Midterm 2

Luther Industries needs to raise $25 million to fund a new office complex. The company plans on issuing ten-year bonds with a face value of $1,000 and a coupon rate of 7.5 % (annual payments). The following table summarizes the YTM for similar ten-year corporate bonds of various credit ratings: Rating AAA AA A BBB BB YTM 6.60 % 6.80 % 6.90 % 7.30 % 7.80 % Assuming that Luther's bonds are rated AAA, their price will be closest to ________. A) $852 B) $1490 C) $1277 D) $1064

$1064 Explanation: FV = $1,000 PMT = $ 75 N = 10 I = 6.60 Compute PV = $ 1064.40 .

You are borrowing money to buy a car. If you can make payments of $320 per month starting one month from now at an interest rate of 12%, how much will you be able to borrow for the car today if you finance the amount over 4 years? A) $7291.00 B) $12,151.67 C) $14,582.00 D) $17,012.34

$12,151.67 Explanation: N = 48 I = 12 /12 PMT = $ 320 FV = 0 PV = $12,151.67

Matthew wants to take out a loan to buy a car. He calculates that he can make repayments of $5000 per year. If he can get a four-year loan with an interest rate of 7.9 %, what is the maximum price he can pay for the car? A) $19,918 B) $26,557 C) $23,237 D) $16,598

$16,598 Explanation: Calculate PV using TVM keys: input PMT = $ 5000, N= 4, and interest rate = 7.9 %; PV = $16,597.5634.

A bank is negotiating a loan. The loan can either be paid off as a lump sum of $80,000 at the end of four years, or as equal annual payments at the end of each of the next four years. If the interest rate on the loan is 6%, what annual payments should be made so that both forms of payment are equivalent? A) $29,259 B) $25,602 C) $14,630 D) $18,287

$18,287 Explanation: Calculate PMT with FV = $80,000 , interest = 6% and N = 4, which gives PMT = $18,287.32.

Dan buys a property for $210,000 . He is offered a 30-year loan by the bank, at an interest rate of 8% per year. What is the annual loan payment Dan must make? A) $26,115.26 B) $18,653.76 C) $29,846.02 D) $22,384.51

$18,653.76 Calculate PMT using TVM keys: input PV = 210,000 , N = 30, and interest rate = 8%; PMT = $18,653.76.

JRN Enterprises just announced that it plans to cut its dividend from $3.00 to $1.50 per share and use the extra funds to expand its operations. Prior to this announcement, JRN's dividends were expected to grow indefinitely at 4% per year and JRN's stock was trading at $25.50 per share. With the new expansion, JRN's dividends are expected to grow at 8% per year indefinitely. Assuming that JRN's risk is unchanged by the expansion, the value of a share of JRN after the announcement is closest to ________. A) $25.50 B) $19.32 C) $38.63 D) $12.75

$19.32 Explanation: Two steps. Step 1: Solve forrE: rE = Div 1 / P0 +g = $3.00/$25.50 +0.04 = 0.15765 or 15.77% Step 2: Solve for new stock price: P0 = Div 1 / (rE - g) = $1.50/(0.15765 - 0.08 ) = $19.32

Shown above is information from FINRA regarding one of Bank of America's bonds. How much would the holder of such a bond earn each coupon payment for each $100 in face value if coupons are paid semiannually? A) $2.32 B) $1.49 C) $4.30 D) $2.15

$2.15 Explanation: 100 × 4.300% = $4.30; $4.30 / 2 = $2.15

Two years ago you purchased a new SUV. You financed your SUV for 60 months (with payments made at the end of the month) with a loan at 5.95 % APR. Your monthly payments are $386.19 and you have just made your 24th monthly payment on your SUV. The amount of your original loan is closest to ________. A) $20,000 B) $22,000 C) $24,000 D) $28,000

$20,000 Explanation: First we need the monthly interest rate = APR/m= 0.0595/12 = 0.004958 or 0.4958 %. Now: I = 0.4958 FV = 0 N = 60 PMT = $ 386.19 Compute PV = $20,000

Martin wants to provide money in his will for an annual bequest to whichever of his living relatives is oldest. That bequest will provide $4000 in the first year, and will grow by 7% per year, forever. If the interest rate is 9%, how much must Martin provide to fund this bequest? A) $200,000.00 B) $240,000.00 C) $160,000.00 D) $100,000.00

$200,000.00 Explanation: PV growth perpetuity = $ 4000 / (0.09 - 0.07) = $200,000.00

Sinclair Pharmaceuticals, a small drug company, develops a vaccine that will protect against Helicobacter pylori, a bacteria that is the cause of a number of diseases of the stomach. It is expected that Sinclair Pharmaceuticals will experience extremely high growth over the next three years and will reinvest all of its earnings in expanding the company over this time. Earnings were $1.10 per share before the development of the vaccine and are expected to grow by 40% per year for the next three years. After this time, it is expected that growth will drop to 5% and stay there for the expected future. Four years from now Sinclair will pay dividends that are 75% of its earnings. If its equity cost of capital is 12%, what is the value of a share of Sinclair Pharmaceuticals today? A) $20.62 B) $33.96 C) $33.51 D) $24.17

$24.17 Explanation: E4 = $3.16932; D4 = $2.37699 ; P3 = $2.37699/(0.12 - 0.05 ) = $33.96 ; P0 = ($33.96 ) / (1 +0.12)3 = $24.17

Clarissa wants to fund a growing perpetuity that will pay $10,000 per year to a local museum, starting next year. She wants the annual amount paid to the museum to grow by 5% per year. Given that the interest rate is 9%, how much does she need to fund this perpetuity? A) $250,000.00 B) $125,000.00 C) $300,000.00 D) $200,000.00

$250,000.00 Explanation: PV growth perpetuity = $ 10,000 / (0.09 - 0.05 ) = $250,000.00

Suppose the term structure of interest rates is shown below: Term 1 year 2 years 3 years 5 years 10 years 20 years Rate (EAR%) 5.00% 4.80% 4.60% 4.50% 4.25% 4.15% The present value (PV) of receiving $1100 per year with certainty at the end of the next three years is closest to ________. A) $4214 B) $3612 C) $3010 D) $2408

$3010 Explanation: PV = $ 1100 / (1 + 0.050) + $ 1100 / (1 + 0.048)2 + $ 1100 / (1 + 0.046)3 = 3010.33

You are considering purchasing a new home. You will need to borrow $290,000 to purchase the home. A mortgage company offers you a 20-year fixed rate mortgage (240 months) at 12% APR (1% month). If you borrow the money from this mortgage company, your monthly mortgage payment will be closest to ________. A) $4470 B) $5109 C) $3193 D) $2554

$3193 Explanation: PV = 290,000 I = 1 N = 240 FV = 0 Compute payment = $3193.15 .

What is the present value (PV) of an investment that pays $100,000 every year for four years if the interest rate is 5% APR, compounded quarterly? A) $424,581 B) $459,963 C) $353,818 D) $389,200

$353,818 Explanation: Calculate EAR = 5.0945 %; Calculate PV Annuity = $353,818

Since your first birthday, your grandparents have been depositing $1200 into a savings account on every one of your birthdays. The account pays 6% interest annually. Immediately after your grandparents make the deposit on your 18th birthday, the amount of money in your savings account will be closest to ________. A) $44,504.14 B) $22,252.07 C) $37,086.78 D) $51,921.49

$37,086.78 Explanation: N = 18 PMT = $ 1200 I = 6 PV = 0 Compute FV = $37,086.78.

What is the coupon payment of a 15-year $10,000 bond with a 9% coupon rate with semiannual payments? A) $1800.00 B) $150.00 C) $450 D) $900.00

$450 Explanation: $10,000 ×0.09/2 = $450

Sunnyfax Publishing pays out all its earnings and has a share price of $37. In order to expand, Sunnyfax Publishing decides to cut its dividend from $3.00 to $2.00 per share and reinvest the retained funds. Once the funds are reinvested, they are expected to grow at a rate of 13%. If the reinvestment does not affect Sunnyfax's equity cost of capital, what is the expected share price as a consequence of this decision? A) $62.86 B) $36.67 C) $52.38 D) $41.90

$52.38 Explanation: Cost of capital = $3/$37 = 0.08108108 ; g = 0.33 ×0.13 = 0.0429 ; P0 = $2 / (0.08108108 - 0.0429 ) = $52.38

Since your first birthday, your grandparents have been depositing $100 into a savings account every month. The account pays 9% interest annually. Immediately after your grandparents make the deposit on your 18th birthday, the amount of money in your savings account will be closest to ________. A) $64,362 B) $75,089 C) $32,181 D) $53,635

$53,635 N = 216 PMT = $ 100 I = 9/12 PV = 0 Compute FV = $53,635.167

Sultan Services has 1.2 million shares outstanding. It expects earnings at the end of the year of $6.0 million. Sultan pays out 60% of its earnings in total: 40% paid out as dividends and 20% used to repurchase shares. If Sultan's earnings are expected to grow by 5% per year, these payout rates do not change, and Sultan's equity cost of capital is 10%, what is Sultan's share price? A) $60.00 B) $24.00 C) $36.00 D) $12.00

$60.00 Explanation: P0 = (0.6 ×$6.0 million) / (0.1 - 0.05 ) = $72 million; P0 = $72 million / 1.2 million = $60.00

Chittenden Enterprises has 643 million shares outstanding. It expects earnings at the end of the year to be $960 million. The firm's equity cost of capital is 9%. Chittenden pays out 30% of its earnings in total: 20% paid out as dividends and 10% used to repurchase shares. If Chittenden's earnings are expected to grow at a constant 3% per year, what is Chittenden's share price? A) $2.24 B) $7.47 C) $3.74 D) $14.94

$7.47 Explanation: P0 = (0.3 ×$960 million) / (0.09 - 0.03 ) = $4800 million; Price per share = $4800 million / 643 million = $7.47

A company has stock which costs $41.50 per share and pays a dividend of $2.50 per share this year. The company's cost of equity is 7%. What is the expected annual growth rate of the company's dividends? A) 1.96 % B) 3.92% C) 0.98 % D) 2.94%

0.98% Explanation: Growth rate = 0.07 - ($2.50 / $41.50 ) = 0.98 %

The Busby Corporation had a share price at the start of the year of $26.10 , paid a dividend of $0.59 at the end of the year, and had a share price of $29.50 at the end of the year. Which of the following is closest to the rate of return of investments in companies with equal risk to The Busby Corporation for this period? A) 12% B) 13% C) 15% D) 14%

15% Explanation: $29.50 +$0.59 - $26.10 = $3.99 ; $3.99 / $26.10 = 15.29 %; rounded to 15%

Luther Industries needs to raise $25 million to fund a new office complex. The company plans on issuing ten-year bonds with a face value of $1,000 and a coupon rate of 5.6 % (annual payments). The following table summarizes the YTM for similar ten-year corporate bonds of various credit ratings: Rating AAA AA A BBB BB YTM 6.86 % 7.06 % 7.16 % 7.56 % 8.06 % Assuming that Luther's bonds receive a AA rating, the number of bonds that Luther must issue to raise the needed $25 million is closest to ________. A) 33,417 B) 22,278 C) 27,848 D) 38,987

27,848 Explanation: FV = $1,000 PMT = $ 56.00 N = 10 I = 7.06 % Compute PV Total number of bonds = $25,000,000 / $ 897.74 = 27,848

What is the internal rate of return (IRR) of an investment that requires an initial investment of $11,000 today and pays $15,400 in one year's time? A) 37% B) 43% C) 44% D) 40%

40% Explanation: Calculate interest rate using TVM keys: input PV = 11,000, N = 1, and FV = -15,400 ; interestrate = 40%.

Luther Industries has a dividend yield of 4.5 % and a cost of equity capital of 10%. Luther Industries' dividends are expected to grow at a constant rate indefinitely. The growth rate of Luther's dividends is closest to ________. A) 5.5 % B) 5.0 % C) 11.0% D) 14.5 %

5.5% Explanation: rE = Div1 / P0 +g 0.1 = 0.045 +g, so g = 5.5 %

You are considering investing in a zero-coupon bond that will pay you its face value of $1000 in twelve years. If the bond is currently selling for $496.97, then the internal rate of return (IRR) for investing in this bond is closest to ________. A) 6.0 % B) 8.2% C) 7.1% D) 5.0 %

6.0% Explanation: PV = -496.97 FV = 1000 PMT = 0 N = 12 Compute I = 6.0 %

Consider the following investment alternatives: Investment APR Compounding A 6.2200 % Annual B 6.0583 % Daily C 6.1277% Quarterly D 6.1204% Monthly Which alternative offers you the highest effective rate of return? A) Investment A B) Investment B C) Investment C D) Investment D

6.1204% Monthly Investment D Explanation: EAR (A) = (1 +APR / m)m- 1 = (1 +0.062200/1)1 - 1 = 6.2200 % EAR (B) = (1 +APR / m)m- 1 = (1 +0.060583/365)365 - 1 = 6.2450 % EAR (C) = (1 +APR / m)m- 1 = (1 +0.061277/4)4 - 1 = 6.2700 % EAR (D)= (1 +APR / m)m- 1 = (1 +0.061204/12)12 - 1 = 6.2950 %

The Sisyphean Company has a bond outstanding with a face value of $1000 that reaches maturity in five years. The bond certificate indicates that the stated coupon rate for this bond is 8.5 % and that the coupon payments are to be made semiannually. Assuming that this bond trades for $1081.73 , then the YTM for this bond is closest to ________. A) 7.87% B) 5.2% C) 9.18 % D) 6.56 %

6.56% Explanation: FV = $1000 PMT = $ 42.50 ($85 / 2) N = 10 (5 × 2) PV = -$1081.73 Compute I = 3.2783 × 2 = 6.5565 %.

What is the real interest rate given a nominal rate of 8.9 % and an inflation rate of 1.9 %? A) 8.2% B) 6.9 % C) 9.6 % D) 11.0%

6.9% Explanation: (0.089 ) / (1+0.019 ) - 1 = 0.06869 ; real rate = 6.869 %

Consider the following investment alternatives: Investment APR Compoundin g A 6.9030 % Annual B 6.6992% Daily C 6.7787% Quarterly D 6.7643 % Monthly Which alternative offers you the lowest effective rate of return? A) Investment A B) Investment B C) Investment C D) Investment D

6.9030% Annual/Investment A Explanation: EAR (A) = (1 +APR / m)m- 1 = (1 +0.069030/1)1 - 1 = 6.9030 % EAR (B) = (1 +APR / m)m- 1 = (1 +0.066992 /365)365 - 1 = 6.9280 % EAR (C) = (1 +APR / m)m- 1 = (1 +0.067787/4)4 - 1 = 6.9530 % EAR (D)= (1 +APR / m)m- 1 = (1 +0.067643 /12)12 - 1 = 6.9780 %

You expect KT industries (KTI) will have earnings per share of $5 this year and expect that they will pay out $1.25 of these earnings to shareholders in the form of a dividend. KTI's return on new investments is 13% and their equity cost of capital is 15%. The expected growth rate for KTI's dividends is closest to ________. A) 3.9 % B) 5.9 % C) 9.8 % D) 11.3%

9.8% Explanation: g = Retention rate ×Return on new investment = ($5 - $1.25 ) / $5 ×0.13 = 0.0975 or 9.8 %

The Sisyphean Company has a bond outstanding with a face value of $5000 that reaches maturity in 8 years. The bond certificate indicates that the stated coupon rate for this bond is 8.2% and that the coupon payments are to be made semiannually. Assuming that this bond trades for $4541.53 , then the YTM for this bond is closest to ________. A) 7.9 % B) 9.9 % C) 13.8 % D) 11.9%

9.9% Explanation: FV = $5000 PMT = $ 205 ($410/2) N = 16 (8 × 2) PV = -$4541.53 Compute I = 4.9426 × 2 = 9.8852%.

What is the yield to maturity of a one-year, risk-free, zero-coupon bond with a $10,000 face value and a price of $9400 when released? A) 6.000 % B) 6.383 % C) 0.009 % D) 3.191%

B Explanation: Calculate the discount rate that equates $10,000 to $9400 in one year. 1 +YTMn = (Face value / price)1/n. YTMn = 6.383 %

Which of the following statements is FALSE? A) Interest rates we observe in the market will vary based on quoting conventions, the term of investment, and risk. B) The opportunity cost of capital is the best available expected return offered in the market on an investment of comparable risk and term of the cash flows being discounted. C) The opportunity cost of capital is the return the investor forgoes when the investor takes on a new investment. D) For a risk-free project, the opportunity cost of capital will typically be greater than the interest rate of U.S. Treasury securities with a similar term.

For a risk-free project, the opportunity cost of capital will typically be greater than the interest rate of U.S. Treasury securities with a similar term.

Which of the following statements is FALSE regarding profitable and unprofitable growth? A) If a firm retains more earnings, it will pay out less of those earnings, reducing its dividends. B) Cutting a firm's dividend to increase investment will raise the stock price if the new investment has a positive net present value (NPV). C) A firm can increase its growth rate by retaining more of its earnings. D) If a firm wants to increase its share price, it must diversify.

If a firm wants to increase its share price, it must diversify

Which of the following investments has a higher present value, assuming the same (strictly positive) interest rate applies to both investments? Year Investment X Investment Y 1 $5,000 $11,000 2 $7,000 $9,000 3 $9,000 $7,000 4 $11,000 $5,000 A) Investment X and Investment Y have the same present value, since the total of the cash flows is the same for both. B) Investment X has a higher present value. C) Investment Y has a higher present value. D) No comparison can be madewe need to know the interest rate to calculate the present value.

Investment Y has a higher present value

Which of the following is/are TRUE? I. The EAR can never exceed the APR. II. The APR can never exceed the EAR. III. The APR and EAR can never be equal. A) Only II. is true. B) Only I. is true. C) Only II. & III. are true. D) Only I. & III. are true.

The APR can never exceed the EAR Only II is true

Which of the following is true about perpetuities? A) Since a perpetuity generates cash flows every period infinitely, its FV is the same as its PV. B) Since a perpetuity generates cash flows every period infinitely, the cash flow generated equals the PV times the interest rate. C) Since a perpetuity generates cash flows every period infinitely, there is no way to solve for the cash flow using the present value and the interest rate. D) Since a perpetuity generates cash flows every period infinitely, initial cash outflow must be discounted to calculate the present value

Since a perpetuity generates cash flows every period infinitely, the cash flow generated equals the PV times the interest rate

Which of the following statements regarding annuities is FALSE? A) The difference between an annuity and a perpetuity is that a perpetuity ends after some fixed number of payments. B) Most car loans, mortgages, and some bonds are annuities. C) PV of an annuity = C × 1r1 - 1(1 +r)N D) An annuity is a stream of N equal cash flows paid at regular intervals.

The difference between an annuity and a perpetuity is that a perpetuity ends after some fixed number A perpetuity never ends

Which of the following statements regarding bonds and their terms is FALSE? A) The internal rate of return (IRR) of an investment in a zero-coupon bond is the rate of return that investors will earn on their money if they buy a default-free bond at its current price and hold it to maturity. B) Financial professionals also use the term spot interest rates to refer to the default-free zero-coupon yields. C) When we calculate a bond's yield to maturity by solving the formula, Price of an n-period bond = Coupon (1 +YTM)1 + Coupon (1 +YTM)2 + ... + Coupon + Face (1 +YTM)n the yield we compute will be a rate per coupon interval. D) The yield to maturity of a bond is the discount rate that sets the future value (FV) of the promised bond payments equal to the current market price of the bond.

The yield to maturity of a bond is the discount rate that sets the future value (FV) of the promised bond payments equal to the current market price of the bond

Which of the following statements regarding growing perpetuities is FALSE? A) PV of a growing perpetuity = C r - g B) To find the value of a growing perpetuity one cash flow at a time would take forever. C) A growing perpetuity is a cash flow stream that occurs at regular intervals and grows at a constant rate forever. D) We assume that r < g for a growing perpetuity

We assume that r < g for a growing perpetuity

0 1 2 3 59 60 +-----+-----+-----+--- . . . -----+-----+ $57.5 $57.5 $57.5 $57.5 $50 57.5 A corporation issues a bond that generates the above cash flows. If the periods are of 3 -month intervals, which of the following best describes that bond? A) a 15 -year bond with a notional value of $5000 and a coupon rate of 1.2% paid annually B) a 60 -year bond with a notional value of $5000 and a coupon rate of 4.6 % paid quarterly C) a 15 -year bond with a notional value of $5000 and a coupon rate of 4.6 % paid quarterly D) a 30 -year bond with a notional value of $5000 and a coupon rate of 3.5 % paid semiannually

a 15-year bond with a notional value of $5000 and a coupon rate of 4.6% paid quarterly

Which of the following bonds is trading at par? A) a bond with a $1,000 face value trading at $1,000 B) a bond with a $2,000 face value trading at $1,987 C) a bond with a $1,000 face value trading at $999 D) a bond with a $2,000 face value trading at $2,012

a bond with a $1,000

If the yield to maturity of all of the following bonds is 6%, which will trade at the greatest premium per $100 face value? A) a bond with a $1,000 face value, five years to maturity and 6.3 % annual coupon payments B) a bond with a $10,000 face value, four years to maturity and 6.2% semiannual coupon payments C) a bond with a $5,000 face value, seven years to maturity and 5.5 % annual coupon payments D) a bond with a $500 face value, seven years to maturity and 5.2% annual coupon payments

a bond with a $1,000 face value, five years to maturity and 6.3% annual coupon payments

The Sisyphean Company has a bond outstanding with a face value of $1000 that reaches maturity in 5 years. The bond certificate indicates that the stated coupon rate for this bond is 10.0 % and that the coupon payments are to be made semiannually. Assuming the appropriate YTM on the Sisyphean bond is 7.5 %, then this bond will trade at ________. A) a discount B) a premium C) par D) none of the above

a premium Explanation: As the coupon rate of 10.0 % is more than the YTM of 7.5 % on the bonds, so the bonds will trade at a premium.

What are dividend payments? A) the difference between the original cost price of a share and the price an investor receives when that share is sold B) a share of the profits paid to each shareholder on the basis of the number of shares they hold C) incremental increases in the value of the stock held by an investor due to rises in share price D) payments made to a company by investors for a share of the ownership of that company

a share of the profits paid to each shareholder on the basis of the number of shares they hold

Which of the following risk-free, zero-coupon bonds could be bought for the lowest price? A) one with a face value of $1,000, a YTM of 4.8%, and 5 years to maturity B) one with a face value of $1,000, a YTM of 5.9%, and 20 years to maturity C) one with a face value of $1,000, a YTM of 3.2%, and 8 years to maturity D) one with a face value of $1,000, a YTM of 6.8%, and 10 years to maturity

one with a face value of $1,000, a YM of 5.9%, and 20 years to maturity Explanation: Price = $1,000 / (1 + 5.9%)20 = $318 (lowest price)

Which of the following formulas is INCORRECT? A) P0 = Div 1 / ( rE - g) B) rE = (Div 1 / P0) - g C) g = Retention Rate ×Return on New Investment D) Div t = EPSt ×Dividend Payout Rate

rE = (Div 1 / P0) - g Explanation: rE = (Div 1 / P0) +g