a wider probability distribution of returns.
The discount rate is a rate at which present and future cash flows are traded off. It incorporates:
(1) Preference for current consumption (Greater ....Higher Discount Rate) (2) Expected inflation (Higher inflation....Higher Discount Rate) (3) Uncertainty in the future cash flows (Higher Risk....Higher Discount Rate
Effect of a call provision
-Allows issuer to refund the bond issue if rates decline (helps the issuer, but hurts the investor). -Borrowers are willing to pay more, and lenders require more, for callable bonds. -Most bonds have a deferred call and a declining call premium.
Hypothetical yield curve
-An upward sloping yield curve. -Upward slope due to an increase in expected inflation and increasing maturity risk premium. -A downward sloping yield curve. -Downward slope due to a decrease in expected inflation.
Present Value Principle 1
-Cash flows at different points in time cannot be compared and aggregated. -All cash flows have to be brought to the same point in time, before comparisons and aggregations are made. -That point of time can be today (present value) or a point in time in the future (future value).
Expected Returns
-Expected returns are based on the probabilities of possible outcomes -In this context, "expected" means average if the process is repeated many times -The "expected" return does not even have to be a possible return
Default risk
-If an issuer defaults, investors receive less than the promised return. Therefore, the expected return on corporate and municipal bonds is less than the promised return. -Influenced by the issuer's financial strength and the terms of the bond contract.
Zero Growth
-If dividends are expected at regular intervals forever, then this is a perpetuity and the present value of expected future dividends can be found using the perpetuity formula: P0 = D / R -Suppose stock is expected to pay a $2.50 dividend every year with the required return of 15%. What is the price? P0 = 2.50 / (.15) = $16.67
Three reasons why a dollar tomorrow is worth less than a dollar today
-Individuals prefer present consumption to future consumption. To induce people to give up present consumption you have to offer them more in the future. -When there is monetary inflation, the value of currency decreases over time. The greater the inflation, the greater the difference in value between a dollar today and a dollar tomorrow. -If there is any uncertainty (risk) associated with the cash flow in the future, the less that cash flow will be valued.
What is investment risk?
-Investment risk is related to the probability of earning a low or negative actual return. -The greater the chance of lower than expected or negative returns, the riskier the investment.
Why is it important to consider effective rates of return?
-Investments with different compounding intervals provide different effective returns. -To compare investments with different compounding intervals, you must look at their effective returns. -See how the effective return varies between investments with the same nominal rate, but different compounding intervals. EARANNUAL 10.00% EARQUARTERLY 10.38% EARMONTHLY 10.47% EARDAILY (365)10.52%
Firm Multiples Method Using P/E
-Let's say your company has earnings of $5.00 per share. -Let's also say that a competing company in your industry has a current P/E ratio of 16. -That means your stock price could be estimated as follows: Comparative P/E = 16 = Price of your stock / 5 Solving for P, or price of your stock = $80
Risk Premiums
-The "extra" return earned for taking on risk -Treasury bills are considered to be risk-free -The risk premium is the return over and above the risk-free rate
Other things remaining equal, the value of cash flows in future time periods will decrease as
-The preference for current consumption increases. -Expected inflation increases. -The uncertainty in the cash flow increases.
Lessons from capital market history
-There is a reward for bearing risk -The greater the potential reward, the greater the risk -This is called the risk-return trade-off
Variance and Standard Deviation
-Variance and standard deviation measure the volatility of asset returns -The greater the volatility, the greater the uncertainty
Semiannual bonds
1. Multiply years by 2 : number of periods = 2n. 2. Divide nominal rate by 2 : periodic rate (I/YR) = rd / 2. 3. Divide annual coupon by 2 : PMT = ann cpn / 2.
Quarterly bonds
1. Multiply years by 4 : number of periods = 4n. 2. Divide nominal rate by 4 : periodic rate (I/YR) = rd / 4. 3. Divide annual coupon by 4 : PMT = ann cpn / 4.
A stock had returns of positive 5%, positive 4%, negative 10% and positive 8% over the past four years. What is the arithmetic average return?
1.75%
Suppose you invest the $1,000 for 10 years at 5%. How much would you have?
10 N; 5 I/Y; 1,000 PV PMT=0 CPT FV = -1,628.90
Identify the periodic rate for this bond: 10% quarterly coupon bond.
2.50%
Suppose you had a relative deposit $10 at 5.5% interest 200 years ago. How much would the investment be worth today?
200 N; 5.5 I/Y; -10 PV PMT=0 CPT FV = -447,189.84
Suppose you invest the $1,000 for 3 years at 5%. How much would you have?
3 N; 5 I/Y; 1,000 PV PMT=0 CPT FV = -1,157.63
For a given interest rate - the longer the time period, the lower the present value What is the present value of $500 to be received in 5 years? 10 years? The discount rate is 10%
5 years: N = 5; I/Y = 10; FV = 500 PMT=0 CPT PV = -310.46 10 years: N = 10; I/Y = 10; FV = 500 PMT=0 CPT PV = -192.77
Suppose your company expects to increase unit sales of widgets by 15% per year for the next 5 years. If you sell 3 million widgets in the current year, how many widgets do you expect to sell in the fifth year?
5=N; 15=I/Y; 3,000,000=PV PMT=0 CPT FV = -6,034,072 units (remember the sign convention)
Annual Percentage Rate (APR)
Also called the quoted or stated rate. An annual rate that ignores compounding effects. APR is stated in contracts. Periods must also be given, e.g. 8% Quarterly or 8% Daily interest.
West Wind Tours stock is currently selling for $48 a share. The stock has a dividend yield of 3.2 percent. How much dividend income will you receive per year if you purchase 200 shares of this stock?
Amount of dividend = $48 X 3.2% = $1.536 200 X $1.536 = $307.20
Periodic rate (PER)
Amount of interest charged each period, e.g. monthly or quarterly. PER = APR / M, where M is the number of compounding periods per year. M = 4 for quarterly and M = 12 for monthly compounding.
Evaluating default risk: Bond ratings
Bond ratings are designed to reflect the probability of a bond issue going into default.
Bonds and Stocks: Similarities
Both provide long-term funding for the organization Both are future funds that an investor must consider Both have future periodic payments Both can be purchased in a marketplace at a price "today"
What is the future value of $1,000 received today (CF0) and $2,000 received 2 years from today (CF2), using 10% interest compounded annually, in 4 years?
CF0=$1,000 (PV) PV = $1,000 N = 4 I = 10% FV = $1,464.10 PMT=0 CF0=$2,000 (PV) PV = $2,000 N = 2 I = 10% FV = $2,420.00 PMT=0 ADD FV's together: $3,884.10
You just sold 300 shares of stock at a price of $42.06 a share. You purchased the stock for $39.80 a share and have received total dividends of $1,272. What is the total capital gain on this investment?
Capital gain = current price - original price Capital gain = $12,618 - $11,940 = $678
Estimating Dividends: Special Cases
Constant dividend: -The firm will pay a constant dividend forever -This is like preferred stock -The price is computed using the perpetuity formula Constant dividend growth: -The firm will increase the dividend by a constant percent every period -The price is computed using the growing perpetuity model
One year ago, you purchased 400 shares of SL Industries stock at a price of $26.15 a share. The stock pays an annual dividend of $1.34 per share. Today, you sold all of your shares for $28.20 per share. What is your total dollar return on this investment?
Current price - original price = capital gains per share $28.20 - $26.15 = $2.05 Capital gains per share + dividends per share = total return per share $2.05 + $1.34 = $3.39 Total dollar return = $3.39 X 400 shares = $1,356 ANSWER
Percentage returns
Dividend yield = income / beginning price Capital gains yield = (ending price - beginning price) / beginning price Total percentage return = dividend yield + capital gains yield
Dividend Growth Model
Dividends are expected to grow at a constant percent per period. P0 = D1 / (R - g) D1=D0x(1+g)
A 12-year, $1,000 face value bond has a 9% annual coupon, and a yield to maturity of 8%. What is the price of the bond?
Enter the following input data in the calculator: N = 12; I/YR = 8; PMT = 90; FV = 1000; Solve for PV = -$1,075.36.
What is the present value of $2,000 received 4 years from now and $1,500 received 2 years from now, assuming an 8% discount rate?
FV = 2,000 I = 8% N = 4 PV = 1,470.06 PMT=0 FV = 1,500 I = 8% N = 2 PV = 1,286.01 PMT=0 PV = 1,470.06 + 1,286.01 PV = 2,756.07
The JB Company just hired you as a financial analyst. They have a project that needs $100,000 in 10 years. They will be able to put away $5,000 each year at the end of the year (ordinary annuity) for 10 years. They also want to make an initial deposit TODAY to make up the difference. They are able to invest all funds at 6% over the 10 years. How much do they have to deposit TODAY that when added to the $5,000 annuity they will have $100,000 in 10 years?
First, find FV of annuity: PMT=5,000 N=10 I=6 FV=65,903.98 PV=0 Second, they need 100,000 in total so they need 100,000 - 65,903.98 = 34,096.02 more at end Third, find PV of 34,096.02(FV): FV=34,096.02 N=10 I=6 PV= $19,039.04 ANSWER
Bonds and Stocks: Differences
From the firm's perspective: a bond is a long-term debt and stock is equity From the firm's perspective: a bond gets paid off at the maturity date; stock continues indefinitely. A bond has coupon payments and a lump-sum payment; stock has dividend payments forever Coupon payments are fixed; stock dividends change or "grow" over time
Generally speaking, which of the following best correspond to a wide frequency distribution?
High standard deviation, large risk premium
Annuity Due (Set calc to BEG)
If the first payment occurs at the beginning of the period
Ordinary annuity
If the first payment occurs at the end of the period
You intend to purchase a 10-year, $1,000 face value bond that pays interest of $60 every 6 months. If your nominal annual required rate of return is 10% with semiannual compounding, how much should you be willing to pay for this bond?
Inputs: N = 20 (10x2); I/YR = 5 (10/2); PMT = 60; FV = 1000. Output: PV = -$1,124.62; VB = $1,124.62.
A $1,000 par value bond pays interest of $35 each quarter and will mature in 10 years. If your nominal yield to maturity is 12% with quarterly compounding, how much should you be willing to pay for this bond?
Inputs: N = 40 (10x4); I/YR = 3 (12/4); PMT = 35; FV = 1000. Output: PV = -$1,115.57; VB = $1,115.57
Miller Brothers Hardware paid an annual dividend of $0.95 per share last month. Today, the company announced that future dividends will be increasing by 2.6 percent annually. If you require a 13 percent rate of return, how much are you willing to pay to purchase one share of this stock today?
Knowns: D0 = $0.95 g = 2.6% r = 13% Can calculate D1 = $0.95 X (1+.026) = $0.975 P0 = D1 / r - g P0 = $0.975 / .13 - .026 P0 = $9.372
A share of common stock has just paid a dividend of $2.00. If the expected long-run growth rate for this stock is 7%, and if investors require an 11% rate of return, what is the price of the stock?
Knowns: D0 = $2.00 g = 7% r = 11% Can calculate D1 = $2.00 X (1+.07) = $2.14 P0 = D1 / r - g P0 = $2.14 / .11 - .07 P0 = $53.50 What is the expected price 4 years from now? PV=P0 = $53.50 PMT=0 N = 4 I = 7 Solve for FV = $70.13
Sessler Manufacturers made two announcements concerning its common stock today. First, the company announced that the next annual dividend will be $1.75 a share. Secondly, all dividends after that will decrease by 1.5 percent annually. What is the maximum amount you should pay to purchase a share of this stock today if you require a 14 percent rate of return?
Knowns: D1 = $1.75 g = -1.5% r = 14% P0 = D1 / r - g P0 = $1.75 / .14 - (-.015) P0 = $11.29
Damon Enterprises' stock is currently sells for $25 per share. The stock's dividend is projected to increase at a constant rate of 7% per year. The required rate of return on the stock, rs, is 10%. What is Damon's expected price 4 years from today?
Knowns: P0 = $25 g = 7% rs = 10% P0 = D1 / (rs - g) $25 = D1 / (.10 - .07) $25 x (.03) = D1 D1 = $0.75 N = 4 PV = $25 PMT=0 I = 7% FV = 32.77
Bauer Inc's bonds currently sell for $1,275 and have a par value of $1,000. They pay a $120 annual coupon and have a 20-year maturity, but they can be called in 5 years at $1,120. What is their yield to maturity (YTM)?
Knowns: PMT = 120 N=20 Years FV = 1,000 Call price in 5 yrs = 1,120 Current price (PV) = 1,275 Solve for I (ytm): 8.99% What is the yield to call? PMT = 120 n = 5 PV = 1,275 FV = 1,120 Solve for I (ytc) = 7.31%
Will the FV of a lump sum be larger or smaller if compounded more often, holding the stated I% constant?
LARGER, as the more frequently compounding occurs, interest is earned on interest more often.
Your parents set up a trust fund for you 10 years ago that is now worth $19,671.51. If the fund earned 7% per year, how much did your parents invest?
N = 10; I/Y = 7; FV = 19,671.51 PMT=0 CPT PV = -10,000
You want to begin saving for your daughter's college education and you estimate that she will need $150,000 in 17 years. If you feel confident that you can earn 8% per year, how much do you need to invest today?
N = 17; I/Y = 8; FV=150,000 PMT=0 CPT PV = -40,540.34 (remember the sign convention
This bond has a $1,000 lump sum (the par value) due at maturity (t = 10), and annual $100 coupon payments beginning at t = 1 and continuing through t = 10, the price of the bond can be found by solving for the PV of these cash flows. Suppose inflation rises by 3%, causing kd = 13%. When kd rises above the coupon rate, the bond's value falls below par, and sells at a discount. Suppose inflation falls by 3%, causing kd = 7%. When kd falls below the coupon rate, the bond's value rises above par, and sells at a premium.
N=10 I/YR=10 PMT=100 FV=1000 PV=X=-1000 N=10 I/YR=13 PMT=100 FV=1000 PV=X=-837.21 N=10 I/YR=7 PMT=100 FV=1000 PV=X=-1210.71
Four years ago, Servee invested $500. Three years ago, Tick invested $600. Today, these two investments are each worth $800. Assume each account continues to earn its respective rate of return. Which one of the following statements is correct concerning these investments?
One year ago, Servee 's investment was worth less than Tick's investment.
