Exam 2 Math Review (5,6,7) FINA 3332
Disney Inc. has just paid a $1.00 dividend at the end of this year. If you expect Disney's dividend to grow by 3% per year forever and Disney's equity cost of capital to be 10%, then the value of a share of Disney's stock is closest to ________. (Exam Review, Q19)
$14.71
What is the coupon payment of a 30-year $1000 bond with an 8.0% coupon rate with semi-annual payments? (Chapter 6, Slide 19, Learning Catalytics)
$40
FPL Inc. pays a dividend of $1.05 per share and is expected to pay this amount indefinitely. If FPL's equity cost of capital is 6%, which of the following would be closest to FPL's stock price? (Exam Review, Q16)
$17.5
What is the coupon payment of a 10-year $100,000 bond with a 5% coupon rate with semiannual payments? (Exam Review, Q9)
$2,500
VMF Inc. is expected to pay a $1.20 dividend at the end of this year. If you expect VMF's dividend to grow by 3% per year forever and VMF's equity cost of capital to be 9%, then the value of a share of VMF stock is closest to ________. (Exam Review, Q18)
$20
Stern deposits a fixed amount monthly in a bank account with an effective annual rate of 10.5%. What is the APR? (Chapter 5, Slide 31)
10.0262%
Suppose your bank account pays interest monthly with an effective annual rate of 5%. What amount of interest will you earn each month? (Chapter 5, Learning Catalytics) If you have no money in the bank today, how much will you need to save at the end of each month to accumulate $150,000 in 20 years? (Chapter 5, Learning Catalytics)
Monthly Rate: 0.4074 AMT to save each month: 369.64
Suppose your bank account pays interest monthly with an effective annual rate of 6% What amount of interest will you earn each month? (PPT Chapter 5, Slide 15)
Monthly Rate: 0.4868%
At the start of 2008, one-year U.S. government bond rates were about 3.3%, while the inflation rate that year was 0.1% . At the start of 2018, one-year interest rates were about 1.8%, and the inflation rate that year was about 1.9%. What were the real interest rates in 2008 and in 2018? (Chapter 5, Slide 60)
in 2008: 3.20% in 2018: -0.10%
Glass Inc. recently paid $3.25 as an annual dividend. Future dividends are projected at $3.50, $4.00, and $4.25 over the next three years, respectively. Beginning four years from now, the dividend is expected to increase by 3.50 percent annually. At a discount rate of 12.5 percent, the value of a share of Glass's stock today is closest to ________. (Exam Review, Q21)
$43.59
Compute the present value of a risk-free five-year annuity of $1000 per year, given the yield curve for November 2008 (Chapter 5, Slide 68) Yield Curve in 2008 (Interest Rates); 1: 0.91% 2: 0.98% 3: 1.26% 4: 1.69% 5: 2.01%
$4775
Boring Co. will pay a dividend of $1.50 per share at this year's end and a dividend of $1.85 per share at the end of next year. It is expected that the price of Boring's stock will be $56 per share after two years. If Boring has an equity cost of capital of 10.5%, what is the maximum price that a prudent investor would be willing to pay for a share of Boring stock today? (Exam Review, Q17)
$48.74
What is the coupon payment of a 10-year $1000 bond with 8.0% coupon rate with annual payments? (Chapter 6, Slide 18)
$80
Consider a 10-year coupon bond and a 30-year coupon bond, both with 10% annual coupons. By what percentage will the price of each bond change if its yield to maturity increases from 5% to 6%? (Chapter 6, Slide 67)
10 year coupon bond with 5% YTM: 138.61 10 year coupon bond with 6% YTM: 129.44 30 year coupon bond with 5% YTM: 176.86 30 year coupon bond with 6% YTM: 155.06 129.44 - 138.61 / 138.61 = 6.6% 155.06-176.86/176.86= 12.3%
Damian is asked to invest $2000 in a friend's business with the promise that the friend will repay $2300 in one year. Damian finds his best alternative to this investment, with similar risk, is one that will pay her $2200 in one year. U.S. securities of similar term offer a rate of return of 7% What is the opportunity cost of capital in this case? (Chapter 5, Slide 80)
10%
Consider three 30-year bonds with annual coupon payments. One bond has a 10% coupon rate, one has a 5% coupon rate, and one has a 3% coupon rate. If the yield to maturity of each bond is 5%, what is the price of each bond per $100 face value? (Chapter 6, Slide 61, Learning Catalytics)
10% Coupon Rate Price: 176.86 5% Coupon Rate Price: 100.00 4% Coupon Rate Price: 69.26
Consider three 30-year bonds with annual coupon payments. One bond has a 10% coupon rate, one has a 5% coupon rate, and one has a 3% coupon rate. If the yield to maturity of each bond is 5%, which bond trades at a premium, which bond trades a discount, which trades at par? (Chapter 6, Slide 60) which trades at a discount, and which trades at par?
10% coupon rate > than 5% YTM= Premium 5% coupon rate = 5% YTM= at par 3% coupon rate = 5% YTM= Discount
Suppose a friend offers to borrow $100 from you today and in return pay you $110 one year from today. Looking in the market for other options for investing $100, you find your best alternative option that you view as equally risky as lending it to your friend. That option has an expected reutrn of 8%. What should you do? (Chapter 5, Slide 78)
101.85 Make the loan since the loan is woth 101.85 today
Consider three 30-year bonds with annual coupon payments. One bond has a 12% coupon rate, one has a 6% coupon rate, and one has a 2% coupon rate. If the yield to maturity of each bond is 6%, which bond trades a premium, which trades at a discount, and which trades at par? (Chapter 6, Slide 63)
12% > 6% YTM = Premium 6% = 6% YTM = Par 2% < 6% YTM = Discount
Consider three 30-year bonds with annual coupon payments. One bond has a 12% coupon rate, one has a 6% coupon rate, and one has a 2% coupon rate. If the yield to maturity of each bond is 6% What is the price of each bond per $100 face value? (Chapter 6, Slide 64)
12% coupon rate price: 182.59 6% coupon rate price: 100.00 2% coupon rate price: 44.94
Lets say that you are three years into your $30,000 car loan from the previous section and decide to sell the car. When you sell the car, you must pay whatever the remaining balance is on your car loan. After 36 months of payments at $590.50, how much do you still owe on your car loan? Interest rate 6.75% APR, compounded monthly (Related to Flashcard #10) (Chapter 5, Slide 42 & 43)
13,222.32 remains left
Suppose the following zero-coupon bonds are trading at the prices down below per $100 face value. Determine the corresponding yield to maturity for each bond (Chapter 6, Slide 25, Learning Catalytics) Maturity Price Year 1: 96.62 Year 2: 92.45 Year 3: 87.63 Year 4: 83.06
1: 3.50% 2: 4.00% 3: 4.50% 4: 4.75%
In 2007, interest rates were about 4.8% and inflation was about 2.5%. What was the real interest rate in 2007? (Chapter 5, Learning Catalytics, Slide 61)
2.24%
Consider the nine-year, $1000 note with a 3% coupon rate and semiannual coupons If this bond is currently trading for a price of $1,038.32 what is the bond's yield to maturity?
2.52%
The prices of default-free three-year zero-coupon bond is $92.21 per $100 of face value. The yield to maturity for this bond is closest to ________. (Exam Review, Q11)
2.74%
Consider the five-year, $1000 bond with a 2.2% coupon rate and semi-annual coupons. If this bond is currently trading for a price of $963.11, what is the bond's yield to maturity? (Chapter 6, Slide 36)
3.00%
What is the yield to maturity of a one-year zero-coupon bond with a $100,000 face value has an initial price of $96,618.36? (Chapter 6, Slide 24)
3.5%
What is the real interest rate given a nominal rate of 5.2% and an inflation rate of 1.4%? (Exam Review, Q6)
3.75%
You deposit a fixed amount quarterly into a saving account with an EAR of 5%. What is the APR (chapter 5, Learning Catalytics)
4.91%
A bank offers a loan that will require you to pay 5% interest compounded weekly. What is the EAR charged by the bank? (Exam Review, Q1)
5.12%
Consider the timeline for a $30,000 car loan with these terms: 6.75% APR for 60 Months. Compute the Loan Payment (Chapter 5, Learning Catalytics, Slide 36)
590.50 - PMT
What is the coupon rate of an eight-year, $1,000 bond with semiannual coupons and a price of $854. 68, if it has a yield to maturity of 8.8%? (Exam Review, Q12)
6.23%
Nile is asked to invest $2500 in a friend's business with the promise that the friend will repay $2640 in one year. Nile finds her best alternative to this investment, with similar risk, is one that will pay her $2674 in one year. U.S. securities of similar term offer a rate of return of 5%. What is the opportunity cost of capital in this case? (Exam Review, Q8)
6.96%
Suppose your bank account pays interest monthly with an effective annual rate of 6% If you have no money in the bank today, how much will you need to save at the end of each month to accumulate 100,000 in 10 years? (PPT Chapter 5, slide 15,16,17)
615.47
A home buyer buys a house for $150,000. She pays 20% cash, and takes a fixed-rate mortgage for ten years at 4.50% APR. If she makes semi-monthly payments, which of the following is closest to each of her payment? (Chapter 5, Learning Catalytics, Slide 38)
621.37- PMT
The 7 percent bonds issued by Modern Kitchens pay interest semi-annually, mature in eight years, and have a $1,000 face value. Currently, the bonds sell $987. What is the yield to maturity? (Chapter 6, Slide 53, Learning Catalytics)
7.22%
What is the yield to maturity of a five-year, $1,000 bond with a 3.4% coupon rate and semiannual coupons if this bond is currently trading for a price of $841.55? (Exam Review, Q13)
7.23%
If the current inflation rate is 3.1%, then the nominal rate necessary for you to earn a(n) 4.4% real interest rate on your investment is closest to ________. (Exam Review, Q7)
7.64%
Given the yield curve shown in Figure 6.2, what is the price of a five-year risk-free zero-coupon bond with a face value of $100? The yield on a five-year bond is 5% in the figure. (Chapter 6, Slide 28)
78.35 - PV
A house costs $115,000. It is to be paid off in exactly ten years, with monthly payments of $1424.50. What is the APR of this loan? (Chapter 5, Learning Catalytics)
8.47%
A bank pays interest quarterly with an EAR of 10%. What is the periodic interest rate applicable quarterly? What is the APR? (Exame Review, Q2)
8.56%
If the current inflation rate is 3.0%, then the nominal rate necessary for you to earn a(n) 5.4% real interest rate on your investment is closest to ____________ (Chapter 5, Slide 62, Learning Catalytics)
8.56%
Consider the nine-year, $1000 bond with a 3% coupon rate and semiannual coupons Suppose interest rates increase, and the bond's yield to maturity increases to 4.0% (an APR with semi-annual compounding) What price is the bond trading for now? (Chapter 6, Slide 45, Learning Catalytics)
925.04- PV
Oil Wells offers 5.65 percent coupon bonds with semiannual payments and a yield to maturity of 6.94 percent. The bonds mature in seven years. What is the market price per bond if the face value is $1,000? (Chapter 6, Slide 50, Learning Catalytics)
929.42- PV
Assume that it is May 21, 2019, and the U.S. Treasury has just issued securities with a May 2024 maturity, $1000 par value, and a 2.2% coupon rate with semiannual coupons. The first coupon payment will be paid on November 21, 2019 (6 months from the issue date). What cash flows will receive if you hold this note until maturity? (Chapter 6, Slide 34)
Cash flows you'll receive: $11
Crane sporting goods expect to have earnings per share of $6 in the coming year (EPS1). Rather than reinvest these earnings and grow, the firm plans to pay out all of its earnings as a dividend (DIV1). With these expectations of no growth, Crane's current share price is $60. Suppose crane could cut its dividend pay-out rate to 75% of earnings for the foreseeable future and use the retained earnings to open new stores. The return on its investment in these stores is expected to be 12%. Assuming its equity cost of capital is unchanged. what effect would this new policy have on Crane's stock price? (Chapter 7, Slide 40 & 41)
Cost of equity capital: 10% New dividend at 75% payout ratio: $4.50 New Growth Rate: 3% New Price: 64.29
Expedia Inc. has a current stock price of $3.95 and is expected to sell for $4.34 in one year's time, immediately after it pays a dividend of $0.25. Which of the following is closest to Expedia's equity cost of capital, dividend yield, and capital gains rate? (Exam Review, Q15)
Equity Cost of Capital: 16.20% Dividend Yield: 6.33% Capital Gains Rate: 9.87%
Turo Inc. will pay a dividend of $0.74 per share this year. It is expected that this dividend will grow by 3% per year each year in the future. The current price of Turo's stock is $26.42 per share. What is Turo's equity cost of capital, dividend yield, and capital gains rate? (Exam Review, Q20)
Equity Cost of Capital: 5.8% Dividend Yield: 2.8% Capitals Gain Rate: 3%
Consider the case of a company is currently not paying dividends. You predict that, in 5 years, the company will pay a dividend for the first time. The dividend will be $.50 per share. You expect this dividend to grow at 10% per year indifenitely. The required return on companies such as this one is 20%. What is the price of the stock today? (Chapter 7, Slide 48 & 49)
Find the price in four years: $5.00 Discount it back four years: $2.41
Lets say that you are now 10 years into a $200,000 mortgage (at 4.80% APR, originally for 360 months) and decide to sell the house. When you sell the house, you must pay whatever the remaining balance is on your mortgage. After 120 months of payments, how much do you still owe on your mortgage? (Chapter 5, Slide 45)
First, solve the payment 1,049.33
Taylor is saving to buy a car. He deposits a fixed amount every month in a bank account with an EAR of 12.3%. If this account pays interest every month, then how much should he save from each monthly paycheck in order to have $18,000 in the account in three years' time? (Exam Review, Q3)
PMT: -420.06
A production equipment costing $24,000 is paid off in 48 monthly installments at 3.50% APR. After one year the company wishes to sell the equipment. What is the minimum price for which they can sell the equipment so that they can cover the cost of the balance remaining on the loan? (Exam Review, Q5)
PMT: -536.54 PV: 18,310.78
A $40,000 new car loan is taken out with the terms 9% APR for 60 months. How much are monthly payments on this loan? (Exam Review, Q4)
PMT: -830.33
A risk-free, zero-coupon bond with a face value of $1,000 has 8 years to maturity. If the YTM is 5.2%, which of the following would be closest to the price this bond will trade at? (Exam Review, Q10)
PV: 666.61
What is the price of a 3-year risk-free zero-coupon bond with a face value of $900 and yield of 4.50%? (Chapter 6, Slide 29, Learning Catalytics)
PV: 788.67
A $1000 bond with a coupon rate of 5.4% paid semiannually has sixteen years to maturity and a yield to maturity of 6.4%. If interest rates rise and the yield to maturity increases to 6.8%, what will happen to the price of the bond? (Exam Revew, Q14)
Price Difference: $36.03
Consider the five-year, $1000 bond with a 2.2% coupon rate and semiannual coupons. Suppose interest rates drop and the bond's yield to maturity decreases to 2% (APR with semiannual compounding) (Chapter 6, Slide 43) What price is the bond trading for now? What is the effective annual yield on this bond?
Price is: 1,009.47 (PV) Annual Yield: 0.0201 (or 2.01%)
Consolidated Edison, Inc. (Con Ed) is regulated uitlity company that services the New York City area. Suppose Con Ed plans to pay $2.30 per share in dividends in the coming year. If its equity cost of capital is 7% and dividends are expected to grow by 2% per year in the future, estimate the value of Con Ed's stock, what is the dividend yield, capital gain rate, and total return of this stock? (Chapter 7, Slide 31)
Price: $46.00 Dividend Yield: 5% Capital Gain Rate: 2% Total Return: 7%
Suppose Crane Sporting Goods cut its dividend payout rate to 75% to invest in new stores, as in Example 7.3. But now, suppose that the return on these new investments is 8%, rather than 12%. Its expected earnings per share this year of $6 and its equity cost of capital of 10% What will happen to Crane's current share price in this case? (Chapter 7, Slide 43 & 44)
Price: $56.25
Suppose you expect Longs Drug Stores to pay an annual dividend of $0.56 per share in the coming year and to trade for $45.50 per share at the end of the year. Investments with equivalent risk to Long's Stock have an expected return of 6.80% What is the most you would pay today for Long's stock? What dividend yield and capital gain rate would you expect at this price? What is the total return? (Chapter 7, Slide 21)
Price: 43.13 Dividend Yield: 1.3% Capital Gain Rate: 5.5% Total Return: 6.8%
Lets say that you are now 10 years into a $200,000 mortgage (at 4.80% APR, originally for 360 months) and decide to sell the house. When you sell the house, you must pay whatever the remaining balance is on your mortgage. After 120 months of payments, how much do you still owe on your mortgage? (Chapter 5, Slide 45)
Solve for PV of the remaining payments 161,694.73
You have just sold your house for $1,000,000 in cash. Your mortgage was originally a 30-year mortgage with monthly payments and an initial balance of $800,000. The mortgage is currently exactly 18.5 years old, and you have just made a payment. If the interest rate on the mortgage is 6.25% (APR), how much cash will you have from the sale once you pay off the mortgage? (Chapter 5, Learning Catalytics, Slide 49)
Solve for the loan balance after 18.5 years 483,963.43 Remaining Cash 1,000,000 - 483,963.43= $516,036.57
Five years ago, you took out a 30-year mortgage with an APR of 6.20% monthly for $206,000. If you were to refinance the mortgage today for 20 years at an APR of 3.95% monthly, how much would your new loan payment be? (Chapter 5, Slide 46, Learning Catalytics)
Solve for the loan balance after 5 years 192,159.69
You have just sold your house for $1,000,000 in cash. Your mortgage was originally a 30-year mortgage with monthly payments and an initial balance of $800,000. The mortgage is currently exactly 18.5 years old, and you have just made a payment. If the interest rate on the mortgage is 6.25% (APR), how much cash will you have from the sale once you pay off the mortgage? (Chapter 5, Learning Catalytics, Slide 49)
Solve for the monthly payment on the original loan 4,925.74
Five years ago, you took out a 30-year mortgage with an APR of 6.20% monthly for $206,000. If you were to refinance the mortgage today for 20 years at an APR of 3.95% monthly, how much would your new loan payment be? (Chapter 5, Slide 46, Learning Catalytics)
Solve for the new payment 1,159.39
Five years ago, you took out a 30-year mortgage with an APR of 6.20% monthly for $206,000. If you were to refinance the mortgage today for 20 years at an APR of 3.95% monthly, how much would your new loan payment be? (Chapter 5, Slide 46, Learning Catalytics)
Solve for the original payment on the original loan 1,261.69
Suppose you estimate the following dividend forecasts for the next three years. After the third year, the dividend will grow at a constant rate of 5% per year. The required return is 10%. What is the value of the stock today? (Chapter 7, Slide 50 & 51) Year 1: $1.00 Year 2: $2.00 Year 3: $2.50
Stock price: $43.88
Titan industries has 217 million shares outstanding and expects earnings at the end of this year of $860 million. Titan plans to pay out 50% of its earnings in total, paying 30% as a dividend and using 20% to repurchase shares. If Titan's earnings are expected to grow by 7.5% per year and these pay-out rates remain constant, determine Titan's share price assuming an equity cost of capital of 10%. (Chapter 7, Slide 61 & 62)
Total Dividends and Repurchases = $860 million x %50 = $430 million PV (Future Total Dividends and Repurchases) = 17.2 billion 17.2 billion/217 million shares= $79.26 per share
Your firm is purchasing a new fleet of trucks that will last for six years. You can purchase the system for an upfront cost of $500,000 or lease the the system from the manufacturer for $8,000, paid at the end of each month for a 72-month. Your firm can borrow at an interest rate of 6% APR with monthly compounding. Should you purchase paying upfront or lease? (Chapter 5, Learning Catalytics)
You should make the 8,000 payments The PV of 8,000 is: 482,716.11 482,716.11 is cheaper than buying the upfront cost of $500,000
Your firm is purchasing a new telephone system that will last for four years. You can purchase the system for an upfront cost of $150,000, or you can lease the system from the manufacturer for $4,000 paid at the end of each month. The lease price is offered for a 48-month lease with no early termination—you cannot end the lease early. Your firm can borrow at an interest rate of 6% APR with monthly compounding. Should you purchase the system outright or pay $4,000 per month? (Chapter 5, Slide 23)
You should purchase the system outright If you make payments of 4,000 you will pay a PV of: 170,321.27
Consider an investment opportunity requires $10 million up-front investment and generates $3 million cash flows per year (Chapter 5, Slide 69)- Example if interest rate is 5%: If interest rate is 9%:
at 5%: 10.638 million at 9%: 9.719 million
