FIRE-311 Module 3 Notes
(1) In 2007, interest rates were about 4.4% and inflation was about 2.9%. What was the real interest rate in 2007, approximately? 6.2% / 2.3% / 1.5% / 1.8% / 7.3% (2) In 2007, interest rates were about 4.5% and inflation was about 2.8%. What was the real interest rate in 2007, approximately? 2.0% / 1.5% / 6.1% / 1.7% / 7.3%
(1) (nominal rate - inflation rate) / (1 + inflation rate) (4.4 - 2.9) / (1 + 0.029) = 1.5 / 1.029 = 1.457726% Answer = 1.5% (2) (nominal rate - inflation rate) / (1 + inflation rate) (4.5 - 2.8) / (1 + 0.028) = 1.653696% Answer = 1.7%
(1) Which of the following bonds will be most sensitive to a change in interest rates if all bonds have the same initial yield to maturity? -a 15-year bond with a $1,000 face value whose coupon rate is 7.4% APR paid semiannually -a 15-year bond with a $1,000 face value whose coupon rate is 5.8% APR paid semiannually -a 30-year bond with a $1,000 face value whose coupon rate is 5.8% APR paid semiannually -a 30-year bond with a $1,000 face value whose coupon rate is 8.7% APR paid semiannually -a 30-year bond with a $1,000 face value whose coupon rate is 7.4% APR paid semiannually -a 15-year bond with a $1,000 face value whose coupon rate is 8.7% APR paid semiannually (2) Which of the following bonds will be most sensitive to a change in interest rates if all bonds have the same initial yield to maturity? -a 20-year bond with a $1,000 face value whose coupon rate is 8.7% APR paid semiannually -a ten-year bond with a $1,000 face value whose coupon rate is 5.8% APR paid semiannually -a ten-year bond with a $1,000 face value whose coupon rate is 7.4% APR paid semiannually -a 20-year bond with a $1,000 face value whose coupon rate is 7.4% APR paid semiannually -a 20-year bond with a $1,000 face value whose coupon rate is 5.8% APR paid semiannually
(1) -the longer the bond, the more sensitive it is -the smaller the coupon rate change, the more sensitive Answer: a 30-year bond with a $1,000 face value whose coupon rate is 5.8% APR paid semiannually (2) -the longer the bond, the more sensitive it is -the smaller the coupon rate change, the more sensitive Answer: a 20-year bond with a $1,000 face value whose coupon rate is 5.8% APR paid semiannually
(1) You have an outstanding student loan with required payments of $500 per month for the next four years. The interest rate on the loan is 9% APR (compounded monthly). Now that you realize your best investment is to prepay your student loan, you decide to prepay as much as you can each month. Looking at your budget, you can afford to pay an extra $175 a month in addition to your required monthly payments of $500, or $675 in total each month. How long will it take you to pay off the loan? (2) You have an outstanding student loan with required payments of $500 per month for the next four years. The interest rate on the loan is 9% APR (compounded monthly). Now that you realize your best investment is to prepay your student loan, you decide to prepay as much as you can each month. Looking at your budget, you can afford to pay an extra $250 a month in addition to your required monthly payments of $500, or $750 in total each month. How long will it take you to pay off the loan?
(1) 12 months per year * 4 years = 48 months 9% / 12 months per year = 0.75% per month Step 1: find PV of the loan (n=48,i/y=0.75,pmt=500,fv=0) PV = $20,092.39 Step 2: use new PV & PMT to solve for N (i/y=0.75,pv=(-)20092.39,pmt=675,fv=0) N = 33.81 months (2) 12 months per year * 4 years = 48 total periods 9% / 12 months per year = 0.75% per month Step 1: find PV of the loan (n=48,i/y=0.75,pmt=500,fv=0) PV = $20,092.39 Step 2: use new PV & PMT to solve for N (i/y=0.75,pv=(-)20092.39,pmt=750,fv=0) N = 30.02 months
(1) A stock is bought for $22.00 and sold for $26.00 one year later, immediately after it has paid a dividend of $1.80. What is the capital gain rate for this transaction? 12.33% / 8.18% / 6.92% / 18.18% / 15.38% / 26.36% (2) A stock is bought for $23.00 and sold for $27.00 one year later, immediately after it has paid a dividend of $1.50. What is the capital gain rate for this transaction? 5.55% / 6.52% / 9.23% / 17.39% / 23.91% / 14.81%
(1) Capital gain rate = (P1 - P0) / P0 (26 - 22) / 22 = 4 / 22 = 0.18181818 Capital gain rate = 18.18% (2) Capital gain rate = (P1 - P0) / P0 (27 - 23) / 23 = 0.173913 Capital gain rate = 17.39%
(1) Treasury = 5.0 / AAA = 5.2 / BBB = 5.8 / B = 6.6 The credit spread of the single B corporate bond is closest to ________. 1.40% / 0.80% / 1.60% / 0.60% / 1.10% (2) Treasury = 5.0 / AAA = 5.2 / BBB = 5.8 / B = 6.6 The credit spread of the BBB corporate bond is closest to ________. 0.60% / 0.80% / 1.60% / 0.40% / 1.10%
(1) Credit spread = Corporate Yield - risk-free yield (the treasury bond is the risk-free yield) Credit spread = B yield - Treasury yield 6.6 - 5.0 = 1.60% (2) Credit spread = Corporate Yield - risk-free yield (the treasury bond is the risk-free yield) Credit spread = BBB yield - Treasury yield 5.8 - 5.0 = 0.8%
(1) A bank offers a loan that will requires you to pay 11% interest compounded semiannually. Which of the following is closest to the EAR charged by the bank? A. 11.3% B. 22.6% C. 9.04% D. 13.56% (2) A bank offers a loan that will requires you to pay 6% interest compounded monthly. Which of the following is closest to the EAR charged by the bank? A. 4.94% B. 12.34% C. 7.4% D. 6.17%
(1) EAR = (1 + (APR/m))^m - 1 (1 + (0.11/2))^2 - 1 0.113025 Answer: 11.3% (2) EAR = (1 + (APR/m))^m - 1 (1 + (0.06/12))^12 - 1 0.061678 Answer: 6.17%
(1) You have been offered a job with an unusual bonus structure. As long as you stay with the firm, you will get an extra $70,000 every seven years, starting seven years from now. What is the present value of this incentive if you plan to work for the company for 42 years and the interest rate is 6.1% (EAR)? (2) You have been offered a job with an unusual bonus structure. As long as you stay with the firm, you will get an extra $72,000 every seven years, starting seven years from now. What is the present value of this incentive if you plan to work for the company for 42 years and the interest rate is 5.8% (EAR)?
(1) Equivalent discount rate: r = (1 + EAR)^n - 1 1.061^7 - 1 = 0.513588 = 51.3588% PV = C/r * (1 - (1 / (1 + r)^n)) 70000/0.513588 * (1-(1/(1+0.513588)^6)) = $124,960.612416 Answer: $124,961 (2) 1.058^7 - 1 = 0.483883 72000/0.483883 * (1-(1/(1+0.483883)^6)) = 134858.501627 = $134,859
(1) A $35,000 new amortizing car loan is taken out with terms 9.00% APR for 60 months. How much are monthly payments on this loan? $685.83 / $784.85 / $762.38 / $717.18 / $726.54 (2) A $50,000 new amortizing car loan is taken out with the terms 12% APR for 48 months. How much are monthly payments on this loan? $ 1316.69 / $ 1225.64 / $ 1371.81 / $ 1041.67 / $ 816.69
(1) Step 1: find monthly rate → 9% / 12 months = 0.75% Step 2: find PMT in financial calculator (N=60, I/Y=0.75, PV=35,000, FV=0) PMT = $726.54 (2) Step 1: find monthly rate → 12% / 12 months = 1% Step 2: find PMT in financial calculator (N=48, I/Y=1, PV=50,000, FV=0) PMT = $1,316.69
(1) Jolana is asked to invest $5000 in a friend's business with the promise that the friend will repay $5800 in one year. Jolana finds her best alternative to this investment, with similar risk, is one that will pay her $5500 in one year for an investment of $5000 today. U.S. Treasury securities of similar term offer a rate of return of 2%. What is the opportunity cost of capital in this case? 8% / 2% / 10% / 12% / 16% (2) Joanna is asked to invest $5100 in a friend's business with the promise that the friend will repay $5610 in one year. Joanna finds her best alternative to this investment, with similar risk, is one that will pay her $5508 in one year. U.S. Treasury securities of similar term offer a rate of return of 7%. What's opportunity cost of capital in this case? 9% / 7% / 10% / 8% / 1%
(1) If they invest in the friend's business, they are giving up the opportunity for an alternative of $5,500 in one year for $5,000 today - so find the rate of that option. Rate of $5,500: (n=1, pv=5,000, pmt=0, fv=5,500) I/Y (what they're giving up) = 10% (2) If they invest in the friend's business, they are giving up the opportunity for an alternative of $5,508 in one year for $5,100 today - so find the rate of that option. Rate of $5,508: (n=1, pv=5,100, pmt=0, fv=5,508) I/Y (what they're giving up) = 8%
(1) Assume Evco, Inc. has a current stock price of $45.97 and will pay a $2.10 dividend in one year; its equity cost of capital is 14%. What price must you expect Evco stock to sell for immediately after the firm pays the dividend in one year to justify its current price? (2) Assume Evco, Inc. has a current stock price of $50.00 and will pay a $2.00 dividend in one year; its equity cost of capital is 15%. What price must you expect Evco stock to sell for immediately after the firm pays the dividend in one year to justify its current price?
(1) P1 = P0 (1 + g) - Div1 P1 = 45.97 * 1.14 - 2.1 P1 = $50.3058 P1 = $50.31 (2) P1 = P0 (1 + g) - Div1 P1 = 50 * 1.15 - 2 P1 = $55.5
(1) A risk-free, zero-coupon bond with a face value of $10,000 has 12 years to maturity. If the YTM is 5.46%, which of the following would be closest to the price this bond will trade at? $4939 / $6584 / $4116 / $5762 / $5284 (2) A risk-free, zero-coupon bond with a face value of $10,000 has 15 years to maturity. If the YTM is 6.1%, which of the following would be closest to the price this bond will trade at? $6582 / $5286 / $4937 / $4114 / $5760
(1) Price = face value / (1 + yield) ^n 10,000 / (1 + 0.0546) ^12 = 5283.805177 = $5,284 (2) Price = face value / (1 + yield) ^n P = 10,000 / (1.061)^15 = 4114.04693 = $4,114
(1) An investor holds a Ford bond with a face value of $5000, a coupon rate of 6.5%, and semiannual payments that matures on January 15, 2029. How much will the investor receive on January 15, 2029? $5325.00 / $5162.50 / $2581.25 / $5016.25 / $5000.00 (2) An investor holds a Ford bond with a face value of $5000, a coupon rate of 8.5%, and semiannual payments that matures on January 15, 2029. How much will the investor receive on January 15, 2029? $5425.00 / $2606.25 / $5212.50 / $5000.00 / $5021.25
(1) Receiving on maturity date with semiannual payments and without known N: face value + face value * coupon rate / 2 $5,000 + $5,000 * 0.065 / 2 = $5,162.50 (2) Receiving on maturity date with semiannual payments and without known N: face value + face value * coupon rate / 2 5000 + 5000 * 0.085 / 2 = $5,212.50
(1) A Xerox DocuColor photocopier costing $48,200 is paid off in 60 monthly installments at 8.40% APR. After three years the company wishes to sell the photocopier. What is the minimum price for which they can sell the copier so that they can cover the cost of the balance remaining on the loan? $25,817 / $23,354 / $28,207 / $15,589 / $19,454 / $21,726 (2) A Xerox DocuColor photocopier costing $44,000 is paid off in 60 monthly installments at 6.90% APR. After three years the company wishes to sell the photocopier. What is the minimum price for which they can sell the copier so that they can cover the cost of the balance remaining on the loan? $21,676 / $28,191 / $15,546 / $23,319 / $25,804 / $19,433
(1) Remaining balance = PV of remaining months (3*12=36) & (8.4/12=0.7%) Step 1: find PMT in calc (n=60,i/y=0.7,pv=48,200,fv=0) PMT = $986.58 Step 2: 60 months - 36 = 24 remaining months Step 3: new PV in calc (n=24,i/y=0.7,pmt=986.58, fv=0) PV= $21,726.08 Answer: $21,726 (2) Remaining balance = PV of remaining months (3*12=36) & (6.9/12=0.575%) Step 1: find PMT in calc (n=60,i/y=0.575,pv=44,000,fv=0) PMT = $869.18 Step 2: 60 months - 36 = 24 remaining months Step 3: new PV in calc (n=24,i/y=0.575,pmt=869.18, fv=0) PV= $19,432.89 Answer: $19,433
(1) A graphic designer needs a new laptop and notices that he can pay $2,800 for a Dell XPS laptop upfront, or lease it from the manufacturer for monthly payments of $78 each for four years. The designer can borrow at an interest rate of 12% APR compounded monthly. What is the cost of leasing the laptop over buying it outright it terms of dollars today? -Leasing costs $32 less than buying. -Leasing costs $162 more than buying. -Leasing costs $162 less than buying. -Leasing costs $126 more than buying. -Leasing costs $32 more than buying. -Leasing costs $126 less than buying. (2) A graphic designer needs a new laptop and notices that he can pay $2600 for a Dell XPS laptop upfront, or lease it from the manufacturer for monthly payments of $75 each for four years. The designer can borrow at an interest rate of 14% APR compounded monthly. What is the cost of leasing the laptop over buying it outright it terms of dollars today? -Leasing costs $22 more than buying. -Leasing costs $145 more than buying. -Leasing costs $22 less than buying. -Leasing costs $116 less than buying. -Leasing costs $145 less than buying. -Leasing costs $116 more than buying.
(1) Step 1: Find monthly rate with compounding → APR / 12 months per year = 12% / 12 = 1% every month Step 2: Find PV of monthly payments with annuity discount rate → 4 years * 12 months = 48 periods → (N=48, I/Y=1, PMT=78, FV=0) → PV = $2,961.97 Step 3: Find the value → 2,961.97 - 2,800 = $161.97 Answer: Leasing costs $162 more than buying. (2) Step 1: Find monthly rate with compounding → APR / 12 months per year = 14% / 12 = 1.166667% every month Step 2: Find PV of monthly payments with annuity discount rate → 4 years * 12 months = 48 periods → (N=48, I/Y=1.166667, PMT=75, FV=0) → PV = $2,744.59 Step 3: Find the value → 2,744.59 - 2,600 = $144.59 Answer: Leasing costs $145 more than buying.
(1) Shore Services has 1.5 million shares outstanding. It expects earnings at the end of the year of $6.0 million. Shore pays out 60% of its earnings in total: 40% paid out as dividends and 20% used to repurchase shares. If Shore's earnings are expected to grow by 5% per year, these payout rates do not change, and Shore's equity cost of capital is 10%, what is Shore's share price? $48 / $24 / $12 / $36 / $60 / $72 (2) Shore Services has 1.2 million shares outstanding. It expects earnings at the end of the year of $6.0 million. Shore pays out 60% of its earnings in total: 40% paid out as dividends and 20% used to repurchase shares. If Shore's earnings are expected to grow by 5% per year, these payout rates do not change, and Shore's equity cost of capital is 10%, what is Shore's share price? $48 / $24 / $12 / $60 / $36 / $72
(1) Step 1: calculate total payouts = payout plan % * expected earnings = 60% * $6.0 million = 0.60 * 6,000,000 = $3,600,000 Step 2: calculate the PV (future total dividends & repurchases) with constant growth rate perpetuity PV = total payouts / (rE - g) PV = 3,600,000 / (0.10 - 0.05) PV = 3,600,000 / 0.05 PV = $72,000,000 Step 3: calculate share price with total payout model P0 = PV(future total dividends & repurchases) / # of shares outstanding P0 = 72,000,000 / 1,500,000 P0 = $48 per share (2) Step 1: calculate total payouts = payout plan % * expected earnings = 0.6 * $6 mil = $3,600,000 Step 2: calculate the PV (future total dividends & repurchases) with constant growth rate perpetuity PV = total payouts / (rE - g) PV = 3600000 / (0.1 - 0.05) = $72,000,000 Step 3: calculate share price with total payout model P0 = PV(future total dividends & repurchases) / # of shares outstanding P0 = 72000000 / 1.2 mil P0 = $60
(1) What must be the price of a $10,000 bond with a 6.2% coupon rate, semiannual coupons, and five years to maturity if it has a yield to maturity of 10% APR? $8,559.50 / $8,532.87 / $10,620.00 / $9,187.22 / $8,485.27 (2) What must be the price of a $10,000 bond with a 6.1% coupon rate, semiannual coupons, and five years to maturity if it has a yield to maturity of 10% APR? $8,494.26 / $8,521.59 / $10,193.11 / $11,891.97 / $10,305.00
(1) Step 1: convert to semiannual 6.2% coupon rate / 2 = 3.1% 5 years * 2 payments = 10 total periods PMT = 0.031 * 10,000 = $310 10% APR / 2 = 5% semiannually Step 2: find PV (n=10, i/y=5, pmt=310, fv=10,000) PV = $8,532.87 (2) Step 1: convert everything to semiannual 6.1% coupon rate / 2 payments per year = 3.05% 5 years * 2 payments per year = 10 total periods PMT = semi coupon rate * face value PMT = 0.0305 * 10000 = $305 10% APR / 2 payments per year = 5% semiannually Step 2: find PV (n=10, i/y=5, pmt=305, fv=10,000) PV = $8,494.26
(1) What is the yield to maturity of a(n) eight-year, $5,000 bond with a 4.4% coupon rate and semiannual coupons if this bond is currently trading for a price of $4,723.70? 6.319% / 5.264% / 2.632% / 2.628% / 5.255% (2) What is the yield to maturity of a eight-year, $5,000 bond with a 4.9% coupon rate and semiannual coupons if this bond is currently trading for a price of $4,367? A. 8.39% B. 3.5% C. 6.99% D. 9.79% (3) What is the yield to maturity of a ten-year, $10,000 bond with a 5% coupon rate and semiannual coupons if this bond is currently trading for a price of $9,155? A. 7.37% B. 8.6% C. 6.14% D. 3.07% (4) What is the yield to maturity of a five-year, $5,000 bond with a 4.6% coupon rate and semiannual coupons if this bond is currently trading for a price of $4,611? A. 7.74% B. 6.45% C. 3.22% D. 9.02%
(1) Step 1: convert to semiannual 8 years * 2 payments = 16 total periods 4.4% coupon rate / 2 payments = 2.2% semiannually PMT = coupon rate * face value = 0.022 * 5,000 = $110 Step 2: find the I/Y in calculator (n=16,pv=-4723.70, pmt=110, fv=5000) --> I/Y = 2.627% Step 3: convert to APR. 2.627 * 2 = 5.254% Answer: 5.255% (2) Step 1: convert to semiannual 8 years * 2 payments = 16 total periods 4.9% coupon rate / 2 payments = 2.45% semiannually PMT = coupon rate * face value = 0.0245 * 5,000 = $122.5 Step 2: find the I/Y in calculator (n=16,pv=-4367, pmt=122.5, fv=5000) --> I/Y = 3.497% Step 3: convert to APR. 3.497 * 2 = 6.994% Answer: 6.99% (3) Step 1: convert to semiannual 10 years * 2 payments per year = 20 total periods 5% coupon rate / 2 payments = 2.5% PMT = coupon rate * face value = 0.025 * 10000 = 250 Step 2: find I/Y in calc (n=20, pv=-9155, pmt=250, fv=10000) so I/Y = 3.072% Step 3: convert to APR: 3.072 * 2 = 6.144% Answer: 6.144% (4) Step 1: convert to semiannual 5 years * 2 payments per year = 10 total periods 4.6% coupon rate / 2 payments = 2.3% PMT = coupon rate * face value = 0.023 * 5000 = 115 Step 2: find I/Y in calc (n=10, pv=-4611, pmt=115, fv=5000) so I/Y = 3.222% Step 3: convert to APR: 3.222 * 2 = 6.444% Answer: 6.45%
(1) Greg is saving for a trip around Asia. He deposits a fixed amount every month in a bank account with an EAR of 8.00%. If this account pays interest every month then how much should he save from each monthly paycheck in order to have $25,000 in the account in four years' time? $370 / $446 / $432 / $396 / $417 (2) Robert is saving for a trip around Europe. He deposits a fixed amount every month in a bank account with an EAR of 14.7%. If this account pays interest every month then how much should he save from each monthly paycheck in order to have $14,000 in the account in four years' time? $ 198 / $ 235 / $ 252 / $ 176 / $ 220
(1) Step 1: find monthly annuity → 4 years * 12 months per year = 48 months of payment Step 2: find monthly interest rate → 1.08^1/12 - 1 = 0.006434 → 0.6434% per month Step 3: find monthly payment (N=48, I/Y=0.6434, PV=0, FV=25,000) → PMT = $446.20 Answer: $446 (2) Step 1: find monthly annuity → 4 years * 12 months per year = 48 months of payment Step 2: find monthly interest rate → 1.147^1/12 - 1 = 0.011495 → 1.1495% per month Step 3: find monthly payment (N=48, I/Y=1.1495, PV=0, FV=14,000) → PMT = $220.20 Answer: $220
(1) A construction company takes a loan of $1,531,000 to cover the cost of a new grader. If the interest rate is 8.50% APR, and payments are made monthly for five years, what is the interest portion and what is the principal portion of the first monthly payment? -interest $21,531.70; principal $10,844.58 -interest $10,844.58; principal $20,566.23 -interest $20,566.23; principal $10,844.58 -interest $10,844.58; principal $21,531.70 -interest $22,936.82; principal $10,844.58 -interest $10,844.58; principal $22,936.82 (2) A construction company takes a loan of $1,531,000 to cover the cost of a new grader. If the interest rate is 6.75% APR, and payments are made monthly for five years, what is the interest portion and what is the principal portion of the first monthly payment? -interest $8,611.88; principal $22,296.51 -interest $21,523.50; principal $8,611.88 -interest $22,296.51; principal $8,611.88 -interest $8,611.88; principal $22,936.82 -interest $8,611.88; principal $21,523.50 -interest $22,936.82; principal $8,611.88
(1) Step 1: find monthly rate → 8.5% / 12 months = 0.708333 Step 2: find PMT in calc → (5 years * 12 months = 60 N (N=60,I/Y=0.708333,PV=1,531,000,FV=0) → PMT=$31,410.81 Step 3: find portion needed to cover interest accrued (loan * rate) → 1,531,000 * 0.00708333 = $10,844.57823 Step 4: subtract to find principal value → 31,410.81 - 10,844.57823 = $20,566.23177 Answer: interest $10,844.58; principal $20,566.23 (2) Step 1: find monthly rate → 6.75% / 12 months = 0.5625 Step 2: find PMT in calc → (5 years * 12 months = 60 N (N=60, I/Y=0.5625, PV=1,531,000, FV=0) → PMT=$30,135.38 Step 3: find portion needed to cover interest accrued (loan * rate) → 1,531,000 * 0.005625 = $8611.875 Step 4: subtract to find principal value → 30135.38 - 8611.875 = $21,523.505 Answer: interest $8,611.88; principal $21,523.50
(1) A bank lends some money to a business. The business will pay the bank a single payment of $185,000 in ten years' time. How much greater is the present value (PV) of this payment if the annual interest rate is 7% rather than 9%? $12,049 / $7,545 / $9,618 / $14,853 / $15,899 (2) A bank lends some money to a business. The business will pay the bank a single payment of $176,000 in ten years' time. How much greater is the present value (PV) of this payment if the annual interest rate is 8% rather than 9%? $8,613 / $7,178 / $10,049 / $9,853 / $5,742
(1) Step 1: find the PV with each rate PV7% = $185,000 / 1.07^10 = $94,044.619045 PV9% = $185,000 / 1.09^10 = $78,145.999276 Step 2: find the value. 94,044.619045 - 78145.999276 = $15,898.619769 Answer: $15,899 (2) Step 1: find the PV with each rate PV8% = $176,000 / 1.08^10 = $81,522.053903 PV9% = $176,000 / 1.09^10 = $74,344.302014 Step 2: find the value. 81522.053903 - 74344.302014 = $7,177.751889 Answer: $7,178
(1) A newly issued, ten-year, zero-coupon bond with a yield to maturity of 3.80% has a face value of $1000. An investor purchases the bond when it is initially traded, and then sells it four years later. What is the annual rate of return of this investment, assuming the yield to maturity does not change? 2.8% / 2.4% / 4.0% / 3.2% / 3.8% (2) A ten-year, zero-coupon bond with a yield to maturity of 4% has a face value of $1000. An investor purchases the bond when it is initially traded, and then sells it four years later. What is the annual rate of return of this investment, assuming the yield to maturity does not change? 3.20% / 2.00% / 3.80% / 2.40% / 4.00%
(1) Step 1: find years left until maturity --> 10 - 4 = 6 years Step 2: find PV of the 6 years left P = face value / (1 + r)^n 1000 / 1.038^6 = $799.495234 Step 3: find PV of full 10 years 1000 / 1.038^10 = $688.694262 Step 4: find rate of return with 4 years Rate of return = (face value / price) ^1/n - 1 Rate of return = (pv remaining / pv maturity) ^1/n - 1 (799.495234 / 688.694262) ^1/4 - 1 = 0.038 Answer: 3.8% (2) Step 1: find years left until maturity --> 10 - 4 = 6 years Step 2: find PV of the 6 years left P = face value / (1 + r)^n 1000 / 1.04^6 = $790.314526 Step 3: find PV of full 10 years 1000 / 1.04^10 = $675.564169 Step 4: find rate of return with 4 years Rate of return = (face value / price) ^1/n - 1 Rate of return = (pv remaining / pv maturity) ^1/n - 1 (790.314526 / 675.564169) ^1/4 - 1 = 0.04 Answer: 4%
(1) Von Bora Corporation (VBC) is expected to pay a $2.00 dividend at the end of this year. If you expect VBC's dividend to grow by 6% per year forever and VBC's equity cost of capital to be 12%, then the value of a share of VBC stock is closest to ________. $33.3 / $39.7 / $27.5 / $37.4 / $35.3 / $42.2 (2) Von Bora Corporation (VBC) is expected to pay a $3.00 dividend at the end of this year. If you expect VBC's dividend to grow by 6% per year forever and VBC's equity cost of capital to be 13%, then the value of a share of VBC stock is closest to ________. $23.07 / $29.67 / $38.40 / $32.14 / $45.43 / $42.86
(1) Stock value with a PV of growing perpetuity: P0 = Div1 / (rE - g) P0 = 2 / (0.12 - 0.06) P0 = 2 / 0.06 P0 = $33.3 (2) Stock value with a PV of growing perpetuity: P0 = Div1 / (rE - g) P0 = 3 / (0.13 - 0.06) P0 = $42.86
(1) Spacefood Products has just paid a dividend of $2.50 per share. It is expected that this dividend will grow by 5.5% per year each year in the future. What will be the current value of a single share of Spacefood's stock if the firm's equity cost of capital is 12.5%? $25.6 / $37.7 / $35.7 / $32.8 / $27.3 / $29.5 (2) Spacefood Products has just paid a dividend of $2.40 per share. It is expected that this dividend will grow by 5% per year each year in the future. What will be the current value of a single share of Spacefood's stock if the firm's equity cost of capital is 12%? $24.00 / $36.00 / $28.50 / $34.29 / $22.29 / $30.86
(1) Stock value with constant dividend growth: If P0 = Div1 / (rE - g), then P0 = (Div0 * (1 + g)) / (rE - g) P0 = (2.5 * 1.055) / (0.125 - 0.055) P0 = 2.6375 / 0.07 P0 = $37.7 (2) Stock value with constant dividend growth: If P0 = Div1 / (rE - g), then P0 = (Div0 * (1 + g)) / (rE - g) P0 = (2.4 * 1.05) / (0.12 - 0.05) P0 = $36
(1) Year 1 = $97.25 / Year 2 = $94.53 / Year 3 = $91.83 / Year 4 = $89.23 / Year 5 = $87.53 The above table shows the price per $100-face value bond of several risk-free, zero-coupon bonds. What is the yield to maturity of the four-year, zero-coupon, risk-free bond shown? 12.07% / 2.89% / 2.85% / 5.79% / 2.83% (2) Year 1 = $97.25 / Year 2 = $94.53 / Year 3 = $91.83 / Year 4 = $89.23 / Year 5 = $87.53 The above table shows the price per $100-face value bond of several risk-free, zero-coupon bonds. What is the yield to maturity of the two-year, zero-coupon, risk-free bond shown? 2.85% / 5.79% / 2.89% / 1.43% / 2.83%
(1) Use the YTM equation to solve year 4. YTM = (face value / price) ^1/n - 1 (100 / 89.23) ^1/4 - 1 = 0.028898 = 2.89% (2) Use the YTM equation to solve year 2. YTM = (face value / price) ^1/n - 1 (100 / 94.53) ^1/2 - 1 = 0.028526 = 2.85%
(1) Which of the following bonds is trading at a premium? -a five-year bond with a $5,000 face value whose yield to maturity is 5.0% and coupon rate is 5.2% APR paid semiannually -a seven-year zero coupon bond whose yield to maturity is 9.0% and the face value is $5,000 -a two-year bond with a $50,000 face value whose yield to maturity is 5.2% and coupon rate is 5.2% APR paid annually -a 15-year bond with a $10,000 face value whose yield to maturity is 8.0% and coupon rate is 7.8% APR paid semiannually -a ten-year bond with a $1,000 face value whose yield to maturity is 6.0% and coupon rate is 5.9% APR paid semiannually (2) Which of the following bonds is trading at a premium? -a ten-year bond with a $4,000 face value whose yield to maturity is 6.0% and coupon rate is 5.9% APR paid semiannually -a seven-year zero coupon bond whose yield to maturity is 9.0% -a 15-year bond with a $10,000 face value whose yield to maturity is 8.0% and coupon rate is 7.8% APR paid semiannually -a two-year bond with a $50,000 face value whose yield to maturity is 5.2% and coupon rate is 5.2% APR paid monthly -a five-year bond with a $2,000 face value whose yield to maturity is 7.0% and coupon rate is 7.2% APR paid semiannually
(1) coupon rate above YTM = premium coupon rate same as YTM = par coupon rate below YTM = discount Answer: a five-year bond with a $5,000 face value whose yield to maturity is 5.0% and coupon rate is 5.2% APR paid semiannually (2) coupon rate above YTM = premium coupon rate same as YTM = par coupon rate below YTM = discount Answer: a five-year bond with a $2,000 face value whose yield to maturity is 7.0% and coupon rate is 7.2% APR paid semiannually
(1) A firm issues 5-year bonds with a coupon rate of 4.7%, paid semiannually. The credit spread for this firm's 5-year debt is 1.5%. New 5-year Treasury notes are being issued at par with a coupon rate of 5.1%. What should the price of the firm's outstanding 5-year bonds be if their face value is $1,000? $923.17 / $935.71 / $938.25 / $920.19 / $1049.53 (2) A firm issues 5-year bonds with a coupon rate of 4.7%, paid semiannually. The credit spread for this firm's 5-year debt is 1.2%. New 5-year Treasury notes are being issued at par with a coupon rate of 5.1%. What should the price of the firm's outstanding 5-year bonds be if their face value is $1,000? $1247.67 / $1035.71 / $932.28 / $933.15 / $931.65
(1) find PV in calc (with semiannual conversions) FV = 1,000 YTM = (treasury rate + credit spread) / 2 payments = (5.1 + 1.5) / 2 = 3.3% PMT = face value * (coupon rate / 2) = 1,000 * (0.047 / 2) = $23.50 N = 5 years * 2 semiannual = 10 periods PV = ? = $920.19 (2) find PV in calc (with semiannual conversions) FV = 1,000 YTM = (treasury rate + credit spread) / 2 payments = (5.1 + 1.2) / 2 = 3.15% PMT = face value * (coupon rate / 2) = 1,000 * (0.047 / 2) = $23.5 N = 5 years * 2 payments per year = 10 total periods PV = ? = $932.28
(1) Luther Industries has a dividend yield of 3.8% and a cost of equity capital of 11%. Luther Industries' dividends are expected to grow at a constant rate indefinitely. The growth rate of Luther's dividends are closest to: A. 7.2% B. 14.4% C. 6.5% D. 14.8% (2) Luther Industries has a dividend yield of 4.3% and a cost of equity capital of 12%. Luther Industries' dividends are expected to grow at a constant rate indefinitely. The growth rate of Luther's dividends are closest to: A. 6.9% B. 16.3% C. 7.7% D. 15.4%
(1) g = rE - (Div1 / P0) g = rE - dividend yield g = 11 - 3.8 g = 7.2% (2) g = rE - (Div1 / P0) g = rE - dividend yield g = 12% - 4.3% g = 7.7%
Which of the following accounts offers the highest interest rate? (Hint: convert each periodic rate to an EAR to compare) -one that pays 3.05% every three months -one that pays 12.32% per year -one that pays 1.00% per month -one that pays 25.55% every two years -one that pays 6.11% every six months
*convert all to annual %* (1 + EAR) ^n - 12/3=4, (1 + 0.0305)^4 = 1.127696 = 12.77% - 12.32% = 12.32% - 12 months, (1 + 0.01)^12 = 1.126825 = 12.68% - 1/2, (1 + 0.2555)^1/2 = 1.120491 = 12.05% - 12/6=2, (1 + 0.0611)^2 = 1.125933 = 12.59% Answer: one that pays 3.05% every three months
Assume a private corporation goes public in an IPO. Which of these is NOT an advantage of going public? -Greater need for regulatory reporting -More information about stock value -Easier access to equity capital -Greater liquidity for company's shares
-Greater need for regulatory reporting
How is preferred stock similar to bonds? -Preferred stockholders receive a dividend payment (much like interest payments to bondholders) that is usually fixed. -Preferred stock is not like bonds in any way. -Dividend payments to preferred shareholders (much like bond interest payments to bondholders) are tax deductible. -Investors can sue the firm if preferred dividend payments are not paid (much like bondholders can sue for nonpayment of interest payments). -Preferred stockholders expect to receive a stated value at maturity (much like bondholders do).
-Preferred stockholders receive a dividend payment (much like interest payments to bondholders) that is usually fixed.
You placed an order to purchase stock where you specified the maximum price you were willing to pay. This type of order is known as a ________. -short order -limit order -maximum order -ceiling order -floor order -market order
-limit order
What was the yield on 30-year Treasury STRIPS on September 29, 2020? (Note, this is discussed in Part 6.2 of Chapter 6 Video Lecture.) Group of answer choices2.1%1.9%1.5%1.3%1.7%
1.5%
If you own 10,000 shares of stock of Nike and it pays a dividend of $0.29 per share, then what is the total dividend you will receive?
10,000 * 0.29 = $2,900
You have taken out a 60-month, $19,000 car loan with an APR of 4%, compounded monthly. The monthly payment on the loan is $349.91. Assume that right after you make your 50th payment, the balance of the loan is $3,435.80. How much of your next payment goes toward principal and how much goes toward interest? Compare this with the principal and interest paid in the first month's payment.
50th month: interest paid = loan balance * monthly rate = 3435.80 * 0.00333333 = $11.452655 Subtract interest paid from the monthly payment = 349.91 - 11.452655 = $338.457345 Interest = $11.45; Principle = $338.46 First month: Monthly rate = 4% / 12 months = 0.333333 → PMT=$349.91 → interest (loan * rate) = 19,000 * 0.00333333 = $63.33327 → principal value = 349.91 - 63.33327 = $286.57673 → Interest = $63.33327; Principal = $286.57673 In the first month, the amount that goes towards principal is $286.58 and toward interest is $63.33. Therefore, you can see that over time, as you pay down the principal of the loan, less of your payment has to go to cover interest and more of your payment can go towards reducing the principal.
What, typically, is used to calculate the opportunity cost of capital on a risk−free investment? A. the interest rate of any investments alternatives that are available B. the interest rate on U.S. Treasury securities with the same term C. the best rate of return offered by U.S. Treasury securities D. the best expected return offered in any investment available in the market
A. no, not any B. yes, same term C. no, not best rate D. no, not best or any Answer: B. the interest rate on U.S. Treasury securities with the same term
Which of the following is FALSE about the constant growth dividend discount model? A. The results from it are very sensitive to small changes in growth rate. B. It requires that the growth rate always be higher than the required rate of return, which is not realistic. C. Future dividend growth rate is often difficult to predict. D. It cannot estimate the value of a stock when the growth rate in dividends is not constant. E. It cannot estimate the value of a stock that pays no dividends.
A. not sure B. no, rate of return should be > cost of capital C. true, there's always uncertainty D. true, the constant growth dividend model values stock by viewing its dividends as a constant growth perpetuity E. true, it views dividends as a constant growth perpetuity Answer: B. It requires that the growth rate always be higher than the required rate of return, which is not realistic.
Which of the following statements is FALSE about interest rates? A. As interest rates may be quoted for different time intervals, it is often necessary to adjust the interest rate to a time period that matches that of cash flows. B. The effective annual rate indicates the amount of interest that will be earned at the end of one year. C. The annual percentage rate indicates the amount of interest including the effect of compounding. D. The annual percentage rate indicates the amount of simple interest earned in one year.
A=true B=true C=false - indicates simple interest without compounding D=true Answer: C. The annual percentage rate indicates the amount of interest including the effect of compounding.
When you borrow money, the interest rate on the borrowed money is the price you pay to be able to convert your future loan payments into money today. (T or F)
True
Which of the following situations would result in lowering of interest rates by the banking authority of a country? A. The level of investment is quite high. B. The economy is slowing down. C. Inflation is rising rapidly. D. The rate of savings is quite low.
B. The economy is slowing down.
You placed an order to purchase stock where you specified the maximum price you were willing to pay. This type of order is known as a ________. A. maximum order B. limit order C. market order D. floor order
B. limit order
Given that the inflation rate in 2006 was about 3.24%, while a short−term municipal bond offered a rate of 2.9%, which of the following statements is correct? A. Nominal interest rate offered by these bonds gave the true increase in purchasing power that resulted from investing in them. B. The real interest rate for investors in these bonds was greater than the rate of inflation. C. Investors in these bonds were able to buy less at the end of the year than they could have purchased at the start of the year. D. The purchasing power of investors in these bonds grew over the course of the year.
C. Investors in these bonds were able to buy less at the end of the year than they could have purchased at the start of the year.
What do you prefer: bank account pays 5.4%/year(EAR)for 3 years or a. An account that pays 2.3% every six months for three years? b. An account that pays 7.5% every 18 months for three years? c. An account that pays 0.72% per month for three years? (Note: Compare your current bank EAR with each of the three alternative accounts. Be careful not to round any intermediate steps less than six decimal places.)
Calculate all options in monthly periods. (3*12=36n) FV = (1 + r)^n (5.4%: 1.054^3 = $1.17091) 2.3%: (2/year*3 years = 6n) 1.023^6 = $1.14618 Which do you prefer? 5.4% because it's greater. 7.5%: (36/18=2 payments) 1.075^2 = $1.15563 Which do you prefer? 5.4% because it's greater. 0.72%: 12*3=36 payments) 1.0072^36 = $1.29469 Which do you prefer? 0.72% because it's greater.
Which of the following accounts pays the lowest interest rate? (Hint: Make sure to convert the rates such that they are comparable.) -one that pays 12.32% per year -one that pays 3.05% every three months -one that pays 1.00% per month -one that pays 6.11% every six months -one that pays 25.55% every two years
Converting = (1 + r)^n 12.32%: (1.1232)^1/12 = 1.009729% 3.05%: (1.0305)^1/3 = 1.010065% 1.00%: (1.01)^1 = 1.01% 6.11%: (1.0611)^1/6 = 1.009933% 22.55%: (0.2255)^1/24 = 1.008509% Answer: one that pays 22.55% every two years
Your company currently has $1,000 par, 5% coupon bonds with 10 years to maturity and a price of $1,087. If you want to issue new 10-year coupon bonds at par, what coupon rate do you need to set? Assume that for both bonds, the next coupon payment is due in exactly six months.
Coupon rate same as YTM = par Step 1: Current YTM = (face value / price) ^1/n - 1 (1000 / 1087)^1/10 - 1 = -0.008307 = -0.8307% Find I/Y in calculator (10*2=20 periods) (0.05*1000/2=25) (n=20, pv=-1087, pmt=25, fv=1000) I/Y = 1.970% Step 2: the bond trades at par when its coupon rate is equal to YTM, however the coupon rate we just found is the semiannual rate, double it to find the matching APR. 1.970 * 2 = 3.94% Answer: 3.94%
(1) Jumbo Transport, an air-cargo company, expects to have earnings per share of $2.00 in the coming year. It decides to retain 20% of these earnings in order to lease new aircraft. The return on this investment will be 15%. If its equity cost of capital is 12%, what is the expected share price of Jumbo Transport? $22.42 / $19.27 / $21.12 / $15.62 / $17.78 / $13.81 (2) Jumbo Transport, an air-cargo company, expects to have earnings per share of $2.00 in the coming year. It decides to retain 10% of these earnings in order to lease new aircraft. The return on this investment will be 25%. If its equity cost of capital is 11%, what is the expected share price of Jumbo Transport? $16.94 / $19.17 / $21.18 / $23.47 / $12.71 / $14.83
Cutting dividends for growth (1) Step 1: calculate dividend under new policy Payout rate = 100% - retention rate = 100 - 20 = 80% Div1 = EPS * payout rate Div1 = 2 * 0.80 Div1 = $1.60 Step 2: calculate growth rate under new policy g = retention rate * return on new investment g = 0.20 * 0.15 = 0.03 = 3% Step 3: calculate new share price P0 = Div1 / (rE - g) P0 = 1.60 / (0.12 - 0.03) P0 = 1.6 / 0.09 P0 = $17.78 (2) Step 1: calculate dividend under new policy Payout rate = 100% - retention rate = 100-10= 90% payout Div1 = EPS * payout rate Div1 = 2 * 0.9 = $1.8 Step 2: calculate growth rate under new policy g = retention rate * return on new investment g = 0.10 * 0.25 g = 0.025 = 2.5% Step 3: calculate new share price P0 = Div1 / (rE - g) P0 = 1.8 / (0.11 - 0.025) P0 = $21.18
(1) JRN Enterprises just announced that it plans to cut its next year's dividend from $3.00 to $2.50 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 $27.60 per share. With the new expansion, JRN's dividends are expected to grow at 6% 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 ________. $25.4 / $15.6 / $37.6 / $18.9 / $28.2 / $31.6 (2) JRN Enterprises just announced that it plans to cut its next year's 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 ________. $25.50 / $29.67 / $38.63 / $19.32 / $32.56 / $12.75
Cutting dividends for profitable growth (1) Step 1: calculate equity cost of capital rE = (Div1 / P0) + g rE = 3 / 27.60 + 0.04 rE = 0.108696 + 0.04 rE = 0.148696 = 14.87% Step 2: calculate share price under new policy P0 = Div1 / (rE - g) P0 = 2.5 / (0.1487 - 0.06) P0 = 2.5 / 0.0887 P0 = $28.2 (2) Step 1: calculate equity cost of capital rE = (Div1 / P0) + g rE = (3 / 25.5) + 0.04 rE = 0.157647 = 15.76% Step 2: calculate share price under new policy P0 = Div1 / (rE - g) P0 = 1.5 / (0.157647 - 0.08) P0 = $19.32
Cooperton Mining just announced it will cut its dividend from $3.78 to $2.45 per share and use the extra funds to expand. Prior to the announcement, Cooperton's dividends were expected to grow at a 3.3% rate, and its share price was $48.07. With the planned expansion, Cooperton's dividends are expected to grow at a 4.6% rate. What share price would you expect after the announcement? (Assume that the new expansion does not change Cooperton's risk.) Is the expansion a good investment?
Cutting dividends for profitable growth New price for stock: Step 1: calculate equity cost of capital rE = (Div0 / P0) + g rE = 3.78 / 48.07 + 0.033 rE = 0.078635 + 0.033 rE = 0.111635 = 11.16% Step 2: calculate share price under new policy P0 = Div1 / (rE - g) P0 = 2.45 / (0.111635 - 0.046) P0 = 2.45 / 0.065635 P0 = $37.327645 P0 = $37.33 No, it is not a good investment.
Which of the following reasons for considering long−term loans inherently more risky than short−term loans is most accurate? A. The penalties for closing out a long term loan early make them unattractive to many investors. B. There's a greater chance inflation may fall in a longer time frame. C. Long−term loans typically have ongoing costs that accumulate over the life of the loan. D. Loan values are very sensitive to changes in market interest rates.
D. Loan values are very sensitive to changes in market interest rates.
A 12% APR with compounding that occurs every two months (six times a year) is equivalent to an EAR of ________. 12.36% / 12.00% / 11.98% / 12.50% / 12.62%
EAR = (1 + (APR/m))^m - 1 EAR = (1 + (0.12 / 6))^6 - 1 = 0.126162 EAR = 12.62%
You are considering two ways of financing a spring break vacation. You could put it on your credit card, at 16% APR, compounded monthly, or borrow the money from your parents, who want an interest payment of 9% every six months. Which is the lower rate? (Note: Be careful not to round any intermediate steps less than six decimal places.)
EAR = (1 + (r/m))^m - 1 16% APR rate EAR = (1+0.16/12))^12-1 = 0.172271 = 17.23% 9%: for the loan from your parents, plug into EAR formula but don't divide the rate by 2 because you're provided with the 6-month rate (not the annual rate compounded semiannually): EAR = [( 1 + r) ^ n] - 1 = (1+0.09)^2 - 1 = 0.1881 = 18.81% The option with the lower effective annual rate is your credit card.
An 18% APR with bimonthly compounding is equivalent to an EAR of ________. 19.41% 18.00% 3.00% 18.37% 17.67% 18.81%
EAR = (1 + (r/m))^m - 1 Bimonthly = 6 periods (1 + (18/6))^6 - 1 = 0.194052 = 19.4052% Answer: 19.41%
A corporate bond makes payments of $9.67 every month for ten years with a final payment of $2009.67. Which of the following best describes this bond? A. a 10−year bond with a face value of $2,009.67 and a coupon rate of 4.8% with monthly payments B. a 10−year bond with a face value of $2,000 and a coupon rate of 4.8% with monthly payments C. a 10−year bond with a face value of $2,000 and a coupon rate of 5.8% with monthly payments D. a 10−year bond with a face value of $2,009.67 and a coupon rate of 5.8% with monthly payments
Face value = $2,000 Rate = (pmt * months per year) / (final payment - monthly payment) $9.67 × 12 / (2,009.67 - 9.67) = 0.05802 Rate = 5.8% Answer: C. a 10−year bond with a face value of $2,000 and a coupon rate of 5.8% with monthly payments
Which of the following is NOT a way that a firm can increase its dividend? -by decreasing its shares outstanding -by increasing its retention rate -by increasing its earnings (net income) -by increasing its dividend payout rate
Firm's can increase its dividend in 3 ways: (1) increase its earning (net income) (2) increase its dividend payout rate (3) decrease its # of shares outstanding Answer (not a way) = by increasing its retention rate
Suppose Compco Systems pays no dividends but spent $5.01 billion on share repurchases last year. If Compco's equity cost of capital is 11.5%, and if the amount spent on repurchases is expected to grow by 8.4% per year, estimate Compco's market capitalization. If Compco has 6.2 billion shares outstanding, to what stock price does this correspond?
Market capitalization: Step 1: calculate total payout = payout last year * (1 + g) 5.01 billion * 1.084 = 5430840000 Step 2: calculate market capitalization equity value = total payout / (rE - g) 5430840000 / (0.115 - 0.084) = 175188387096.7742 market cap = $175.19 billion Stock price: Step 3: find P0 for stock price P0 = equity value / # of shares P0 = 175.19 billion / 6.2 billion = 28.256191 P0 = $28.26
You are looking to buy a car and you have been offered a loan with an APR of 6.1%, compounded monthly. a. What is the true monthly rate of interest? b. What is the EAR?
Monthly interest rate: 6.1% / 12 months per year = 0.5083 EAR: (1 + (r/m))^m - 1 = (1 + (0.061/12))^12 - 1 = 0.062735 = 6.2735%
Bond / Coupon Rate (annual payments) / Maturity (years) A 0.0% 15 B 0.0% 10 C 3.7% 15 D 7.6% 10 Which of the bonds A to D is most sensitive to a 1% drop in interest rates from 6.1% to 5.1%? Which bond is least sensitive?
Most sensitive: -the longer the bond, the more sensitive it is (this knocks out B and D) -the smaller the coupon rate change, the more sensitive (this knocks out C) Answer: Bond A is most sensitive Least sensitive: -the shorter the bond, the less sensitive it is (this knocks out A and C) -the greater the coupon rate change, the less sensitive (this knocks out B) Answer: Bond D is the least sensitive
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. -Only II. is true -Only I. is true -Only II. and III. are true -Only I. and III. are true -Only III. is true
Only II. is true
YTM: Year 1 = 5.03% / Year 2 = 5.45% / Year 3 = 5.73% / Year 4 = 5.99% / Year 5 = 6.03% What is the price per $100 face value of a two-year, zero-coupon, risk-free bond?
P = FV / (1 + y)^n --> 100 / 1.0545^2 = 89.930464 = $89.93
You are thinking about investing $4,883 in your friend's landscaping business. Even though you know the investment is risky and you can't be sure, you expect your investment to be worth $5,677 next year. You notice that the rate for one-year Treasury bills is 1%. However, you feel that other investments of equal risk to your friend's landscape business offer an expected return of 8% for the year. What should you do?
PV of return = FV / (1 + r)^n = 5,677/1.08^1 = $5256.481481 You should: invest in the business.
You have decided to refinance your mortgage. You plan to borrow whatever is outstanding on your current mortgage. The current monthly payment is $1,850 and you have made every payment on time. The original term of the mortgage was 30 years, and the mortgage is exactly four years and eight months old. You have just made your monthly payment. The mortgage interest rate is 5.750% (APR). How much do you owe on the mortgage today?
Remaining balance = PV of remaining months (30*12=360) & (4*12+8=56) & (5.750/12=0.479167%) 1: PMT = $1,850 2: 360 months - 56 = 304 remaining months 3: new PV in calc (n=304,i/y=0.479167,pmt=1850, fv=0) PV= $295,810.56 Answer: $295,811
In an effort to maintain price stability, it is expected that the European Central Bank will raise interest rates in the future. Which of the following is the most likely effect of such an action on short-term and long-term interest rates in Europe? -Both long & short-term interest rates expected to fall sharply. -The yield curve is expected to become inverted. -No relative change in short & long-term interest rates be predicted. -Long-term interest rates about the same as short-term interest rates. -Long-term interest rates tend to be higher than short-term rates.
Sharply increasing (steep) yield curve with long-term rates much higher than short-term rates indicates interest rates are expected to rise in the future. Answer: Long-term interest rates tend to be higher than short-term rates.
Assume Coleco pays an annual dividend of $1.45 and has a share price of $37.91. It announces that its annual dividend will increase to $1.72. If its dividend yield stays the same, what should be its new share price?
Step 1: calculate expected return rE = Div1 / P0 rE = 1.45 / 37.91 rE = 0.038248 rE = 3.8248% Step 2: calculate new share price P0 = Div1 / rE P0 = 1.72 / 0.038248 P0 = 44.969672 P0 = $44.97
Shatin Intl. has 9.8million shares, an equity cost of capital of 12.9% and is expected to pay a total dividend of $20.9 million each year forever. It announces that it will increase its payout to shareholders. Instead of increasing its dividend, it will keep it constant and will start repurchasing $9.6 million of stock each year as well. What is your estimate of Shatin's stock price after this announcement?
Step 1: calculate the PV (future total dividends & repurchases) PV = (dividends + repurchases) / rE PV = (20.9 million + 9.6 million) / 0.129 PV = $236,434,108.527132 Step 2: calculate stock price P0 = PV(future total dividends & repurchases) / shares outstanding P0 = 236,434,108.527132 / 9.8 million P0 = $24.125929 per share P0 = $24.13
Laurel Enterprises expects earnings next year of $4.11 per share and has a 40% retention rate, which it plans to keep constant. Its equity cost of capital is 11%, which is also its expected return on new investment. Its earnings are expected to grow forever at a rate of 4.4% per year. If its next dividend is due in one year, what do you estimate the firm's current stock price to be?
Step 1: calculate the dividend price at the end of year Div1 = EPS * payout ratio Div1 = 4.11 * (100% - 40% retention = 60% payout = 0.6) Div1 = $2.466 Step 2: calculate growth rate g = retention rate * return on investment/cost of cap g = 0.4 * 0.11 g = 0.044 Step 3: calculate current stock price P0 = Div1 / (rE - g) P0 = 2.466 / ( 0.11 - 0.044) P0 = 2.466 / 0.066 P0 = 37.363636 P0 = $37.36
AFW Industries has 212 million shares outstanding and expects earnings at the end of this year of $658 million. AFW plans to pay out 58% of its earnings in total, paying 34% as a dividend and using 24% to repurchase shares. If AFW's earnings are expected to grow by 7.6% per year and these payout rates remain constant, determine AFW's share price assuming an equity cost of capital of 11.8%.
Step 1: calculate total payout = earnings * payout ratio $658 million * 58% = 658,000,000 * 0.58 = 381640000 Step 2: find PV of total payout PV = total payout / (rE - g) PV = 381640000 / (0.118 - 0.076) = 9086666666.666668 PV = $9,086,666,666.67 Step 3: value equity using growing perpetuity formula P0 (share price) = PV / # of shares P0 = 9086666666.666668 / 212 million = 42.861635 P0 = $42.86
Achi Corp. has preferred stock with an annual dividend of $3.08. If the required return on Achi's preferred stock is 8.1%, what is its price? (Hint: For a preferred stock, the dividend growth rate is zero.)
Step 1: calculate with constant dividend growth formula P0 = Div1 / (r - g) P0 = 3.08 / (0.081 - 0) P0 = 38.024691 P0 = $38.02
Suppose a five-year, $1,000 bond with annual coupons has a price of $895.94 and a yield to maturity of 6.4%. What is the bond's coupon rate?
Step 1: find PMT (n=5, i/y=6.4, pv=-895.94, fv=1000) PMT = $39.03 (aka CPN) Step 2: find the coupon rate --> r=CPN/FV 39.03/ 1000 = 0.03903 Answer: 3.903%
CX Enterprises has the following expected dividends: $1.11 in one year, $1.19 in two years, and $1.29 in three years. After that, its dividends are expected to grow at 4.4% per year forever (so that year 4's dividend will be 4.4% more than $1.29 and so on). If CX's equity cost of capital is 11.6%, what is the current price of its stock?
Step 1: find PV of growing dividends at end of year three PV3 = Div4 / (rE - g) PV3 = (1.29 * (1 + 0.044)) / (0.116 - 0.044) PV3 = $18.705 Step 2: find price of the stock where P0 = (Div1 / (1 + rE)) + (Div2 / (1 + rE)^2) + ((Div3 + PV3) / (1 + rE)^3) (1.11 / 1.116) + (1.19 / (1.116)^2) + ((1.29 + 18.705) / (1.116)^3) P0 = $16.335725 P0 = $16.34
You have just taken out a $26,000 car loan with a 5% APR, compounded monthly. The loan is for five years. When you make your first payment in one month, how much of the payment will go toward the principal of the loan and how much will go toward interest?
Step 1: find monthly rate → 5% / 12 months = 0.416667 Step 2: find PMT in calc → (5 years * 12 months = 60 N (N=60,I/Y=0.416667,PV=26,000,FV=0)→PMT=$490.65 Step 3: find portion needed to cover interest accrued (loan * rate) → 26,000 * 0.00416667 = $108.33342 Step 4: subtract to find principal value → PMT - portion = 490.65 - 108.33342 = $382.31658 Interest $108.33; principal $382.32
Suppose Capital One is advertising a 60-month, 5.82% APR motorcycle loan. If you need to borrow $8,600 to purchase your dream Harley-Davidson, what will be your monthly payment?
Step 1: find monthly rate → 5.82/12 = 0.485% Step 2: find PMT in calc (n=60, i/y=0.485, pv=8600, fv=0) Monthly payment = $165.54
You have been accepted into college. The college guarantees that your tuition will not increase for the four years you attend college. The first $10,900 tuition payment is due in six months. After that, the same payment is due every six months until you have made a total of eight payments. The college offers a bank account that allows you to withdraw money every six months and has a fixed APR of 3.8% (with semiannual compounding) guaranteed to remain the same over the next four years. How much money must you deposit today if you intend to make no further deposits and would like to make all the tuition payments from this account, leaving the account empty when the last payment is made?
Step 1: find semiannual discount rate (r = APR / 2) 3.8% / 2 = 1.9% Step 2: find pv of annuity → C/r * (1 - (1 / (1 + r)^n)) 10900/0.019 * (1 - (1 / (1 + 0.019)^8)) = 80192.996597 (n=8,i/y=1.9,pmt=10900,fv=0) so PV = $80,193.00
Summit Systems will pay a dividend of $1.69 this year. If you expect Summit's dividend to grow by 6.9% per year, what is its price per share if the firm's equity cost of capital is 10.7%?
Stock value with a PV of growing perpetuity: P0 = Div1 / (rE - g) P0 = 1.69 / (0.107 - 0.069) P0 = 1.69 / 0.038 P0 = $44.473684 P0 = $44.47
Security Yield (%) Treasury 3.11 AAA corporate 3.22 BBB corporate 4.25 B corporate 4.94 a. What is the price (expressed as a percentage of the face value) of a one-year, zero-coupon corporate bond with a AAA rating? b. What is the credit spread on AAA-rated corporate bonds? c. What is the credit spread on B-rated corporate bonds? d. How does the credit spread change with the bond rating? Why?
a. P = FV / (1 + YTM)^n --> 100 / 1.0322^1 = 96.88045 = 96.880% b. Spread=AAA bond yield-treasury yield-->3.22-3.11=0.11 = 0.11% c. Spread=B bond yield-treasury yield--> 4.94-3.11 = 1.83 = 1.83% d. The credit spread increases as the bond rating falls because lower-rated bonds are riskier.
Assume General Energy just paid a dividend of $2 per share. Analysts expect the dividends to grow at 10% for next two years. After that, the dividend growth rate is expected to decline to a long-term perpetual growth rate of 2%. If the cost of equity capital for General Energy is 6%, what is the value estimate of its stock price today? $48.33 / $52.14 / $50.18 / $60.50 / $55.00 / $59.15
Valuing a firm with changing growth rates (no payout) (N = last year used in equation) Step 1: create timeline Year 0 = ? / Year 1 = 2*(1+0.1) / Year 2 = 2*(1+0.1)^2 / Year 3 = PN ... Step 2: calculate PN PN = (DivN + (1+g)) / (rE - g) PN = ((2*(1+0.1)^2)*(1+0.02)/(0.06-0.02) PN = $61.71 Step 3: calculate current price P0=(P1/(1+rE))+(P2/(1+rE)^2)+(P3/(1+rE)^3)+(PN/(1+rE)^N) P0 = ((2*1.1)/1.06) + ((2*(1.1)^2)/1.06^2) + (61.71/1.06^2) P0 = $59.150943 P0 = $59.15
Solar Energy is a fast growing manufacturer of solar panels for home builders. The company just reported $4 earnings per share this past year. Assume that these earnings are expected to grow at a 15% growth rate for next two years. Also assume that after that, the earnings growth rate is expected to decline to an estimated long-term perpetual growth rate of 5%. Solar has not been paying any regular dividends yet, but it is expected that two years from now the company will pay its first dividend. The dividend payout is expected at 40% from the expected earnings at that time. If the cost of equity capital for Solar Energy is 13%, what is the value estimate of its stock price today given the assumptions? $62.58 / $26.45 / $28.19 / $23.41 / $68.23 / $66.13
Valuing a firm with changing growth rates (with payout) Step 1: organize info / EPS0 = $4 / g up to year 2 = 15% / payout stating at year 2 = 40% / g starting at year 3 = 5% / rE = 13% / dividends start at year 2 Step 2: calculate EPS2 EPS0 = $4 --> * growth rate 15% = EPS1 = $4.6 --> * 0.15 = EPS2 = $5.29 Step 3: calculate dividend of year 2 Div2 = EPS2 * payout rate Div2 = 5.29 * 0.40 Div2 = $2.12 Step 4: calculate share price at end of year 1 P1 = Div2 / (rE - g) P1 = 2.12 / (0.13 - 0.05) P1 = 2.12 / 0.08 P1 = $26.5 Step 5: calculate value of share today with dividend discount model P0 = P1 / (1 + rE)^1 P0 = 26.5 / 1.13 P0 = $23.45 Answer = $23.41
Your company wants to raise $10.0 million by issuing 20-year zero-coupon bonds. If the yield to maturity on the bonds will be 6% (annual compounded APR), what total face value amount of bonds must you issue?
YTM = (face value / price) ^1/n - 1 0.06 = (x / 10,000,000) ^1/20 - 1 32,071,350
For each of the following pairs of Treasury securities (each with $1,000 par value), identify which will have the higher price: a. A three-year zero-coupon bond or a five-year zero-coupon bond? b. A three-year zero-coupon bond or a three-year 4% coupon bond? c. A two-year 5% coupon bond or a two-year 6% coupon bond?
a. A three-year zero-coupon bond, because the future value is received sooner and the present value is higher. b. The three-year 4% coupon bond, because the 4% coupon bond pays interest payments; whereas the zero-coupon bond is a pure discount bond. c. The two-year 6% coupon bond, because the coupon (interest) payments are higher, even though the timing is the same.
Suppose a ten-year, $1,000 bond with an 8.8% coupon rate and semiannual coupons is trading for $1,035.68. a. What is the bond's yield to maturity (expressed as an APR with semiannual compounding)? b. If the bond's yield to maturity changes to 9.9% APR, what will be the bond's price?
a. Step 1: convert to semiannual 10 years * 2 payments = 20 total periods 8.8% coupon rate / 2 payments = 4.4% semiannually PMT = coupon rate * face value = 0.044 * 1,000 = $44 Step 2: find the I/Y in calculator (n=20,pv=-1035.68, pmt=44, fv=1000) --> I/Y = 4.134% Step 3: convert to APR. 4.134 * 2 = 8.268% Answer: 8.27% b. Find PV in calculator. N = 20 I/Y = 9.9 / 2 = 4.95 PMT = 0.44 * 1000 = 44 FV = 1000 PV = $931.17
Suppose you purchase a 10-year bond with 6.4% annual coupons. You hold the bond for four years, and sell it immediately after receiving the fourth coupon. If the bond's yield to maturity was 5.3% when you purchased and sold the bond, a. what cash flows will you pay and receive from your investment in the bond per $100 face value? b. what is the annual rate of return of your investment?
a. Step 1: find initial price with PV (n=10, i/y=5.3, pmt=6.4, fv=100) PV = $108.37 Step 2: find price at which it sold (10 - 4 = 6 years) (n=6, i/y=5.3, pmt=6.4, fv=100) PV = $105.53 Step 3: put together the timeline Year0=-108.37, Year1=6.4, Year2=6.4, Year3=6.4, Year4=6.4+105.33=111.73 b. find I/Y (n=4, pv=-108.37, pmt=6.4, fv=105.53) Rate of return = 5.3%
Year 1 = $95.94 / Year 2 = $91.57 / Year 3 = $86.94 / Year 4 = $82.05 / Year 5 = $77.04 / face value = $100 The following table summarizes prices of various default-free zero-coupon bonds (expressed as a percentage of the face value): a. Compute the yield to maturity for each bond. b. Plot the zero-coupon yield curve (for the first five years). c. Is the yield curve upward sloping, downward sloping, or flat?
a. YTM = (face value / price) ^1/n - 1 year 1 = (100 / 95.94) ^1/1 - 1 = 0.042318 = 4.23% year 2 = (100 / 91.57) ^1/2 - 1 = 0.045017 = 4.50% year 3 = (100 / 86.94) ^1/3 - 1 = 0.047756 = 4.78% year 4 = (100 / 82.05) ^1/4 - 1 = 0.050704 = 5.07% year 5 = (100 / 77.04) ^1/5 - 1 = 0.053554 = 5.36% b. it increase from left to right c. upward sloping
Consider a 10-year bond with a face value of $1,000 that has a coupon rate of 5.7%, with semiannual payments. a. What is the coupon payment for this bond? b. Draw the cash flows for the bond on a timeline.
a. coupon payment = (coupon rate * face value) / # of coupon payments per year 0.057 * 1,000 / 2 = $28.50 b. (p=period) p0=0, p1=28.5, p2=28.5, p3=28.5, ..., p20=1028.5
Suppose a seven-year, $1,000 bond with an 8.2% coupon rate and semiannual coupons is trading with a yield to maturity of 6.26%. a. Is this bond currently trading at a discount, at par, or at a premium? Explain. b. If the yield to maturity of the bond rises to 7.03% (APR with semiannual compounding), what price will the bond trade for?
a. coupon rate above YTM = premium Because the yield to maturity is less than the coupon rate, the bond is trading at a premium. b. Find PV in calc (7.03/2=3.515) (0.082*1000/2=41) (n=14, i/y=3.515, pmt=41, fv=1000) PV = $1,063.82
HMK Enterprises would like to raise $10.0 million to invest in capital expenditures. The company plans to issue five-year bonds with a face value of $1,000 and a coupon rate of 6.56% (annual payments). The following table summarizes the yield to maturity for five-year (annual-payment) coupon corporate bonds of various ratings: Rating = YTM / AAA = 6.14% // AA = 6.32% // A = 6.56% // BBB = 6.95% // BB = 7.59% a. Assuming the bonds will be rated AA, what will be the price of the bonds? b. How much of the total principal amount of these bonds must HMK issue to raise $10.0 million today, assuming the bonds are AA rated? (Because HMK cannot issue a fraction of a bond, assume that all fractions are rounded to the nearest whole number.) c. What must be the rating of the bonds for them to sell at par? d. Suppose that when the bonds are issued, the price of each bond is $958.43. What is the likely rating of the bonds? Are they junk bonds?
a. find PV in calculator (pmt=0.0656*1000=65.6) (n=5, i/y=6.32, pmt=65.6, fv=1000) Price = $1,010.02 b. find the total principal amount given the last price principal amount = face value * # of bonds # of bonds = amount to raise / bond's price # of bonds = 10 mil / 1010.02 = 9900.794044 bonds = 9901 principal amount = 1000 * 9900.794044 = 9900794.044 Total principal amount = $9,900,794.04 c. we must equal the yield of the bond, our coupon rate is 6.56% so our rating must also be 6.56%, same as "A" d. find I/Y (n=5, pv=-958.43, pmt=65.6, fv=1000) Rate = 7.59%, likely BB bond, yes it's junk.
Anle Corporation has a current stock price of $16.05 and is expected to pay a dividend of $1.15 in one year. Its expected stock price right after paying that dividend is $18.21. a. What is Anle's equity cost of capital? b. How much of Anle's equity cost of capital is expected to be satisfied by dividend yield and how much by capital gain?
a. find expected return (equity cost of capital) rE = ((Div1 + P1) / P0) - 1 rE = ((1.15 + 18.21) / 16.05) - 1 rE = 0.206231 rE = 20.62% b. dividend yield = Div1 / P0 = 1.15 / 16.05 = 0.071651 = 7.17% capital gain rate = (P1 - P0) / P0 = (18.21 - 16.05) / 16.05 = 0.134579 = 13.46%
Dorpac Corporation has a dividend yield of 1.8%. Its equity cost of capital is 7.8%, and its dividends are expected to grow at a constant rate. a. What is the expected growth rate of Dorpac's dividends? b. What is the expected growth rate of Dorpac's share price?
a. g = rE - (Div1 / P0) g = rE - dividend yield g = 7.8 - 1.8 = 6.0% b. With constant dividend growth, Dorpac's share price is expected to grow at rate g = 6.0%.
Which of the following statements regarding bonds and their terms is FALSE? a. Time remaining until repayment date is the term of the bond. b. Annual coupon's determined by the coupon rate and the face value. c. By convention, coupon rate's expressed as an effective annual rate. d. Bonds are securities sold by governments and corporations to raise money from investors today in exchange for a promised future payment. e. Bonds typically make two types of payments to their holders.
a. true b. true c. false d. true e. true Answer: By convention, coupon rate's expressed as an effective annual rate.