FINC 350 ch 10,11,12 homework problems
What is present value of 1000, 5 year with stated coupon rate 8% and market rate 10%
$900 1000* 8%=80 find on table present value of annuity= 5-10%- 3.79. 80*3.79= 303 and add to present value of principal payment
Calculate the present value of the bonds interest payments. The interest payment $200 annually for 6 years at a discount rate of 6%
$983.46 use table (PVAF) find 6 yrs 6% multiply 200*4.91
Common stock has a dividend of $2.00 at the end of the first year, a growth rate of 6%, and a price of $100. What is the required rate of return?
(2/100)+ 6%= 8%
Preferred stock as constant annual dividend payment $20 and a required rate of return of 5%. What is price preferred stock.
5/100=20/x; 5x= 2000; x=400
A 20000, 5 year bond has a stated rate of 6% and sells for 20,000. What is the yield to maturity?
6%
**a company's after-tax cost of debt is 6.5% and tax rate is 35%. What is the YTM?
=6.5%/(1-.35)=10%
A bond with a par value of $1000 is trading at $1100 and pays a $100 coupon. Similar bonds are yielding 10%. The current yield of the bond is
take 100/1100=9.09%
In the case of the baker corporation, we shall assume the annual dividend is $10.50. Preferred stock is $100 and Flotation or selling cost is $4.
using k= d/(p-f) 10.5/(100-4)= 10.5/96=10.94%
The price of a 500,000 10yr bod with a stated rate of 10% compounding semiannually, and a yield to maturity of 12% is [$ ]
N=20, (10*2), I/y= 6 (12/2), PMT= -25000 (500,000/5%), FV= 500,000 answer: 442650
Assume you are risk-averse and have the following three choices. Expected Standard value deviation A $ 2,010 $ 1,700 B 2,420 2,260 C 2,180 1,340
a. 1700/2010=0.846 2260/2420=.934 1340/2180=.615 Project c because has lowest risk Explanation: a. A $ 1,700 / $2,010 = .846 B 2,260 /$2,420 = .934 C $ 1,340/$2,180 = .615 b. Based on the coefficient of variation, you should select Project C as it is the least risky.
Essex Biochemical Co. has a $1,000 par value bond outstanding that pays 14 percent annual interest. The current yield to maturity on such bonds in the market is 9 percent. Use Appendix B and Appendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods. Compute the price of the bonds for the maturity dates: (Do not round intermediate calculations. Round your final answer to 2 decimal places. Assume interest payments are annual.)
a. 40yrs b. 17 yrs c. 5 yrs Explanation: Calculator Solution: a. 40 years to maturity: N I/Y PV PMT FV 40 9 CPTPV −1,537.87 140 1,000 Answer: $1,537.87 b. 17 years to maturity: N I/Y PV PMT FV 17 9 CPTPV −1,427.18 140 1,000 Answer: $1,427.18 c. 5 years to maturity: N I/Y PV PMT FV 5 9 CPTPV −1,194.48 140 1,000 Answer: $1,194.48 Appendix Solutions: a. 40 years to maturity: Appendix D Present value of interest payments: PVA = A × PVIFA (9%, 40) = $140.00 × 10.757 = $1,505.98 Appendix B Present value of principal payment: PV = FV × PVIF (9%, 40) = $1,000 × .032 = $32.00 Total present value = $1,505.98 + 32.00 = $1,537.98 b. 17 years to maturity: Appendix D Present value of interest payments: PVA = A × PVIFA (9%, 17) = $140.00 × 8.544 = $1,196.16 Appendix B Present value of principal payment: PV = FV × PVIF (9%, 17) = $1,000 × .231 = $231.00 Total present value = $1,196.16 + 231.00 = $1,427.16 c. 5 years to maturity: Appendix D Present value of interest payments: PVA = A × PVIFA (9%, 5) = $140.00 × 3.890 = $544.60 Appendix B Present value of principal payment: PV = FV × PVIF (9%, 5) = $1,000 × .650 = $650.00 Total present value = $544.60 + 650.00 = $1,194.60
Calculate the present value of the bonds principal payment for 5,000, 10 year bond w/ stated rate of 10% compounded annually, and yield of 12%.
$1610 use the formula in table discount/market rate of 12%=.32197. Muliply by $5000 = 1609.87
what is the present value of interest payment for 1000, 5 year bond with a stated coupon rate 8% and market rate of 10%
$303, to determine the annuity (interest payment) 1000*8%=80 go to PV of annuity $1 table find 5 periods at 10% discount (PAVF) rate=3.791. 80*3.79=303.2
What is the present value of interest payments for a 10,000, 10 year bond that pays an 8% coupon rate semiannually if the market rate of 10%?
$4900 To determine the annuity (interest payments) multiply 10000 by 4%=400, go to the PV of annuity of $1 table and find the table factor associated w/ 20 periods at a 5% discount/market rate= 12.462 Multiply $400 by table factor 12.462=4984.80
Calculate the present value of 5000, 10 year bonds with stated rate of 12% and market rate 10%
$5614 To determine the annuity (interest payments) multiply 5000*12=600, use table find discount/market rate of 10%=6.14456... Multiply 600 interest payment by 6.14456..=3686.75 present value of principal payment of 5,000/(1.10^10)=1927.72 Present value bond == 3686.75+1927.72=5614.46
what is the present value of principal payment for 1000, 5yr bond with coupon rate 8%, market rate of 10%
$621 go to PV of $1 table find 5 periods at 10% rate=0.62 (PVIF) 1000*.62=620
if the stated interest rate on the bond is 10%, what is the yield to maturity (discount rate) that will cause the bond to trade at par value?
10%
If the investors total rate of return is 5% in a 3% inflationary economy, the lender is earning ___ percent in purchasing power for use of the funds.
2%
***Using the 7year MACRS what is the amount of deprecation in year 2 for manufacturing equipment that cost the company 200,000 and has a residual/salvage value of 5,000?
49,000
Debby's Dance Studios is considering the purchase of new sound equipment that will enhance the popularity of its aerobics dancing. The equipment will cost $34,500. Debby is not sure how many members the new equipment will attract, but she estimates that her increased annual cash flows for each of the next five years will have the following probability distribution. Debby's cost of capital is 13 percent. Use Appendix D for an approximate answer but calculate your final answers using the formula and financial calculator methods. Cash Flow Probability $ 3,760 .2 5,760 .4 7,950 .3 10,050 .1 a. What is the expected value of the cash flow? The value you compute will apply to each of the five years. b. What is the expected net present value? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places.) c. Should Debby buy the new equipment? Yes No
Cash Flow Probability $ 3,760* .2 5,760* .4 7,950* .3 10,050* .1 Explanation: a. Cash Flow P Cash Flow × Probability $ 3,760 × .2 $ 752 5,760 × .4 2,304 7,950 × .3 2,385 10,050 × .1 1,005 Expected cash flow $ 6,446 b. NPV = −$34,500 + $6,446 × ({1 − [1 / 1.135]} / .13) = -$11,827.93 c. Debby should not buy this new equipment because the net present value is negative. Calculator solution: Press the following keys: CF, 2nd, CLR WORK. Calculator displays CFo, enter 34,500 and press +|-, press the Enter key. Press down arrow, enter 6,446, and press Enter. Press down arrow, enter 5, and press Enter. Press NPV; the calculator shows I = 0; enter 13 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = −11,827.93 Appendix Solution: b. PV of inflows = Expected cash flow × PVIFA (13%,5) = $6,446 × 3.517 = $22,670.58 NPV = PV of inflows - PV of outflows = $22,670.58 - 34,500 = −$11,829.42
assume a 10% $1000 par value bond has maturity of 20 years. annual yeld to maturity si 12 percent. semi annual interest bond prices
Divide annual interest rate by 2 multiply number of years by 2 divide annual yield to maturity by 2 10%/2=5% * 1000= 50 20*2=40 12%/2=6 n=40 i/y= 6 pmt=50 fv 1000
Assume a corporation has earnings before depreciation and taxes of $111,000, depreciation of $49,000 and that it is in a 35 percent tax bracket. Compute its cash flow using the following format. (Input all answers as positive values.)
Earnings before depreciation and taxes: 111,000 depreciation 49000 earnings before taxes 62000 taxes 21700 earnings after taxes 40300 depreciation 49000 cash flow 89300 Explanation: Taxes = Tax rate × Earnings before taxes = .35 × $62,000 = $21,700
Maxwell Communications paid a dividend of $1.35 last year. Over the next 12 months, the dividend is expected to grow at 11 percent, which is the constant growth rate for the firm (g). The new dividend after 12 months will represent D1. The required rate of return (Ke) is 24 percent. Compute the price of the stock (P0). (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Explanation: P0 = D1 / (Ke − g) = [(D1 × (1 + g)] / (Ke − g) = ($1.35 × 1.11) / (.24 − .11) = $11.53
You are called in as a financial analyst to appraise the bonds of Olsen's Clothing Stores. The $1,000 par value bonds have a quoted annual interest rate of 10 percent, which is paid semiannually. The yield to maturity on the bonds is 10 percent annual interest. There are 10 years to maturity. Use Appendix B and Appendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods. a. Compute the price of the bonds based on semiannual analysis. (Do not round intermediate calculations. Round your final answer to 2 decimal places.) b. With 5 years to maturity, if yield to maturity goes down substantially to 10 percent, what will be the new price of the bonds? (Do not round intermediate calculations. Round your final answer to 2 decimal places.)
Explanation: Calculator Solution: a. N I/Y PV PMT FV 10 × 2 10 / 2 CPT PV −1,000.00 100 / 2 1,000 10%/2=5% *1000= 50 n=20 i=5% pmt 50 fv 1000 Answer: $1,000.00 b. N I/Y PV PMT FV 5 × 2 10 / 2 CPT PV −1,000.00 100 / 2 1,000 n=10 pmt 50 i 5% fv 1000 Answer: $1,000.00 Appendix Solution: a. Appendix D Present value of interest payments: PVA = A × PVIFA (5%, 20) = $50 × 12.462 = $623.10 Appendix B Present value of principal payment at maturity: PV = FV × PVIF (5%, 20) = $1,000 × .377 = $377.00 Bond price = $623.10 + 377.00 = $1,000.10 b. Appendix D Present value of interest payments: PVA = A × PVIFA (5%, 10) = $50 × 7.722 = $386.10 Appendix B Present value of principal payment at maturity: PV = FV × PVIF (5%, 10) = $1,000 × .614 = $614.00 Bond price = $386.10 + 614.00 = $1,000.10
Russell Container Corporation has a $1,000 par value bond outstanding with 20 years to maturity. The bond carries an annual interest payment of $130 and is currently selling for $800 per bond. Russell Corp. is in a 25 percent tax bracket. The firm wishes to know what the aftertax cost of a new bond issue is likely to be. The yield to maturity on the new issue will be the same as the yield to maturity on the old issue because the risk and maturity date will be similar. a. Compute the yield to maturity on the old issue and use this as the yield for the new issue. (Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.) b. Make the appropriate tax adjustment to determine the aftertax cost of debt. (Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.)
Explanation: Calculator Solution: a. N I/Y PV PMT FV 20 CPT I/Y 16.46 −800 130 1,000 Answer: 16.46% b. Kd = Yield (1 − T) = 16.46% (1 - .25) = 12.34%
Bonds issued by the Coleman Manufacturing Company have a par value of $1,000, which of course is also the amount of principal to be paid at maturity. The bonds are currently selling for $750. They have 10 years remaining to maturity. The annual interest payment is 13 percent ($130). Compute the yield to maturity. (Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.)
Explanation: Calculator Solution: N I/Y PV PMT FV 10 CPT I/Y 18.70 −750 130 1,000 Answer: 18.70%
Tim Trepid is highly risk-averse while Mike Macho actually enjoys taking a risk. Investments Returns: Expected Value Standard Deviation Buy stocks $ 9,380 $ 6,540 Buy bonds 7,770 2,420 Buy commodity futures 21,600 25,200 Buy options 20,500 12,700 a-2. Which one of the following four investments should Tim choose? b. Which one of the four investments should Mike choose?
Explanation: Coefficient of variation (V) = Standard deviation / Expected value a-1. Buy stocks $6,540 / $9,380 = .697 Buy bonds $2,420 /$7,770 = .311 Buy commodity futures $25,200 / $21,600 = 1.167 Buy options $12,700 / $20,500 = .620 a-2. Tim should buy the bonds because bonds have the lowest coefficient of variation. b. Mike should buy the commodity futures because they have the highest coefficient of variation.
Five investment alternatives have the following returns and standard deviations of returns. Alternatives Returns: Expected Value Standard Deviation A $ 1,210 $ 1,210 B 1,300 650 C 7,100 2,200 D 1,840 1,390 E 64,300 13,800
Explanation: Coefficient of variation (V) = Standard deviation / Mean return Ranking from Lowest to Highest A $1,210 / $1,210 = 1.000 E B $650 / $1,300 = .500 C C $2,200 / $7,100 = .310 B D $1,390 / $1,840 = .755 D E $13,800 / $64,300 = .215 A
Wallace Container Company issued $100 par value preferred stock 10 years ago. The stock provided a 7 percent yield at the time of issue. The preferred stock is now selling for $80. What is the current yield or cost of the preferred stock? (Disregard flotation costs.) (Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.)
Explanation: Current yield = Dp / Pp = (.07 × $100) / $80 = .0875, or 8.75%
Tom Cruise Lines Inc. issued bonds five years ago at $1,000 per bond. These bonds had a 30-year life when issued and the annual interest payment was then 15 percent. This return was in line with the required returns by bondholders at that point as described below: Real rate of return 5 % Inflation premium 6 Risk premium 4 Total return 15 % Assume that five years later the inflation premium is only 2 percent and is appropriately reflected in the required return (or yield to maturity) of the bonds. The bonds have 25 years remaining until maturity. Compute the new price of the bond. Use Appendix B and Appendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods. (Do not round intermediate calculations. Round your final answer to 2 decimal places. Assume interest payments are annual.)
Explanation: First compute the new required rate of return (yield to maturity): Current yield to maturity = Real rate of return + Inflation premium + Risk premium = 5% + 2 + 4 = 11% Price = [A × ({1 − [1 / (1 + i)n]} / i)] + [FV / (1 + i)n] = [(.15 × $1,000) × ({1 − [1 / (1.11)25]} / .11)] + [$1,000 / 1.1125] = $1,336.87 Then, use this value to find the price of the bond. Calculator Solution: Present value of interest payments: N I/Y PV PMT FV 25 11 CPT PV −1,336.87 150 1,000 Answer: $1,336.87 Appendix Solution: Appendix D Present value of interest payments: PVA = A × PVIFA (11%, 25) = $150 × 8.422 = $1,263.30 Appendix B Present value of principal payment at maturity: PV = FV × PVIF (11%, 25) = $1,000 × .074 = $74.00 Bond price = $1,263.30 + 74.00 = $1,337.30
A firm pays a $13.80 dividend at the end of year one (D1), has a stock price of $149, and a constant growth rate (g) of 5 percent. Compute the required rate of return (Ke). (Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.)
Explanation: Ke = D1 / P0 + g = $13.80 / $149 + .05 = .1426, or 14.26%
Treynor Pie Company is a food company specializing in high-calorie snack foods. It is seeking to diversify its food business and lower its risks. It is examining three companies—a gourmet restaurant chain, a baby food company, and a nutritional products firm. Each of these companies can be bought at the same multiple of earnings. The following represents information about all the companies. Company Correlation with Treynor Pie Company Sales ($ millions) Expected Earnings ($ millions) Standard Deviation in Earnings ($ millions) Treynor PieCompany + 1.0 $ 189 $ 8 $ 2.0 Gourmet restaurant + .4 63 7 1.4 Baby food company + .3 57 4 1.6 Nutritionalproducts company − .5 76 5 3.3 a-1. Compute the coefficient of variation for each of the four companies. (Enter your answers in millions (e.g., $100,000 should be entered as ".10"). Round your answers to 3 decimal places.) a-2. Which company is the least risky? Gourmet restaurant correct a-3. Which company is the most risky? Nutritional products company correct b. Which of the acquisition candidates is most likely to reduce Treynor Pie Company's risk? Nutritional products company correct
Explanation: a-1. Coefficient of variation (V) = Standard deviation Expected value (millions) Treynor Pie Company $2.0 / $8.0 = .250 Gourmet restaurant 1.4 / 7.0 = .200 Baby food company 1.6 / 4.0 = .400 Nutritional products company 3.3 / 5.0 = .660 a-2. The gourmet restaurant chain is the least risky with a coefficient of variation of .200. a-3. The nutritional products firm has the highest risk with a coefficient of variation of .660. b. Because the nutritional products firm is highly negatively correlated (-.5) with Treynor Pie Company, it is most likely to reduce risk. It would appear that the demand for high-calorie snack foods moves in the opposite direction as the demand for nutritional items. Thus, Treynor Pie Company would reduce its risk to the largest extent by acquiring the company with the highest coefficient of variation (.660) as computed in part a. This would appear to represent a paradox, but it is not. It simply reflects the fact that the interaction between two companies is much more important than the individual risk of the companies.
The Short-Line Railroad is considering a $135,000 investment in either of two companies. The cash flows are as follows: Year Electric Co. Water Works 1 $ 85,000 $ 15,000 2 15,000 35,000 3 35,000 85,000 4 - 10 20,000 20,000 a. Compute the payback period for both companies. (Round your answers to 1 decimal place.) b. Which of the investments is superior from the information provided? Electric Co. correct
Explanation: a. Electric Co.: Cash flows Amount Yet To Be Recovered Initial investment $ 135,000 Year 1 $ 85,000 50,000 Year 2 15,000 35,000 Year 3 35,000 0 Year 4 20,000 0 The initial investment is fully recovered in exactly 3 years. Water Works: Cash flows Amount Yet To Be Recovered Initial investment $ 135,000 Year 1 $ 15,000 120,000 Year 2 35,000 85,000 Year 3 85,000 0 Year 4 20,000 0 The initial investment is fully recovered in exactly 3 years. b. The Electric Co. is a superior investment because it produces a large cash inflow in the first year, while the large recovery for Water Works is not until the third year. The problem is that the payback method does not consider the time value of money.
King's Department Store is contemplating the purchase of a new machine at a cost of $24,032. The machine will provide $3,700 per year in cash flow for eleven years. King's has a cost of capital of 12 percent. Use Appendix D for an approximate answer but calculate your final answer using the financial calculator method. a. What is the internal rate of return? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) b. Should the project be undertaken?
Explanation: a. IRR is the interest rate that makes the NPV equal to zero. NPV = $0 = -$24,032 + $3,700PVIFA (IRR, 11) The IRR must be calculated using a financial calculator, computer, a present value of annuity table, or trial-and-error. b. The machine should not be purchased since its return is less than the 12 percent cost of capital. Calculator Solution: Press the following keys: CF, 2nd, CLR WORK. Calculator displays CFo, enter 24,032 +|- key, press Enter key. Press down arrow, enter 3,700 and press Enter. Press down arrow, enter 11 and press Enter. Press IRR; calculator shows IRR = 0. Press CPT, calculator shows IRR = 10.00. Answer: IRR = 10.00% Appendix Solution: Appendix D: PVIFA = $24,032 / $3,700 = 6.495 For n = 11, we find 6.495 under the 10 percent column. IRR = 10%
Assume a $90,000 investment and the following cash flows for two alternatives. Year Investment A Investment B 1 $ 30,000 $ 30,000 2 25,000 30,000 3 20,000 40,000 4 30,000 — 5 25,000 — a. Calculate the payback for investment A and B. (Round your answers to 2 decimal places.) b. Which investment would you select under the payback method? Investment B correct c. If the inflow in the fifth year for Investment A was $25,000,000 instead of $25,000, would your answer change under the payback method? No correct
Explanation: a. Investment A: Cash flows Amount Yet To Be Recovered Initial investment $ 90,000 Year 1 $ 30,000 60,000 Year 2 25,000 35,000 Year 3 20,000 15,000 Year 4 30,000 0 Year 5 25,000 0 The initial investment is fully recovered between Year 3 and Year 4. The partial year is computed as the amount that still needs to be recovered at the end of Year 3 divided by the Year 4 cash flow, so: Payback periodA = 3 + ($15,000 / $30,000) = 3.50 years Investment B: Cash flows Amount Yet To Be Recovered Initial investment $ 90,000 Year 1 $ 30,000 60,000 Year 2 30,000 30,000 Year 3 40,000 0 The initial investment is fully recovered between Year 2 and Year 3. The partial year is computed as the amount that still needs to be recovered at the end of Year 2 divided by the Year 3 cash flow, so: Payback periodB = 2 + ($30,000 / $40,000) = 2.75 years b. Investment B would be selected because of the faster payback. c. The $25,000,000 inflow would still leave the payback period for investment A at 3.50 years. It would remain inferior to Investment B under the payback method.
The McGee Corporation finds it is necessary to determine its marginal cost of capital. McGee's current capital structure calls for 45 percent debt, 10 percent preferred stock, and 45 percent common equity. Initially, common equity will be in the form of retained earnings (Ke) and then new common stock (Kn). The costs of the various sources of financing are as follows: debt, 5.0 percent; preferred stock, 6.0 percent; retained earnings, 11.0 percent; and new common stock, 12.4 percent. a. What is the initial weighted average cost of capital? (Include debt, preferred stock, and common equity in the form of retained earnings, Ke.) (Do not round intermediate calculations. Input your answers as a percent rounded to 2 decimal places.) b. If the firm has $31.5 million in retained earnings, at what size capital structure will the firm run out of retained earnings? (Enter your answer in millions of dollars (e.g., $10 million should be entered as "10").) c. What will the marginal cost of capital be immediately after that point? (Equity will remain at 45 percent of the capital structure, but will all be in the form of new common stock, Kn.) (Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.) d. The 5.0 percent cost of debt referred to above applies only to the first $27 million of debt. After that, the cost of debt will be 8.5 percent. At what size capital structure will there be a change in the cost of debt? (Enter your answer in millions of dollars (e.g., $10 million should be entered as "10").) e. What will the marginal cost of capital be immediately after that point? (Consider the facts in both parts c and d.) (Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.)
Explanation: a. Cost (aftertax) Weights Weighted Cost Debt Kd 5.00 % 45 % 2.25 % Preferred stock Kp 6.00 10 .60 Common equity Ke (retained earnings) 11.00 45 4.95 Weighted average cost of capital Ka 7.80 % b. X = Retained earnings / Weight of common equity = $31.5 million / .45 = $70 million c. Cost (aftertax) Weights Weighted Cost Debt Kd 5.00 % 45 % 2.25 % Preferred stock Kp 6.00 10 .60 New common stock Kn 12.40 45 5.58 Marginal cost of capital Kmc 8.43 % d. Z = Amount of lower cost debt / Weight of debt = $27 million / .45 = $60 million e. Cost (aftertax) Weights Weighted Cost Debt Kd 8.50 % 45 % 3.83 % Preferred stock Kp 6.00 10 .60 New common stock Kn 12.40 45 5.58 Marginal cost of capital Kmc 10.01 %
Justin Cement Company has had the following pattern of earnings per share over the last five years: Year Earnings Per Share 20X1 $ 8.00 20X2 8.48 20X3 8.99 20X4 9.53 20X5 10.10 The earnings per share have grown at a constant rate (on a rounded basis) and will continue to do so in the future. Dividends represent 40 percent of earnings. a. Project earnings and dividends for the next year (20X6). (Round the growth rate to the nearest whole percent. Do not round any other intermediate calculations. Round your answers to 2 decimal places.) b. If the required rate of return (Ke) is 13 percent, what is the anticipated stock price (P0) at the beginning of 20X6? (Round the growth rate to the nearest whole percent. Do not round any other intermediate calculations. Round your answer to 2 decimal places.)
Explanation: a. Earnings growth rate: 20X1-20X2: ($8.48 − 8.00) / $8.00 = .06, or 6% 20X2-20X3: ($8.99 − 8.48) / $8.48 = .06, or 6% 20X3-20X4: ($9.53 − 8.99) / $8.99 = .06, or 6% 20X4-20X5: ($10.10 − 9.53) / $9.53 = .06, or 6% 20X6 Earnings = 20X5 Earnings × (1 + g) = $10.10 × 1.06 = $10.71 20X6 Dividends = .40 × 20X6 Earnings = .40 × $10.71 = $4.28 b. P0 = D1 / (Ke − g) = $4.28 / (.13 − .06) = $61.18
The treasurer of Riley Coal Co. is asked to compute the cost of fixed income securities for her corporation. Even before making the calculations, she assumes the aftertax cost of debt is at least 3 percent less than that for preferred stock. Debt can be issued at a yield of 11.0 percent, and the corporate tax rate is 20 percent. Preferred stock will be priced at $60 and pay a dividend of $6.40. The flotation cost on the preferred stock is $6. a. Compute the aftertax cost of debt. (Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.) b. Compute the aftertax cost of preferred stock. (Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.) c. Based on the facts given above, is the treasurer correct? Yes, the treasurer is correct. correct
Explanation: a. Kd = Yield (1 − T) = 11.0% (1 − .20) = 8.80% b. Kp = Dp / (Pp − F) = $6.40 / ($60 − 6) = .1185, or 11.85% c. Yes, the treasurer is correct. The difference is 3.05% (8.80% versus 11.85%).
Murray Motor Company wants you to calculate its cost of common stock. During the next 12 months, the company expects to pay dividends (D1) of $1.80 per share, and the current price of its common stock is $36 per share. The expected growth rate is 9 percent. a. Compute the cost of retained earnings (Ke). (Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.) b. If a $3 flotation cost is involved, compute the cost of new common stock (Kn). (Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.)
Explanation: a. Ke = D1 / P0 + g = $1.80 / $36 + .09 = .1400, or 14.00% b. Kn = D1 / (P0 − F) + g = $1.80 / ($36 − 3) + .09 = .1445, or 14.45%
The Horizon Company will invest $92,000 in a temporary project that will generate the following cash inflows for the next three years. Use Appendix B for an approximate answer but calculate your final answer using the formula and financial calculator methods. Year Cash Flow 1 $ 30,000 2 26,000 3 72,000 The firm will also be required to spend $14,000 to close down the project at the end of the three years. a. Compute the net present value if the cost of capital is 11 percent. (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places.) b. Should the investment be undertaken? No correct
Explanation: a. NPV = −$92,000 + ($30,000 / 1.11) + ($26,000 / 1.112) + (($72,000 − 14,000) / 1.113) = −$1,461.69 b. Since the net present value is negative, the project should not be undertaken. Calculator Solution: Press the following keys: CF, 2nd, Clear. Calculator displays CFo, enter 92,000 +|- key, press the Enter key Press down arrow, enter 30,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 26,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 58,000, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 11 and press Enter. Press down arrow; calculator shows NPV = 0. Press CPT; calculator shows NPV = −1,461.69. Note, the $14,000 outflow in year 3 has been subtracted from the $72,000 inflow in the third year, and thus the year 3 net cash flow is $58,000. Appendix Solution: Present value of inflows: Year Cash Flow × PVIF at 11% Present Value 1 $ 30,000 .901 $ 27,030 2 26,000 .812 21,112 3 72,000 .731 52,632 $ 100,774 Present value of outflows: Year Cash Flow × PVIF at 11% Present Value 0 $ 92,000 1.000 $ 92,000 3 14,000 .731 10,234 $ 102,234 NPV = PV of inflows − PV of outflows = $100,774 − 102,234 = −$1,460
You are asked to evaluate the following two projects for the Norton corporation. Use a discount rate of 11 percent. Use Appendix B for an approximate answer but calculate your final answer using the formula and financial calculator methods. Project X (Videotapes of the Weather Report) ($56,000 Investment) Project Y (Slow-Motion Replays of Commercials) ($76,000 Investment) Year Cash Flow Year Cash Flow 1 $ 28,000 1 $ 38,000 2 26,000 2 31,000 3 26,000 3 32,000 4 20,600 4 34,000 a. Calculate the profitability index for project X. (Do not round intermediate calculations and round your answer to 2 decimal places.) b. Calculate the profitability index for project Y. (Do not round intermediate calculations and round your answer to 2 decimal places.) c. Which project would you select? Project X correct
Explanation: a. PIX = [($28,000 / 1.11) + ($26,000 / 1.112) + ($26,000 / 1.113) + ($20,600 / 1.114)] / $56,000 = 1.41 b. PIY = [($38,000 / 1.11) + ($31,000 / 1.112) + ($32,000 / 1.113) + ($34,000 / 1.114)] / $76,000 = 1.38 c. You should select Project X because it has the higher profitability index. This is true in spite of the fact that it has a lower net present value. The profitability index may be appropriate when you have different size investments. Calculator Solution: a. Press the following keys: CF, 2nd, Clear. Calculator displays CFo, enter 0, press the Enter key. Press down arrow, enter 28,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 26,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 26,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 20,600, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; the calculator shows I = 0; enter 11 and press Enter. Press down arrow; calculator shows NPV = 0. Press CPT; calculator shows NPV = 78,908.24. Profitability index = Present value of inflows / Present value of outflows = $78,908.24 / $56,000 = 1.41 b. Press the following keys: CF, 2nd, Clear. Calculator displays CFo, enter 0, press the Enter key. Press down arrow, enter 38,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 31,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 32,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 34,000, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 11 and press Enter. Press down arrow; calculator shows NPV = 0. Press CPT; calculator shows NPV = 105,189.51. Profitability index = Present value of inflows / Present value of outflows = $105,189.51 / $76,000 = 1.38 Appendix Solutions: a. NPV for project X Year Cash Flow × PVIF at 11% Present Value 1 $ 28,000 .901 $ 25,228 2 26,000 .812 21,112 3 26,000 .731 19,006 4 20,600 .659 13,575 Present value of inflows $ 78,921 Present value of outflows(Cost) − 56,000 Net present value $ 22,921 PIX = Present value of inflows / Present value of outflows = $78,921 / $56,000 = 1.41 b. NPV for project Y Year Cash Flow × PVIF at 11% Present Value 1 $ 38,000 .901 $ 34,238 2 31,000 .812 25,172 3 32,000 .731 23,392 4 34,000 .659 22,406 Present value of inflows $ 105,208 Present value of outflows(Cost) − 76,000 Net present value $ 29,208 PIY = Present value of inflows / Present value of outflows = $105,208 / $76,000 = 1.38
Assume a $65,000 investment and the following cash flows for two alternatives. Year Investment X Investment Y 1 $20,000 $25,000 2 10,000 20,000 3 15,000 25,000 4 40,000 — 5 25,000 — a. Calculate the payback for investment X and Y. (Do not round intermediate calculations. Round your answers to 2 decimal places.) b. Which alternative would you select under the payback method? Investment Y correct
Explanation: a. Product X: Cash flows Amount Yet To Be Recovered Initial investment $ 65,000 Year 1 $ 20,000 45,000 Year 2 10,000 35,000 Year 3 15,000 20,000 Year 4 40,000 0 Year 5 25,000 0 The initial investment is fully recovered between Year 3 and Year 4. The partial year is computed as the amount that still needs to be recovered at the end of Year 3 divided by the Year 4 cash flow, so: Payback periodX = 3 + ($20,000 / $40,000) = 3.50 years Product Y: Cash flows Amount Yet To Be Recovered Initial investment $ 65,000 Year 1 $ 25,000 40,000 Year 2 20,000 20,000 Year 3 25,000 0 The initial investment is fully recovered between Year 2 and Year 3. The partial year is computed as the amount that still needs to be recovered at the end of Year 2 divided by the Year 3 cash flow, so: Payback periodY = 2 + ($20,000 / $25,000) = 2.80 years b. Investment Y would be selected because of the faster payback.
Speedy Delivery Systems can buy a piece of equipment that is anticipated to provide an 5 percent return and can be financed at 2 percent with debt. Later in the year, the firm turns down an opportunity to buy a new machine that would yield a 9 percent return but would cost 11 percent to finance through common equity. Assume debt and common equity each represent 50 percent of the firm's capital structure. a. Compute the weighted average cost of capital. (Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.) b. Which project(s) should be accepted?
Explanation: a. WACC = (Weight of debt × Cost of debt) + (Weight of equity × Cost of equity) = (.5× .02) + (.5× .11) = .0650, or 6.50% b. The new machine should be financed because its expected rate of return exceeds the weighted average cost of capital (WACC) of 6.50 percent.
Aerospace Dynamics will invest $158,000 in a project that will produce the following cash flows. The cost of capital is 11 percent. (Note that the fourth year's cash flow is negative.) Use Appendix B for an approximate answer but calculate your final answer using the formula and financial calculator methods. Year Cash Flow 1 $ 49,000 2 59,000 3 50,000 4 (54,000 ) 5 110,000 a. What is the net present value of the project? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places.) b. Should the project be undertaken? Yes correct
Explanation: a. NPV = −$158,000 + ($49,000 / 1.11) + ($59,000 / 1.112) + ($50,000 / 1.113) + (−$54,000 / 1.114) + ($110,000 / 1.115) = $297.61 b. Since the NPV is positive the project should be undertaken. Calculator Solution: Press the following keys: CF, 2nd, Clear. Calculator displays CFo, enter 158,000 +|- key, press Enter. Press down arrow, enter 49,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 59,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 50,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 54,000 +|-, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 110,000, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 11 and press Enter. Press down arrow; calculator shows NPV = 0. Press CPT; the calculator shows NPV = 297.61. Appendix Solution: Year Cash Flow × PVIF at 11% Present Value 1 $ 49,000 .901 $ 44,149 2 59,000 .812 47,908 3 50,000 .731 36,550 4 (54,000 ) .659 (35,586 ) 5 110,000 .593 65,230 Present value of inflows $ 158,251 Present value of outflows 158,000 Net present value $ 251
X-Tech Company issued preferred stock many years ago. It carries a fixed dividend of $9 per share. With the passage of time, yields have soared from the original 13 percent to 17 percent (yield is the same as required rate of return). a. What was the original issue price? (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. What is the current value of this preferred stock? (Do not round intermediate calculations. Round your answer to 2 decimal places.) c. If the yield on the Standard & Poor's Preferred Stock Index declines, how will the price of the preferred stock be affected? The price of preferred stock will increase. correct
Explanation: a. Original price: Pp = Dp / Kp = $9 / .13 = $69.23 b. Current value: Pp = Dp / Kp = $9 / .17 = $52.94 c. The price of preferred stock will increase as yields decline. Since preferred stock is a fixed income security, its price is inversely related to yields as would be true with bond prices. The present value of an income stream has a higher present value as the discount rate declines, and a lower present value as the discount rate increases.
Baker corporation: we assume the following values Rf=5.5% Km=12% B=1
Kj=Rf + B(beta coefficient)(Km-Rf) 5.5%+ 1*(12%-5.5%) 5.5%+6.5%=12%
The Lone Star Company has $1,000 par value bonds outstanding at 10 percent interest. The bonds will mature in 18 years. Use Appendix B and Appendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods. Compute the current price of the bonds if the present yield to maturity is. (Do not round intermediate calculations. Round your final answers to 2 decimal places. Assume interest payments are annual.)
a.7perc 1301.77 b.9perc 1087.56 c. 12perc 855.01 7 percent yield to maturity: Calculator Solution: a. 7 percent yield to maturity: N I/Y PV PMT FV 18 7 CPTPV −1,301.77 100 1,000 Answer: $1,301.77 b. 9 percent yield to maturity: N I/Y PV PMT FV 18 9 CPTPV −1,087.56 100 1,000 Answer: $1,087.56 c. 12 percent yield to maturity: N I/Y PV PMT FV 18 12 CPTPV −855.01 100 1,000 Answer: $855.01 Appendix Solutions: a. 7 percent yield to maturity: Appendix D Present value of interest payments: PVA = A × PVIFA (7%, 18) PVA = $100 × 10.059 = $1,005.90 Appendix B Present value of principal payment at maturity: PV = FV × PVIF (7%, 18) PV = $1,000 × .296 = $296.00 Total present value = $1,005.90 + 296.00 = $1,301.90 b. 9 percent yield to maturity: Appendix D Present value of interest payments: PVA = A × PVIFA (9%, 18) PVA = $100 × 8.756 = $875.60 Appendix B Present value of principal payment at maturity: PV = FV × PVIF (9%, 18) PV = $1,000 × .212 = $212.00 Total present value = $875.60 + 212.00 = $1,087.60 c. 12 percent yield to maturity: Appendix D Present value of interest payments: PVA = A × PVIFA (12%, 18) PVA = $100 × 7.250 = $725.00 Appendix B Present value of principal payment at maturity: PV = FV × PVIF (12%, 18) PV = $1,000 × .130 = $130.00 Total present value = $725.00 + 130.00 = $855.00
calculate the present value of the bonds principal payment for a 5,000, 10 year bond with a stated rate of 10% compounded annually, and yield of 12%?
answer: 1610 n=10 i/1=12 pmt=0 fv=5000 CPTPV=1609.87
firms operating at a loss deficit display ___ symbol on P/E ration for Barron's
dd
Assume the debt issue pays $100/yr in interest, has 15yr life principal amount 1000 will be paid. is selling for 939. yied to maturity is the interst rate that the market uses to price the bond.
n=15 pv -939 don't forget negative pmt 100 fv 1000 cpt i/y = 10.84
If dividend at end of first year is $2, price of stock today $40, growth rate of 7% what is rate of return required K?
p=d/k-g k= d/p + g 2/40=5% 5%+7%=12%
Sauer Milk Inc. wants to determine the minimum cost of capital point for the firm. Assume it is considering the following financial plans: Cost (aftertax) Weights Plan A Debt 5.0 % 20 % Preferred stock 10.0 10 Common equity 14.0 70 Plan B Debt 5.8 % 30 % Preferred stock 10.8 10 Common equity 15.0 60 Plan C Debt 6.0 % 40 % Preferred stock 11.7 10 Common equity 17.8 50 Plan D Debt 10.0 % 50 % Preferred stock 12.4 10 Common equity 19.5 40 a-1. Compute the weighted average cost for four plans. (Do not round intermediate calculations. Input your answers as a percent rounded to 2 decimal places.) a-2. Which of the four plans has the lowest weighted average cost of capital? Plan A correct b. What is the relationship between the various types of financing costs and the debt-to-equity ratio? All types of financing costs increase as the debt-to-equity ratio increases. correct
xplanation: a-1. Sauer Milk Inc. Cost (aftertax) Weights Weighted Cost Plan A: Debt 5.0 % 20 % 1.00 % Preferred stock 10.0 10 1.00 Common equity 14.0 70 9.80 11.80 % Plan B: Debt 5.8 % 30 % 1.74 % Preferred stock 10.8 10 1.08 Common equity 15.0 60 9.00 11.82 % Plan C: Debt 6.0 % 40 % 2.40 % Preferred stock 11.7 10 1.17 Common equity 17.8 50 8.90 12.47 % Plan D: Debt 10.0 % 50 % 5.00 % Preferred stock 12.4 10 1.24 Common equity 19.5 40 7.80 14.04 % a-2. Plan A has the lowest weighted average cost of capital. b. As the debt-to-equity ratio increases, the cost of every type of financing increases due to the increased risk level of the firm.
