FIN 4502 Exam 2
A coupon bond that pays semiannual interest is reported in the Wall Street Journal as having an ask price of 113% of its $1,000 par value. If the last interest payment was made 3 months ago and the coupon rate is 5.60%, the invoice price of the bond will be _________. $1,130.00 $1,158.00 $1,144.00 $1,102.00
$1,144.00 Invoice price = 1.13(1,000) + 28.00(3/6) = 1,144.00
A bond pays a semi-annual coupon and the last coupon was paid 61 days ago. If the annual coupon payment is $75, what is the accrued interest? A. $13.21B. $12.57C. $15.44D. $16.32
$12.57 75/2)*(61/182.5)
You have purchased a guaranteed investment contract (GIC) from an insurance firm that promises to pay you a 5% compound rate of return per year for 6 years. If you pay $15,000 for the GIC today and receive no interest along the way, you will get __________ in 6 years (to the nearest dollar) $19,500 $20,073 $20,101 $19,144
$20,101 N= 6 I= 5 PV= -15000 PMT=0 FV=?
Assuming semiannual compounding, a 10-year zero coupon bond with a par value of $1,000 and a required return of 11.2% would be priced at _________. $336.30 $345.90 $899.28 $946.97
$336.30 N= 20 I= 5.6 PV=? PMT= 0 FV=-1000
ART has come out with a new and improved product. As a result, the firm projects an ROE of 23%, and it will maintain a plowback ratio of 0.25. Its earnings this year will be $4.0 per share. Investors expect a 15% rate of return on the stock. What price do you expect ART shares to sell for in 4 years? $38.35 $63.92 $40.56 $44.56
$40.56 P0 =4.0 (1 - 0.25)= 32.430.15 - 0.23 (.25) P4=P0(1 +g)4= 32.43(1.0575)4= 40.56
You are considering acquiring a common share of Sahali Shopping Center Corporation that you would like to hold for 1 year. You expect to receive both $1.35 in dividends and $45 from the sale of the share at the end of the year. The maximum price you would pay for a share today is __________ if you wanted to earn a 10% return. $40.91 $42.14 $41.72 $51.50
$42.14 V0 =1.35 + 45 / (1+.10) = 42.14
Weyerhaeuser Incorporated has a balance sheet that lists $111 million in assets, $63 million in liabilities, and $48 million in common shareholders' equity. It has 1 million common shares outstanding. The replacement cost of its assets is $121 million. Its share price in the market is $57. Its book value per share is _________. $10 $48 $64 $58
$48
You buy a TIPS at issue at par for $1,000. The bond has a 4.9% coupon. Inflation turns out to be 3.9%, 4.9%, and 5.9% over the next 3 years. The total annual coupon income you will receive in year 3 is _________. $49.00 $51.40 $56.56 $53.90
$56.56 ($49)(1.039)(1.049)(1.059) = $56.56
years to maturity YTM 1 6% 2 7.49% 3 7.99% 4 8.49% The expected one-year interest rate two years from now should be A) 7.00% B) 8.00% C) 9.00% D)10.00%
(1+0.0799)^3=((1+0.0749)^2(1+f23); then f23 =(1+0.0799)^3 / (1+0.0749)^2 - 1 = 9%
Suppose that in 2018 the expected dividends of the stocks in a broad market index equaled $240 million when the discount rate was 8% and the expected growth rate of the dividends equaled 6%. Using the constant-growth formula for valuation, if interest rates increase to 9%, the value of the market will change by _____. -10% -20% -25% -33%
-33% Original value=240/(0.08−0.06)=12,000 Million New value =240/0.09−0.06=8,000 Million %Δ=8,000−12,000/12,000=−33.33%
Lifecycle Motorcycle Company is expected to pay a dividend in year 1 of $2.00, a dividend in year 2 of $3.00, and a dividend in year 3 of $4.00. After year 3, dividends are expected to grow at the rate of 7% per year. An appropriate required return for the stock is 12%. Using the multistage DDM, the stock should be worth __________ today. A) $63.80 B) $65.13 C) $67.98 D)$85.60
. PV0 = D1/(1+K) +D2/(1+K)^2+(D3+PV3)/(1+K)^3 where PV3 = D4/(k-g) = 4*1.07/(.12-.07) =85.6 PV0 = 2/1.12+3/1.12^2+(4+85.6)/1.12^3 = 1.786+2.392+63.776=67.96
A firm has current assets that could be sold for their book value of $10 million. The book value of its fixed assets is $60 million, but they could be sold for $90 million today. The firm has total debt with a book value of $40 million, but interest rate declines have caused the market value of the debt to increase to $50 million. What is this firm's market-to-book ratio?
1.67 Market value of the firm = Market value of assets − Market value of debts = ($10 million + $90 million) − $50 million = $50 million Book value of the firm = Book value of assets − Book value of debts = ($10 million + $60 million) − $40 million = $30 million Market-to-book ratio = $50 million/$30 million = 1.67
A pension plan is obligated to make disbursements of $1 million, $2 million, and $1 million at the end of each of the next three years, respectively. Find the duration of the plan's obligations if the interest rate is 10% annually.
1.9524 years duration table
1ART has come out with a new and improved product. As a result, the firm projects an ROE of 25%, and it will maintain a plowback ratio of 0.20. Its earnings this year will be $3 per share. Investors expect a 12% rate of return on the stock. 1. At what price would you expect ART to sell? A) $25.00 B) $34.29 C) $42.86 D) none of the above 2. At what P/E ratio would you expect ART to sell? A) 8.33 B) 11.43 C) 14.29 D) none of the above 3. What is the present value of growth opportunities for ART? A) $8.57 B) $9.29 C) $14.29 D) none of the above 4. What price do you expect ART shares to sell for in 4 years? ? A) $53.96 B) $44.95 C) $41.68 D)none of the above
1.B; 2.B; 3.B; 4.C 1.V0 = D1/(k-g) = E1*(1-b)/(k-ROE*b) = 3(1-0.2)/(.12-.25*.2) =34.29 2.2. P/E = 34.29/3 = 11.43 3.3. PVGO = V0-E1/k = 34.29-3/.12 = 9.29 4.4. D5 =D1*(1+g)^4 = 2.4*1.05)^4=2.917; P4 = D5/(k-g) = 2.917/(.12-.05) = 41.68
A bond with a coupon rate of 7% makes semiannual coupon payments on January 15 and July 15 of each year. The Wall Street Journal reports the ask price for the bond on January 30 at 100.125. What is the invoice price of the bond? The coupon period has 182 days
1004.14 The reported bond price is $1,001.25.15 days have passed since the last semiannual coupon was paid, so there is an accrued interest, which can be calculated as:Accrued interest = (Annual coupon payment/2) × (Days since last coupon payment/Days separating coupon payment)= $35 × (15/182) = $2.8846The invoice price is the reported price plus accrued interest:$1,001.25 + $2.8846 = $1,004.13.
If the price of a $10,000 par Treasury bond is $10,425.00, the quote would be listed in the newspaper as ________. 104.109 103.972 104.250 104.632
104.250 PQUOTE = (10,425.0010,000) (100)=104.2500
The market capitalization rate on the stock of Aberdeen Wholesale Company is 10%. Its expected ROE is 12%, and its expected EPS is $5. If the firm's plowback ratio is 50%, its P/E ratio will be _________. 8.33 12.5 19.23 24.15
12.5 Dividend payout ratio = 1 − 0.5 = 0.5Expected dividend = 0.5 × $5 = $2.50Growth rate = 0.5 × 12% = 6%Value = $2.50/(0.10 − 0.06) = $62.50P/E = $62.50/$5 = 12.5
A perpetuity pays $100 each and every year forever. The duration of this perpetuity will be __________ if its yield is 8.4%. 7.75 8.40 6.40 12.90
12.90 D =1+0.0840/0.084 = 12.90
A firm has PVGO of 0 and a market capitalization rate of 7.0%. What is the firm's P/E ratio? 7.00 14.29 10.64 24.93
14.29 1/.07
Eagle Products' EBIT is $300, its tax rate is 21%, depreciation is $20, capital expenditures are $60, and the planned increase in net working capital is $30. What is the free cash flow to the firm?
167 FCFF = EBIT × (1 − tc) + Depreciation − Capital expenditures − Increase in NWC = $300 × (1 − 0.21) + $20 − $60 − $30 = $167
Brevik Builders has an expected ROE of 25%. Its dividend growth rate will be __________ if it follows a policy of paying 30% of earnings in the form of dividends. 5% 15% 17.5% 45%
17.5% g = 0.25(1 − 0.3) = 0.175
. A bond pays annual interest. Its coupon rate is 7%. Its value at maturity is $1,000. It matures in three years. Its yield to maturity is presently 8%. The duration of this bond is __________. A) 2.60 B) 2.73 C) 2.81 D) 3.00
2.8 duration table
FinCorp's free cash flow to the firm is reported as $205 million. The firm's interest expense is $22 million. Assume the corporate tax rate is 21% and the net debt of the firm increases by $3 million. What is the market value of equity if the FCFE is projected to grow at 3% indefinitely and the cost of equity is 12%?
2118 FCFE = FCFF − Interest expenses × (1 − tc) + Increases in net debtFCFE = $205 − $22 × (1 − 0.21) + $3 = $190.62 (million)Market value of equity = $190.62 / (0.12 − 0.03) = $2,118.00 (million)
Deployment Specialists pays a current (annual) dividend of $1 and is expected to grow at 20% for two years and then at 4% thereafter. If the required return for Deployment Specialists is 8.5%, what is the intrinsic value of its stock?
30.60 Intrinsic value = V0 = D1/(1 + k ) + D2/(1 + k)2 + ... + (DH + PH)/(1 + k)H = ($1 × 1.20)/(1 + 0.085) + ($1 × 1.202)/(1 + 0.085)2 + ($1 × 1.202 × 1.04)/((0.085 − 0.04) × (1 + 0.085)2) = $30.60
A coupon bond that pays interest of $53 annually has a par value of $1,000, matures in 5 years, and is selling today at a $73.50 discount from par value. The current yield on this bond is _________. 5.30% 5.72% 7.76% 5.60%
5.72% Current price = $1,000 - 73.50 = $926.50, so current yield = $53/$926.50 = 5.72%
a. Find the duration of a 6% coupon bond making annual coupon payments if it has three years until maturity and a yield to maturity of 6%. b. What is the duration if the yield to maturity is 10%?
6% = 2.8330 years 10% = 2.8240 years duration table
A coupon bond that pays interest of $60 annually has a par value of $1,000, matures in 5 years, and is selling today at an $84.52 discount from par value. The yield to maturity on this bond is _________. 6% 7.23% 8.12% 9.45%
8.12% N= 5 I=? PV=1000-84.52 PMT=60 FV=1000
Treasury bonds paying an 8% coupon rate with semiannual payments currently sell at par value. What coupon rate would they have to pay in order to sell at par if they paid their coupons annually?
8.16% (1.04)2 − 1 = 8.16
Jand, Incorporated, currently pays a dividend of $1.22, which is expected to grow indefinitely at 5%. If the current value of Jand's shares based on the constant-growth dividend discount model is $32.03, what is the required rate of return?
9% Intrinsic value = V0 = (D0 × (1 + g))/(k − g): $32.03 = ($1.22 × 1.05)/(k − 0.05) ⇒⇒ k = 0.089994 or 9.00%
Suppose a firm is expected to increase dividends by 20% in one year and by 15% in the next two years. After that dividends will increase at a rate of 5% per year indefinitely. If the last dividend was $1 and the required return is 20%, what is the price of the stock?
9.3 Given: g1 = 20% for year 1, g2=15% for year 2 and 3, g3 = 5% after year 3, D0 = 1, k= 20% D1 = 1*1.2 =1.2; D2 = 1.2*1.15 =1.38,; D3 = 1.38*1.15 = 1.587; D4 = 1.587*1.05=1.666 After year 3, there is a constant growth rate 5%, we are able to use constant dividend growth model to calculate present value at year 3: PV3 = D4/(k-g3) =1.666/(.20-.05)=11.11; then PV0 =D1/(1+k) +D2/(1+k)^2+(D3+PV3)+(1+k)^3 = 1.2/1.2 +1.38/1.2^2+(1.578+11.11)/1.2^3 = 1+0.958+7.343=9.30
A bond currently sells for $1,050, which gives it a yield to maturity of 6%. Suppose that if the yield increases by 25 basis points, the price of the bond falls to $1,025. What is the modified duration of this bond?
9.5238 Change in price = −(Modified duration × Change in YTM) × Price = − D/(1 + y) × Δy × P Given the current bond price is $1,050, yield to maturity is 6%, and the increase in YTM and new price, we can calculate D: $1,025 − $1,050 = − D/(1 + 0.06) × 0.0025 × $1,050 ⇒⇒ D = 10.0952 Modified duration = D* = D/(1 + y) = 10.0952/1.06 = 9.5238
In an efficient market, professional portfolio management can offer all of the following benefits except which of the following? Low-cost diversification. A targeted risk level. Low-cost record keeping. A superior risk-return trade-off
A superior risk-return trade-off
Gagliardi Way Corporation has an expected ROE of 15%. Its dividend growth rate will be __________ if it follows a policy of paying 30% of earning in the form of dividends. A) 4.5% B) 10.5% C) 15.0% D) 30.0%
Answer: B Difficulty: Medium. g = ROE*b = 15%*(1-.30) = 10.5%
Rose Hill Trading Company is expected to have EPS in the upcoming year of $6.00. The expected ROE is 18.0%. An appropriate required return on the stock is 14%. If the firm has a plowback ratio of 70%, its intrinsic value should be __________. A) $20.93 B) $69.77 C) $128.57 D) $150.00
Answer: C Difficulty: Hard. V = D1/(k-g) = 6*(1-0.7)/(.14-.18*0.7) = 128.57
Rose Hill Trading Company is expected to have EPS in the upcoming year of $8.00. The expected ROE is 18.0%. An appropriate required return on the stock is 14%. If the firm has a plowback ratio of 70%, its dividend in the upcoming year should be __________. A) $1.12 B) $1.44 C) $2.40 D) $5.60
Answer: C Difficulty: Medium. D1/E1 = 1-b = 1-.70 = 0.3; D1 = 0.3* E1 = 0.3*8 = 2.4
You know that firm XYZ is very poorly run. On a scale of 1 (worst) to 10 (best), you would give it a score of 3. The market consensus evaluation is that the management score is only 2. Should you buy or sell the stock? Buy Sell
Buy
1. A bond is presently worth $1,080.00 and its yield to maturity is 8%. If the yield to maturity goes down to 7.84%, the value of the bond will go to __________ if the duration of the bond is 9. A) $1,034.88 B) $1,036.00 C) $1,094.00 D) $1,123.60
C) $1,094.00 D= - (dP/P)/(dY/(1+Y), dP/P = -D*(dY/(1+Y) = -9*(.0784-0,08)/1.08 = 0.013; dP = 0.13*1080 = 14.4; P1 = 1080+14.4 = 1094.4
A coupon bond which pays interest of $50 annually, has a par value of $1,000, matures in 5 years, and is selling today at an $84.52 discount from par value. The current yield on this bond is A) 5% B) 5.46% C) 5.94% D) 6.00%
Current yield = annual coupon payment/current price = 50/(1000-84.52) = 5.46%
A bond presently has a price of $1,030. The present yield on the bond is 8.00%. If the yield changes from 8.00% to 8.10%, the price of the bond will go down to $1,020. The duration of this bond is __________. A) -10.5 B) -8.5 C) 9.7 D) 10.5
D = -(dP/P)/(dY/(1+Y) =-[(1020-1030)/1030]/[(0.081-0.08)/(1+0.08)] = 10.5%
Quiz 3 #8
DO it
A nine-year bond paying coupons annually has a yield of 10% and a duration of 7.194 years. If the bond's yield changes by 50 basis points, what is the percentage change in the bond's price?
Decreases by 3.27% ΔP/P = −Duration × Δy/(1 + y) = −7.194 × 0.0050/1.10 = −0.0327 or a 3.27% decline
A bank has $50 million in assets, $47 million in liabilities and $3 million in shareholders' equity. If the duration of its liabilities are 1.3 and the bank wants to immunize its net worth against interest rate risk and thus set the duration of equity equal to zero, it should select assets with an average duration of a 1.22b. 1.50c. 1.60d. 2.00
Duration of asset =D = (47/50)*1.3 +(3/50)*0 = 1.22
Which of the following would most appear to contradict the proposition that the stock market is weakly efficient? Over 25% of mutual funds outperform the market on average. Insiders earn abnormal trading profits. Every January, the stock market earns abnormal returns
Every January, the stock market earns abnormal returns
1.A coupon bond which pays interest semi-annually, has a par value of $1,000, matures in 5 years, and has a yield to maturity of 8%. If the coupon rate is 10%, the intrinsic value of the bond today will be __________. A) $855.55 B) $1,000 C) $1,081 D)$1,100
Given: FV=1000, N=10, I=8/2=4, PMT = 1000*10%/2 = 50; PV = 1081.11
A coupon bond which pays interest of $40 annually, has a par value of $1,000, matures in 5 years, and is selling today at a $159.71 discount from par value. The actual yield to maturity on this bond is __________. A) 5% B) 6% C) 7% D) 8%
Given: PMT = 40, FV=1000, N=5, FV=159.71-1000 = -840.29, I= 8%
Suppose the 8% coupon (semiannual payment), 30-year maturity bond sells for $1,150 and is callable in 10 years at a call price of $1,100. What is the yield to maturity and yield to call?
Given: PMT: 40; N: 60; FV:1000; PV: -1150 -> YTM = 6.82% Given: PMT: 40, N: 20; FV:1100; PV: -1150 -> YTC = 6.64%
You purchased a 5-year annual interest coupon bond one year ago. Its coupon interest rate was 6% and its par value was $1,000. At the time you purchased the bond, the yield to maturity was 4%. If you sold the bond after receiving the first interest payment and the bond's yield to maturity had changed to 3%, your annual total rate of return on holding the bond for that year would have been A) 5.00% B) 5.51% C) 7.61% D) 8.95%
Given: n=5, pmt=60, fv=1000,i=4; your purchased price = pv = 1089.04; Given: n=4, pmt=60;fv=1000, i=3, your selling price = pv = 1111.51 HPR = (1111.51+60-1089.04)/1089.04 = 7.6%
A callable bond pays annual interest of $60, has a par value of $1,000, matures in 20 years but is callable in 10 years at a price of $1,100, and has a value today of $1055.84. The yield to call on this bond is __________. A) 6.00% B) 6.58% C) 7.20% D) 8.00%
Given: pmt=60, fv=1100, n=10, pv=-1055.84; yield = 6%
Which of the following statements are true if the efficient market hypothesis holds? It implies that future events can be forecast with perfect accuracy. It implies that prices reflect all available information. It implies that security prices change for no discernible reason. It implies that prices do not fluctuate.
It implies that prices reflect all available information.
Cache Creek Manufacturing Company is expected to pay a dividend of $3.36 in the upcoming year. Dividends are expected to grow at 8% per year. The riskfree rate of return is 4% and the expected return on the market portfolio is 14%. Investors use the CAPM to compute the market capitalization rate, and the constant growth DDM to determine the value of the stock. The stock's current price is $84.00. Using the constant growth DDM, the market capitalization rate is __________. A) 9% B) 12% C) 14% D) 18%
K = D1/P0 +g = 3.36/84+8% = 12%
Caribou Gold Mining Corporation is expected to pay a dividend of $6 in the upcoming year. Dividends are expected to decline at the rate of 3% per year. The risk-free rate of return is 5% and the expected return on the market portfolio is 13%. The stock of Caribou Gold Mining Corporation has a beta of -0.50. Using the constant growth DDM, the intrinsic value of the stock is __________. A) $50.00 B) $150.00 C) $200.00 D) $400.00
K = rf+beta*(rm-rf) = 5%+(-0.5)*(13%-5%) = 1%; V = D1/(k-g) = 6/(.01-(-0.03)) =150
Which of the following observations would provide evidence against the semistrong form of the efficient market theory? Mutual fund managers do not on average make superior returns .You cannot make superior profits by buying (or selling) stocks after the announcement of an abnormal rise in dividends. Low P/E stocks tend to have positive abnormal returns. In any year approximately 50% of mutual funds outperform the market.
Low P/E stocks tend to have positive abnormal returns.
A convertible bond has a par value of $1,000 but its current market price is $833. The current price of the issuing company's stock is $22 and the conversion ratio is 40 shares. The bond's market conversion value is a. $1,000 B $880 c. $833 d. $800
Market conversion value = 22*40 = 880
Suppose you find that before large dividend increases, stocks show on average consistently positive abnormal returns. Is this a violation of the EMH? Yes No
NO
Suppose that, after conducting an analysis of past stock prices, you come up with the following observations. Which would appear to contradict the weak form of the efficient market hypothesis? The average rate of return is significantly greater than zero. The correlation between the return during a given week and the return during the following week is zero. One could have made superior returns by buying stock after a 10% rise in price and selling after a 10% fall. One could have made higher-than-average capital gains by holding stocks with low dividend yields.
One could have made superior returns by buying stock after a 10% rise in price and selling after a 10% fall.
The market capitalization rate on the stock of Aberdeen Wholesale Company is 10%. Its expected ROE is 12% and its expected EPS is $5.00. If the firm's plow-back ratio is 40%, its P/E ratio will be __________. A) 8.33 B) 11.54 C) 19.23 D) 50.00
P = D1/(k-g) = E1*(1-b)/(k-ROE*b); P/E1 = (1-b)/(k-ROE*b)= (1-0.4)/(0.10-.12*.4) = 11.54
Which of the following sources of market inefficiency would be most easily exploited? A stock price drops suddenly due to a large block sale by an institution. A stock is overpriced because traders are restricted from short sales. Stocks are overvalued because investors are exuberant over increased productivity in the economy.
Stocks are overvalued because investors are exuberant over increased productivity in the economy.
Which version of the efficient market hypothesis focuses on the most inclusive set of information? Strong-form Semistrong-form Weak-form
Strong-form
Two bonds have identical times to maturity and coupon rates. One is callable at 105, the other at 110. Which should have the higher yield to maturity? The bond callable at 105 should have the higher yield to maturity. The bond callable at 110 should have the higher yield to maturity.
The bond callable at 105 should have the higher yield to maturity.
An investor believes that a bond may temporarily increase in credit risk. Which of the following would be the most liquid method of exploiting this? The short sale of the bond. The sale of a credit default swap. The purchase of a credit default swap
The purchase of a credit default swap
Miltmar Corporation will pay a year-end dividend of $4, and dividends thereafter are expected to grow at the constant rate of 4% per year. The risk-free rate is 4%, and the expected return on the market portfolio is 12%. The stock has a beta of 0.75. a. Calculate the market capitalization rate. b. What is the intrinsic value of the stock?
a. 10% b. 66.67 a. Market capitalization rate = k = rf + β × [E(rM) − rf] = 0.04 + 0.75 × (0.12 − 0.04) = 0.10 = 10% b. Intrinsic value = V0 = D1/(k − g) = $4/(0.10 − 0.04) = $66.67
A two-year bond with par value $1,000 making annual coupon payments of $100 is priced at $1,000. a. What is the yield to maturity of the bond? b. What will be the realized compound yield to maturity if the one-year interest rate next year turns out to be (a) 8%, (b) 10%, (c) 12%?
a. 10% b.) 1. 9.91, b. 10, c. 10.09 The bond is selling at par value. Its yield to maturity equals the coupon rate, 10%. If the first-year coupon is reinvested at an interest rate of r percent, then total proceeds at the end of the second year will be: [100 × (1 + r) + 1,100]. Therefore, realized compound yield to maturity will be a function of r as given in the following table:
The market consensus is that Analog Electronic Corporation has an ROE of 9% and a beta of 1.25. It plans to maintain indefinitely its traditional plowback ratio of 2/3. This year's earnings were $3 per share. The annual dividend was just paid. The consensus estimate of the coming year's market return is 14%, and T-bills currently offer a 6% return. a. Find the price at which Analog stock should sell b. Calculate the P/E ratio. Leading?Trailing? c. Calculate the present value of growth opportunities. d. Suppose your research convinces you Analog will announce momentarily that it will immediately reduce its plowback ratio to 1/3. Find the intrinsic value of the stock.
a. 10.60 b. leading= 3.33 trailing 3.53 c. -9.28 d. 15.85 a.k = rf + β × [E(rM) − rf] = 0.06 + 1.25 × (0.14 − 0.06) = 0.16 or 16%g = ROE × b = 0.09 × (2/3) = 0.06 or 6%D1 = E0 × (1 + g) × (1 − b) = $3 × 1.06 × (1/3) = $1.06 P0 = D1/(k − g) = $1.06/(0.16 − 0.06) = $10.60 b.Leading P0/E1 = $10.60/$3.18 = 3.33Trailing P0/E0 = $10.60/$3.00 = 3.53c. PVGO = P0 − (E1/k) = $10.60 − ($3.18/0.16) = −$9.28 The low P/E ratios and negative PVGO are due to a poor ROE (9%) that is less than the market capitalization rate (16%).d.Now, you revise the plowback ratio in the calculation so that b = 1/3:g = ROE × b = 0.09 × 1/3 = 0.03 or 3%D1 = E0 × (1 + g) × (1 − b) = 3 × 1.03 × (2/3) = $2.06 Intrinsic value = V0 = D1/(k − g) = $2.06/(0.16 − 0.03) = $15.85
a. Computer stocks currently provide an expected rate of return of 16%. MBI, a large computer company, will pay a year-end dividend of $2 per share. If the stock is selling at $50 per share, what must be the market's expectation of the growth rate of MBI dividends? b. If dividend growth forecasts for MBI are revised downward to 5% per year, what will happen to the price of MBI stock? c. What (qualitatively) will happen to the company's price-earnings ratio? The P/E ratio will decrease. The P/E ratio will increase
a. 12% b. 18.18 c. The P/E ratio will decrease. a. Using the constant-growth DDM, P0 = D1/(k − g) $50 = $2/(0.16 − g) ⇒⇒ g = 0.12 or 12% b. P0 = D1/(k − g) = $2/(0.16 − 0.05) = $18.18 c.The price falls in response to the more pessimistic forecast of dividend growth. The forecast for current earnings, however, is unchanged. Therefore, the P/E ratio decreases. The lower P/E ratio is evidence of the diminished optimism concerning the firm's growth prospects.
A 30-year maturity bond making annual coupon payments with a coupon rate of 12% has duration of 11.54 years and convexity of 192.4. The bond currently sells at a yield to maturity of 8%. a. Find the price of the bond if its yield to maturity falls to 7% b. What price would be predicted by the duration rule, if its yield to maturity falls to 7%? c. What price would be predicted by the duration-with-convexity rule, if its yield to maturity falls to 7%? d-1. What is the percent error for each rule, if its yield to maturity falls to 7%?
a. 1620.45 b. 1605.28 c. duration rule = 0.94% convexity= 0.075% a. Using a financial calculator, we find that the price of the bond is:For y = 7%: N = 30; I/Y = 7; FV = 1000; PMT = 120 → PV = $1,620.45For y = 8%: N = 30; I/Y = 8; FV = 1000; PMT = 120 → PV = $1,450.31For y = 9%: N = 30; I/Y = 9; FV = 1000; PMT = 120 → PV = $1,308.21 b. Using the duration rule, assuming yield to maturity falls from 8% to 7%: Predicted price change = −Duration × Δy/(1 + y) × P0 = −11.54 × −0.01/1.08 × $1,450.31 = $154.97Therefore: Predicted price = $154.97 + $1,450.31 = $1,605.28 c. Using the duration-with-convexity rule, if yield to maturity falls from 8% to 7%: Predicted price change = [−Duration × Δy/(1 + y) + (0.5 × Convexity × (Δy)2)] × P0Predicted price change = [-Duration × ∆y/1 + y + 0.5 × Convexity × ∆y2] × P0 =[(−11.54 × (−0.01/1.08)) + (0.5 × 192.4 × (−0.01)2)] × $1,450.31 = $168.92=[-11.54 × -0.01/1.08 + 0.5 × 192.4 × -0.012] × $1,450.31 = $168.92 Predicted price = $168.92 + $1,450.31 = $1,619.23
Sisters Corporation expects to earn $6 per share next year. The firm's ROE is 15% and its plowback ratio is 60%. The firm's market capitalization rate is 10%. a. Calculate the price with the constant dividend growth model b. Calculate the price with no growth. c. What is the present value of its growth opportunities?
a. 240 b. 60 c. 180 a.Given EPS = $6, ROE = 15%, plowback ratio = 0.60, and k = 10%, we first calculate the price with the constant dividend growth model: P0 = D1/(k − g) = (EPS × (1 − b))/(k − ROE × b) = ($6 × (1 − 0.60))/(0.10 − 0.15 × 0.60) = $2.40/(0.10 − 0.09) = $240 b. & c.Then, knowing that the price is equal to the price with no growth plus the present value of the growth opportunity, we can solve the following equation: Price = $240 = E1/k + PVGO = $6/0.10 + PVGO ⇒⇒ PVGO = $240 − $60 = $180
A 30-year maturity, 6% coupon bond paying coupons semiannually is callable in five years at a call price of $1,100. The bond currently sells at a yield to maturity of 5% (2.5% per half-year). a. What is the yield to call? b. What is the yield to call if the call price is only $1,050? c. What is the yield to call if the call price is $1,100 but the bond can be called in two years instead of five years?
a. 4.34 b. 3.52 c. 2.89 a. Using your calculator: n = 60;I/Y = 2.5; FV = 1,000; PMT = 30PV = $1,154.5433 based on the 2.5% yield to maturityUsing your calculator: n = 10; PV = −1,154.54; FV = 1,100; PMT = 30Therefore, yield to call is 2.1703% semiannually, 4.34% annually. b. Using your calculator: n = 10; PV = −1,154.54; FV = 1,050; PMT = 30Therefore, yield to call is 1.7625% semiannually, 3.52% annually. c. Using your calculator: n = 4; PV = −1,154.54; FV = 1,100; PMT = 30Therefore, yield to call is 1.4426% semiannually, 2.89% annually.
Pension funds pay lifetime annuities to recipients. If a firm remains in business indefinitely, the pension obligation will resemble a perpetuity. Suppose, therefore, that you are managing a pension fund with obligations to make perpetual payments of $2 million per year to beneficiaries. The yield to maturity on all bonds is 16%. a. If the duration of 5-year maturity bonds with coupon rates of 12% (paid annually) is four years and the duration of 20-year maturity bonds with coupon rates of 6% (paid annually) is eight years, how much of each of these coupon bonds (in market value) will you want to hold to both fully fund and immunize your obligation? b. What will be the par value of your holdings in the 20-year coupon bond?
a. 5-year bond = 2.34375 million 10-year bond= 10.15625 million b. parvalue= 24946.827 PV of obligation = $2 million/0.16 = $12.5 millionDuration of obligation = 1.16/0.16 = 7.25 yearsCall w the weight on the five-year maturity bond (with duration of 4 years) and (1-w) the weight on the 20-year bond. Then:(w × 4) + (1 − w) × 8 = 7.25 ⇒⇒ w = 0.1875 and 1 − w = 0.8125Therefore:0.1875 × $12.5 = $2.34375 million in the 5-year bond, and0.8125 × $12.5 = $10.15625 million in the 20-year bond. b. The price of the 20-year bond is:$60 × AF(16%, 20) + $1,000 × PV factor(16%, 20) = $60 × 1 − 1.6020/0.16 + $1,000 × 1/1.6020 = $407.12 Therefore, the bond sells for 0.4071 times its par value, so that:Market value = Par value × 0.4071$10.15625 million = Par value × 0.4071 ⇒⇒ Par value = $24.947 millionAnother way to see this is to note that each bond with par value $1,000 sells for $407.11. If total market value is $10.15625 million, then you need to buy:$10,156,250/407.11 = 24,947 bondsTherefore, total par value is $24,946,827.
The market capitalization rate for Admiral Motors Company is 8%. Its expected ROE is 10% and its expected EPS is $5. The firm's plowback ratio is 60%. a. Calculate the growth rate. b. What will be its P/E ratio?
a. 6% b. 20 a. g = ROE × b = 0.10 × 0.60 = 0.06 or 6% b. P/E = (1 − b)/(k − g) = (1 − 0.60)/(0.08 − 0.06) = 20
Fincorp issues two bonds with 20-year maturities. Both bonds are callable at $1,050. The first bond is issued at a deep discount with a coupon rate of 4% and a price of $580 to yield 8.4%. The second bond is issued at par value with a coupon rate of 8.75%. a. What is the yield to maturity of the par bond? b. If you expect rates to fall substantially in the next two years, which bond would you prefer to hold? Bond with a coupon rate 4% Bond with a coupon rate 8.75%
a. 8.75 b. bond with a coupon rate 4% a. The yield to maturity of the par bond equals its coupon rate, 8.75%. b. All else equal, the 4% coupon bond would be more attractive because its coupon rate is far below current market yields, and its price is far below the call price. Therefore, if yields fall, capital gains on the bond will not be limited by the call price. In contrast, the 8.75% coupon bond can increase in value to at most $1050, offering a maximum possible gain of only 5%. The disadvantage of the 8.75% coupon bond in terms of vulnerability to a call shows up in its higher promised yield to maturity. If an investor expects rates to fall substantially, the 4% bond offers a greater expected return.
A 20-year maturity bond with par value $1,000 makes semiannual coupon payments at a coupon rate of 8%. a. Find the bond equivalent and effective annual yield to maturity of the bond if the bond price is $950 .b. Find the bond equivalent and effective annual yield to maturity of the bond if the bond price is $1,000 c. Find the bond equivalent and effective annual yield to maturity of the bond if the bond price is $1,050.
a. bond equivalent yield= 8.52; effective annual ytm= 8.52 b. bond equivalent yield= 8; effective annual ytm=8.16 c. bond equivalent yield= 7.52; effective annual ytm=7.66 Use the following inputs: n = 40, FV = 1,000, PV = −950, PMT = 40. We will find that the yield to maturity on a semi-annual basis is 4.26%. This implies a bond equivalent yield to maturity of: 4.26% × 2 = 8.52%Effective annual yield to maturity = (1.0426)2 − 1 = 0.0870 = 8.70% Since the bond is selling at par, the yield to maturity on a semi-annual basis is the same as the semi-annual coupon, 4%. The bond equivalent yield to maturity is 8%.Effective annual yield to maturity = (1.04)2 − 1 = 0.0816 = 8.16% Use the following inputs: n = 40, FV = 1,000, PV = -1,050, PMT = 40, we find a bond equivalent yield to maturity of 7.52%, or 3.76% on a semi-annual basis.Effective annual yield to maturity = (1.0376)2 − 1 = 0.0766 = 7.66%
You manage a pension fund that will provide retired workers with lifetime annuities. You determine that the payouts of the fund are going to closely resemble level perpetuities of $1 million per year. The interest rate is 10%. You plan to fully fund the obligation using 5-year and 20-year maturity zero-coupon bonds. a. How much market value of each of the zeros will be necessary to fund the plan if you desire an immunized position? b. What must be the face value of each of the two zeros to fund the plan?
a. five year = 6 million twenty year= 4 million b. five year= 9.66 million twenty year= 26.91 million The duration of the perpetuity is: 1.10/0.10 = 11 yearsThe present value of the payments is: $1 million/0.10 = $10 millionLet w be the weight of the five-year zero-coupon bond and (1 − w) is the weight of the twenty-year zero-coupon bond. Then we find w by solving: (w × 5) + (1 − w) × 20 = 11 ⇒⇒ w = 9/15 = 0.60 w = 60% invested in the five-year zero-coupon bond1 − w = 40% in the twenty-year zero-coupon bond.Therefore, the market value of the five-year zero is:$10 million × 0.60 = $6 million Similarly, the market value of the twenty-year zero is:$10 million × 0.40 = $4 million b. Face value of the five-year zero-coupon bond is:$6 million × (1.10)5 = $9,663,060.00 = $9.66 millionFace value of the twenty-year zero-coupon bond is:$4 million × (1.10)20 = $26,909,999.80 = $26.91 million
You are managing a portfolio of $1 million. Your target duration is 10 years, and you can choose from two bonds: a zero-coupon bond with maturity five years and a perpetuity, each currently yielding 5%. a. How much of (i) the zero-coupon bond and (ii) the perpetuity will you hold in your portfolio? b. How will these fractions change next year if target duration is now nine years?
a. zero-coupon bond = 68.75% perpetuity bond= 31.25% b. zero-coupon bond = 70.59% perpetuity = 29.41% The duration of the perpetuity is: 1.05/0.05 = 21 yearsLet w be the weight of the zero-coupon bond and (1 − w) be the weight of the perpetuity; find w by solving:(w × 5) + (1 − w) × 21 = 10 ⇒⇒ w = 11/16 = 0.6875Therefore, the portfolio will be 68.75 percent invested in the zero-coupon bond and 31.25 percent in the perpetuity. b. The zero-coupon bond will then have a duration of 4 years while the perpetuity will still have a 21-year duration. To have a portfolio with duration equal to nine years, which is now the duration of the obligation, we again solve for w:(w × 4) + (1 − w) × 21 = 9 ⇒⇒ w = 12/17 = 0.7059So the proportion invested in the zero increases to 70.59 percent and the proportion in the perpetuity falls to 29.41 percent.
The weak form of the EMH states that ________ must be reflected in the current stock price all past information, including security price and volume data all publicly available information all information, including inside information all costless information
all past information, including security price and volume data
The semistrong form of the EMH states that ________ must be reflected in the current stock price. all security price and volume data all publicly available information all information, including inside information all costless information
all publicly available information
An 8%, 30-year bond has a yield-to-maturity of 10% and a modified duration of 8.0 years. If the market yield drops by 15 basis points, there will be a __________ in the bond's price a. 1.15% decrease b 1.20% increase c. 1.53% increase d. 2.43% decrease
b 1.20% increase
create a portfolio with a duration of 4 years, using a 5 year zero-coupon bond and a 3 year 8% annual coupon bond with a yield to maturity of 10%, one would have to invest ________ of the portfolio value in the zero-coupon bond. A) 50% B) 55% C) 60% D)75%
b. 55% duration table for both 4 =w*5 +(1-w)*2.77; w = 55%
The yield curve for default-free zero-coupon bonds is currently as follows: HW chapter 10 number 10
go back
You own a fixed-income asset with a duration of five years. If the level of interest rates, which is currently 8%, goes down by 10 basis points, how much do you expect the price of the asset to go up/down (in percentage terms)?
increases by 0.46% ΔP/P = −D × Δy/1 + y = −5.0 × −0.0010/1.08 = 0.0046 or a 0.46% increases.
Random price movements indicate ________. irrational markets that prices cannot equal fundamental values that technical analysis to uncover trends can be quite useful that markets are functioning efficiently
that markets are functioning efficiently
You own a bond that has a duration of 5 years. Interest rates are currently 6%, but you believe the Fed is about to increase interest rates by 29 basis points. Your predicted price change on this bond is +1.37% −1.37% −4.72% +4.72%
−1.37% -5* 0.029/(1.06)
