exam solution 9 fundamentals of corporate finance, 4th edition brealey

AK/ADMS 3530.03 Finance Midterm Exam Winter 2007 Solutions Type A Exam Numerical questions (4 points each) (Q in B) The Joshua Co plans on saving money to buy some new equipment The company is opening an account today with a deposit of $15,000 and expects To earn 4% interest annually After years, the firm wants to add an additional $50,000 to the account If the account continues and earns 4% interest compounded semi-annually after years, how much money will the Joshua Co have in their account five years from now? A) $66,872.96 B) $68,249.79 C) $70,952.96 D) $72,385.44 Answer D Using FV = PV × (1+r)^t formula FV in 3yrs = $15,000 × (1 + 0.04) ^3 = $16,872.96 FV in yrs = $(16,872.96 + 50,000) × (1 + 0.04 / 2)^ = $72,385.44 (Q in B) I want to buy a car that I know will cost me $43,860 (before taxes) in ten years How much must I save annually, beginning one year from now, in order to accumulate the purchase price plus all applicable taxes by the end of Year 10? In this case taxes are 6% GST and 8% PST which are each applied to the purchase price Assume that interest is calculated at percent annually A) $2,887 B) $3,291 C) $4,500 D) $4,587 Answer B Amount required in ten years = $43,860 × (1.14) = $50,000.40 Using the FV annuity formula where FV= PMT× ((1+r)^t – 1) r ((1.09)10 − 1) $50,000 = PMT × 09 = PMT × 15.1929 PMT = $3,291.04 (Q in B) A credit card company sends you a promotion that says it will charge you an interest rate of 1.25% monthly In this case the annual percentage rate (APR) is and the effective annual rate (EAR) is _ and if I carried a $300 balance throughout the year I would owe _ at the end of the year A) 16.08%; 15.00%; $348.24 B) 15.00%; 14.55%; $345.00 C) 14.55%; 15.00%; $345.00 D) 15.00%; 16.08%; $348.24 Answer D APR = 1.25% × 12 = 15% EAR = (1+1.25%)^12 – = 16.08% Balance owing = 300 × (1+0.1608) = $348.24 (Q in B) Prizes are often not “worth” as much as claimed Place a value on a prize of $5,000,000 that is to be received in equal annual payments over the next 20 years, with the first payment beginning today Assume an interest rate of percent over the 20-year period A) $2,212,652 B) $2,648,504 C) $2,833,899 D) $2,950,567 Answer C Annual payment = $5,000,000 / 20 = $250,000 1   − i i(1 + i)n  (for annuities due) PV = PMT + PMT   1  −  19  07 07(1.07)  = $250,000 + $250,000  = $250,000 + $250,000 [10.3356] =$2,833,898.81 (Q in B) Which of the following strategies will allow real retirement spending to remain approximately equal, assuming savings of $1,000,000 invested at percent annually, a 25-year time horizon, and a percent expected annual inflation rate? A) Spend approximately $63,000 annually B) Spend approximately $78,225 annually C) Spend approximately $93,680 annually D) Spend approximately $127,500 annually Answer A Using the formula where + real rate = Real rate =  1.08     1.04. + nominal rate + inflation rate – = 3.85% 1  Then using the formula where PV of an annuity = C ×  − t   r r(1 + r )   1  −  25  0385 0385(1.0385)  $1,000,000 = pmt  $63,001 = pmt (Q in B) You are saving money to buy a house in ten years You will need $75,000 to make the down payment at that time Due to some other financial commitments you won’t be able to deposit any money in years and 10 towards this down payment How much equal amounts must you deposit in a savings account at the end of each year (other than years and 10) in order to save $75,000 if the savings account pays interest at 10 percent per year compounded annually? A) $3,875 B) $4,115 C) $5,420 D) $6,558 Answer C The timeline of your savings account is as follows: 10 I I I I I I I I I I -I R R R R R R R R $75,000 = R × (FVIFA 10%, 8yrs) × (FVIF 10%, 2yrs) $75,000 = R x 11.4359 x 1.21 $75,000 = 13.8374R R = $5,420.09 (Q in B) You are planning to establish a 30-year scholarship fund at York University that will pay $12,000 at the end of the first year and then increase by 1.5% per year The scholarship fund will be managed by a successful fund manager, Chris Robinson Chris guarantees that the fund will earn a 6.75% annual rate of return How much should you donate to York today in order to maintain this scholarship? A) $50,346.20 B) $146,508.84 C) $178,225.23 D) $228,571.43 Answer C This is a growing annuity   1.015  30  $12,000  = $178,225.23 × 1 − PV = 0.0675 − 0.015  1.0675   (Q 10 in B) You want to buy a house that costs $400,000 You make a 25% down payment and finance the rest with a 15 year mortgage The mortgage has a five year renewal term for which the annual mortgage rate is 6.5% compounded semi-annually What will the remaining principal of the loan be at the end of the 5-year term? A) $229,787.77 B) $289,459.98 C) $304,514.42 D) $317,182.54 Answer A 0.065 ) − = 6.605625% Monthly rate is r = (1+0.06605625)1/12 - = 0.005345 = 0.5345% Monthly payment: N=180, I/Y=0.5345%, PV=-$300,000, FV=0, CPTỈ PMT=$2,599.15 Remaining principal at the end of 5-year term is the PV of remaining payments: N=120, I/Y=0.5345%, PMT=$2,599.15, FV=0, CPTỈ PV=$229,787.77 EAR = (1 + (Q in B) A deposit of $3,500 made three years ago is worth $5,200 today The deposit pays interest quarterly What is the APR with quarterly compounding on this deposit? A) 12.97% B) 13.42% C) 14.15% D) 15.54% Answer B N=12, PMT=0, FV=$5,200, PV=-$3,500, CPTỈI/Y=3.3541 (this is the quarterly rate), APR = 3.3541% × = 13.4164% 10 (Q in B) How much interest is to be earned between the end of year and the end of year on a $1,000 deposit made today that earns 7% interest compounded annually? A) $189.93 B) $194.11 C) $206.52 D) $246.28 Answer A The difference between the FV6 and FV4 is the interest you earn over these two years With your calculator, PV= -1000, N=6, i=7%, PMT=0 FV=? FV6 = 1500.73 PV= -1000, N=4, i=7%, PMT=0 FV=? FV4 = 1310.80 So interest earned = $1,500.73 - $1,310.80 = $189.93 11 (Q 16 in B) When an investor purchases a $1,000 par value bond that was quoted at 97.16, the investor: A) pays $971.60 for the bond B) pays $1,029.23 for the bond C) receives $971.60 upon the maturity date of the bond D) receives 97.16 percent of the stated coupon payments Answer A Bond prices are quoted as a percentage of their face value So the bond in question has a price of 97.16% × $1,000 = $971.60 12 (Q 17 in B) What is the yield to maturity for a bond paying $100 coupon annually that has six years until maturity and sells for $1,074.22? The bond has a face value of $1,000 and pays semi-annual coupons A) 4.20 percent B) 4.66 percent C) 8.40 percent D) 9.31 percent Answer C Using your calculator, 50 (PMT), 1000 (FV), 12 (N), -1074.22 (PV), CPT I/Y = 4.2% So the YTM is 4.2% × = 8.4% Alternatively, if you use the approximate formula, you should get: $(1,000 − 1,074.22) $100 + = 8.45% $(1,000 + 1,074.22) / 13 (Q 18 in B) What happens to the price of a three-year bond with an percent coupon rate, semi-annual coupons, when interest rates change from percent to percent? The bond has a par value of $1,000 A) A price decrease of $27.03 B) A price decrease of $27.53 C) A price increase of $27.03 D) A price increase of $27.53 Answer D At the 7% interest rate, the bond price is: 1 $1,000 ]+ − = $1,026.64 0.035 0.035 × (1.035 ) (1.035 ) At the 6% interest rate, the bond price becomes: 1 $1,000 $40 × [ − ]+ = $1,054.17 0.03 0.03 × (1.03 ) (1.036 ) So the bond price increases by $1,054.17 - $1,026.64 = $27.53 $40 × [ 14 (Q 19 in B) What is the rate of return for an investor who pays $1,054.47 for a three-year bond with a percent coupon and sells the bond one year later for $1,037.19? Assume the investor can reinvest the coupons at a 9% APR with semi-annual compounding The bond pays coupons semi-annually and has a face value of $1,000 A) 5.00 percent B) 5.15 percent C) 5.30 percent D) 8.43 percent Answer B The rate of return is calculated as: $35 × (1.045) + $35 + $(1,037.19 − 1,054.47) = 5.15% $1,054.47 15 (Q 20 in B) Deferred coupon bonds are bonds whose coupon payments are deferred for a specified number of years That is, there are no coupon payments during the deferred period Consider a 15-year deferred coupon bond with $1,000 face value The deferred period is the first years in the life of the bond After the deferred period, the issuer will pay X% of the par as annual coupons (i.e coupons are paid once per year) until maturity to bond investors, with the first payment occurring year after the deferred period The bond is yielding 7% annually and selling for $926.21 What is the value of X? A) 10.54% B) 11.26% C) 12.05% D) 12.55% Answer B The coupons from this bond are a 10-year annuity of X% of the par ($1,000) This annuity is delayed for years, i.e the first coupon payment is to be received at the end of Year So the price of the bond is given by: 1 coupon × [ − ] r r (1 + r ) t face value Pr ice = + n (1 + r ) (1 + r ) m 1 X% × $1,000 × [ − ] 0.07 0.07(1.0710 ) $1,000 = + (1.07 ) (1.0715 ) X% × $1,000 × 7.0236 = + $362.4460 = X% × $1,000 × 5.0076 + $362.4460 = $926.21 1.4026 ⇒ X = 11.2582% 16 (Q 11 in B) What is the expected constant growth rate of dividends for a stock currently priced at $50, that just paid a dividend of $4, and has a required rate of return of 18 percent? A) 3.41 percent B) 5.50 percent C) 9.26 percent D) 12.50 percent Answer C $50 = $4(1 + g)/(0.18 – g), so r = 9.26% 17 (Q 12 in B) What proportion of earnings is being retained by the firm if the sustainable growth rate is percent and the firm's ROE is 20 percent? A) 8% B) 12% C) 20% D) 40% Answer D 8% = 20% × plowback 40% = plowback 18 (Q 13 in B) What is the most likely value of the PVGO for a stock with a current price of $50, expected earnings of $6 per share, and a required rate of return of 20 percent? A) $10 B) $20 C) $25 D) $30 Answer B With 100 percent payout ratio, the stock would be valued at $30 ($6/0.2 = $30) Thus, the $20 of additional price must represent the PVGO 19 (Q 14 in B) What would be the price of a stock today when dividends are expected to grow at a 25 percent rate for three years, then grow at a constant rate of percent forever, if the stock's required rate of return is 13 percent and next year's dividend will be $4? A) $61.60 B) $62.08 C) $68.64 D) $79.44 Answer C $4.00 (1.13) + $4.00(1.25) (1.13)2 + $4.00(1.25)2 (1.13)3 $4.00(1.25)2 (1.05) + 13 −.05 (1.13)3 Po = $5.00 1.2769 + $6.25 1.4429 + 6.56 08 1.4429 = $3.54 + = $(3.54 + 3.92 + 4.33 + 56.85) = $68.64 20 (Q 15 in B) How much should you pay now for a share of stock that offers a constant growth rate of 10 percent, requires a 16 percent rate of return, and is expected to sell for $50 one year from now? A) $42.00 B) $45.00 C) $45.45 D) $47.00 Answer C The easiest way to solve this problem is to realize: Expected rate of return = expected dividend yield + expected capital appreciation Also: Expected rate of return = expected dividend yield + constant growth rate Then: Expected capital appreciation = constant growth rate (10%) So: P1 = 110% of Po $50.00 = 1.1Po, $45.45 = Po Conceptual questions (2 points each) 21 (Q 21 in B) Which of the following is least likely to represent an agency problem? A) Lavish spending on expense accounts B) Plush remodeling of the executive suite C) Excessive investment in "safe" projects D) Executive incentive compensation plans Answer D 22 (Q 27 in B) Under which of the following conditions will a future value calculated with simple interest exceed a future value calculated with compound interest at the same rate? A) The interest rate is very high B) The investment period is very long C) The compounding is annually D) This is not possible with positive interest rates Answer D 10 23 (Q 28 in B) Which of the following statements best describes the real interest rate? A) Real interest rates exceed inflation rates B) Real interest rates can decline only to zero C) Real interest rates can be negative, zero, or positive D) Real interest rates traditionally exceed nominal rates Answer C 24 (Q 29 in B) As long as the interest rate is greater than zero, the present value of a single sum will always: A) be less than the future value B) decrease as the period of time decreases C) equal the future value if the time period is one year D) increase as the number of periods increases Answer A 25 (Q 30 in B) Which of the following statements is wrong about the time value of money (TVM)? A) Converting an annuity to an annuity due increases the present value B) An effective annual rate is always higher than an annual percentage rate, other things being equal C) The more frequent the compounding, the higher the future value, other things being equal D) For a given amount, the higher the discount rate, the lower the present value Answer B 26 (Q 22 in B) Cash flows occurring in different periods should not be compared unless: A) interest rates are expected to be stable B) the cash flows occur no more than one year from each other C) higher rates of interest can be earned on the cash flows D) the cash flows have been discounted to a common date Answer D 27 (Q 23 in B) Which of the following will increase the present value of an annuity, other things being equal? A) Increasing the interest rate 11 B) Decreasing the interest rate C) Decreasing the number of payments D) Decreasing the amount of the payments Answer B 28 (Q 24 in B) Which of the following statements about a bond’s coupon rate, current yield, and yield to maturity (YTM) is correct? A) When the bond sells at a premium, its coupon rate is higher than yield, and its coupon rate is also higher than the YTM B) When the bond sells at a premium, its coupon rate is lower than yield, and its coupon rate is higher than the YTM C) When the bond sells at a discount, its coupon rate is higher than yield, and its coupon rate is lower than the YTM D) When the bond sells at a discount, its coupon rate is lower than yield, and its coupon rate is higher than the YTM the current the current the current the current Answer A 29 (Q 25 in B) Reinvesting earnings into a firm will not increase the stock price unless: A) the new paradigm of stock pricing is maintained B) true depreciation is less than reported depreciation C) the firm's dividends are growing also D) the ROE of new investments exceeds the firm's required rate of return Answer D 30 (Q 26 in B) The purpose of a sinking fund is to: A) reduce the par value of stock over time B) take advantage of the tax break on preferred stock C) periodically retire debt prior to final maturity D) allow risky corporations to avoid bankruptcy Answer C 12 ... (1+0.06605625)1/12 - = 0.005345 = 0.5345% Monthly payment: N=180, I/Y=0.5345%, PV =-$ 300,000, FV=0, CPTỈ PMT=$2,599.15 Remaining principal at the end of 5-year term is the PV of remaining payments:... price of a three-year bond with an percent coupon rate, semi-annual coupons, when interest rates change from percent to percent? The bond has a par value of $1,000 A) A price decrease of $27.03... in B) What is the most likely value of the PVGO for a stock with a current price of $50, expected earnings of $6 per share, and a required rate of return of 20 percent? A) $10 B) $20 C) $25 D)