FINN FINAL FINAL

Rate of Return Formula

coupon income + (new price-old price) /old price

The First Commerce Bank offers a Certificate of Deposit (CD) that pays you $5,000 in five years. The CD can be purchased today for $3,200. Assuming you hold the CD to maturity, what annual interest rate is the bank paying on this CD?

i= 9.34

E. If interest rates change, do the prices of high coupon bonds change proportionately more than that of low coupon bonds? (wait to work on this question until we cover duration)

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If the bond yield to maturity is greater than the coupon, is the price of the bond greater or less than 100?

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If the price of a bond exceeds 100, is the yield to maturity greater or less than the coupon?

less

After completing a long and successful career as senior vice president for a large bank, you are preparing for retirement. Visiting the human resource office, you find that you have several retirement options: (1) you can receive an immediate cash payment of $950,000 (2) you can receive $80,000 per year for life (you have a life expectancy of 25 years), or (3) you can receive $70,000 per year for 12 years and then $90,000 per year for life (this option is intended to give you some protection against inflation). You have determined that you can earn 5 percent on your investment. Which option do you prefer and why?

1) PV=950,000 2) N=25 i=5 PMT=-80,000 FV=0 PV=1,127,515.57 3) Reset Cash Flow registers before each exercise: [CF] [2nd] [CE/C] To input cash flows to the calculator: [CF] [2nd] [CE/C] 0 [ENTER] [ down key ] 70,000 [ENTER] [ down key ] 12 [ENTER] [ down key ] 90,000 [ENTER] [ down key ] 13 [ENTER] [ down key ] [ENTER] [ down key ] To compute NPV at 5% discount rates: [NPV] 5 [ENTER] [ down key ] [CPT] answer = $1,091,189.98 Choose option 2.

An 8%, five year bond yields 6%. If this yield to maturity remains unchanged, what will be its price one year hence? Assume annual coupon payments and face value of $100. What is the total return to an investor who held the bond over this year?

1. N=4 i=6 FV=100 PMT=8 PV=(-)106.93 2. N=5 i=6 FV=100 PMT=8 PV=(-)108.42, Return 1= (8 + 106.93 - 108.42) / 108.42 = 6%

Right now Aaa bonds yield 3.4% and Baa bonds yield 4.4%. If some bad news causes a 10% five year bond to be unexpectedly downrated from Aaa to Baa, what would be the change in the bond price? (Assume annual coupons).

1. N=5 i=3.4 FV=1000 PMT=100 PV=(-)1,298.84, 2. N=5 i=4.4 FV=1000 PMT=100 PV=(-)1,246.53, Return 1= (1246.53 - 1298.84) / 1298.84 = - 4.03%

The interest rate is 10%: What's the PV of an asset that pays $1 a year in perpetuity? What is the approximate PV of an asset that pays $1 for each of the next seven years? A piece of land produces an income that grows by 5% per annum. If the first year's income is $10,000, what is the value of the land?

1. PV = 1 / 10% = 10 2. N=7 i=10 FV=0 PMT=1 PV=(-)4.86, 3. PV = CF / (r-g) = 10,000 / (10%-5%) = 200,000

If you invest in a security that pays 11% interest annually and inflation is 5%, what is your real interest rate?

1.11/1.05=.0571

Project A is expected to produce CF = $150 mil for each of five years. It is purely equity financed. Given a risk free rate of 5%, a market premium of 7%, and beta of 1.5, what is the PV of the project?

= 5 + 1.5(7) = 15.5% N=5 i=15.5 PMT=-150 FV=0 PV = 496.93

Company Y does not plow back any earnings and is expected to produce a level dividend stream of $5 a share. If the current stock price is $40, what is the market capitalization rate?

= Div1/P0 = 5/40 = 12.5%

If the rate of interest is 8%, how much would you need to set aside to provide each of the following? A. $1 billion at the end of each year in perpetuity. B. A perpetuity that pays $1 billion at the end of the first year and that grows at 4% a year. C. $1 billion at the end of each year for 20 years. D. $1 billion spread evenly over 20 years.

A. 1 / 8% = $12.5 billion B. 1 / (8%-4%) = $25 billion C. C0=0, C01=1, F01=20, i=8, NPV= 9.82 billion D. C0=0, C01=50 million, F01=20, i=8, NPV= 490.91 million

Suppose you deposit $1,000 today in a bank account that pays 12% interest per year. How much do you have after 10 years?

FV= 3,105.85

Suppose you save $2,500 per year for 25 years, beginning one year from today. The savings bank pays you 7% interest per year. How much will you have at the end of 25 years?

FV=158,122.59

If today is October 1, 2015, what is the value of the following bond? An IBM Bond pays $55 every September 30 for 10 years. In September 20205 it pays an additional $1000 and retires the bond. The bond is rated AAA (WSJ AAA YTM is 3.5%)

N=10 i=3.5 FV=1000 PMT=55 PV=(-)1,166.33,

A 10-year German government bond (bund) has a face value of 100 euros and a coupon rate of 5% paid annually. Assume that the interest rate in euros is 6% a year. What is the bond's PV?

N=10 i=6 FV=100 PMT=5 PV=(-)92.64,

You are a financial adviser working with a client who wants to retire in 10 years. The client has a savings account with a local bank that pays 8 percent and she wants to deposit an amount that will provide her with $1,000,000 when she retires. Currently, she has $180,000 in the account. How much additional money should she deposit now?

N=10 i=8 PMT=0 FV=-1,000,000 PV=463,193.49; deposit = 463,193.49 - 180,000 = 283,193.49

SB is 65 years of age and has a life expectancy of 12 more years. He wishes to invest $20,000 in an annuity that will make a level payment at the end of each year until his death. If the interest rate is 8%, what income can SB expect to receive each year?

N=12 i=8 PV=-20,000 FV=0 PMT=(-)2,653.90,

A 10-year semiannual payment US T-bond with face value of $1,000 pays a coupon of 5.5% (2.75% of face value every six months). The reported yield to maturity is 5.2% (a sixmonth discount rate of 5.2/2=2.6%)

N=20 i=2.6 FV=1000 PMT=27.5 PV=(-)1023.16

What is the price of a 5.25% annual coupon bond, with a $1,000 face value, which matures in 5 years? Assume a required return of 0.55%.

N=5 i=0.55 FV=1000 PMT=52.5 PV=(-)1,231.17

David and Helen Zhang are saving to buy a boat at the end of five years. If the boat costs $20,000 and they can earn 10% a year on their savings, how much do they need to put aside at the end of years 1 through 5.

N=5 i=10 FV=-20,000 PV=0 PMT=(-)3,275.95,

In October 2012 you purchase bonds of 1000 euros of face value in Italy which pay a 5.25% coupon every year. If the bond matures in 2018 and the YTM is 1%, what is the value of the bond?

N=6 i=1 FV=1000 PMT=52.5 PV=(-)1,246.31

Suppose your salary was going to grow 12% per year. How long would it take to double your salary?

N=6.12

Judge Tafari has decided to set up an educational fund for his favorite granddaughter, Baako, who will start college in three years. The judge plans to deposit an amount in a saving account that pays 10 percent interest. He wants to deposit an amount that is sufficient to permit Baako to withdraw $30,000 starting in three year and continuing each year for a total of four years. How much should he deposit today to provide Baako with a fund to pay for her college tuition?

N=7 i=10 PMT=30,000 FV=0 PV=146,052.56 N=3 i=10 PMT=30,000 FV=0 PV=74,605.56

An annuity's first cash flow is expected to occur 3 years from today. There are 5 cash flows in this annuity, with each cash flow being $1,000. At an interest rate of 12% per year, find the annuity's present value.

N=7 i=12 PMT=-1,000 FV=0 PV=4,563.76 N=3 i=12 PMT=-1,000 FV=0 PV=2,401.83 o PV of the deferred annuity = PV of 7 year ordinary annuity - PV of 3 year ordinary annuity = 2,161.93. o But you can also use the multiple uneven cash flow approach to get the PV, especially if we do not have a deferred annuity, but just deferred multiple uneven cash flows.

If you invest $100 at an interest rate of 15%, how much will you have at the end of eight years?

N=8 i=15 PV=-100 PMT=0 FV=305.90

If the cost of capital is 9%, what is the PV of $374 paid in year 9?

N=9 i=9 FV=374 PMT=0 PV=(-)172.20

An investment costs $1,548 and pays $138 in perpetuity. If the interest rate is 9%, what's the NPV?

NPV = -1,548 + 138 / 9% = -14.67

Company Z's earnings and dividends per share will grow indefinitely by 5% a year. If next year's dividend is $10 and the market capitalization rate is 8%, what is the current stock price?

P0 = Div1 /(r-g) = 10/(8%-5%) = 333.33

You wish to retire 35 years from today with $3,000,000 in the bank. If the bank pays 9% interest per year, how much should you save each year to reach your goal?

PMT=13,907.51

Rob borrows $20,000 to be repaid in 5 equal annual installments, beginning one year from today. What is Rob's annual payment on this loan if the bank charges him 12% interest per year?

PMT=5548.19

Current forecasts are for XYZ Company to pay dividends of $3, $3.24, and $3.50 over the next three years, respectively. At the end of three years you anticipate selling your stock at a market price of $94.48. What is the price of the stock given a 12% expected return?

PV = 3.00 (1 + .12)1 + 3.24 (1 + .12)2 + 3.50 + 94.48 (1 + .12)3 = $75.00

Fledgling Electronics is forecasted to pay a $5.00 dividend at the end of year one and a $5.50 dividend at the end of year two. At the end of the second year the stock will be sold for $121. If the discount rate is 15%, what is the price of the stock?

PV = 6.00 (1 + .12)1 + 6.50 + 116 (1 + .12)2 = $103.01

What is the present value of $10,000 paid at the end of every year in perpetuity, assuming a rate of return of 10% and a constant growth rate of 5%?

PV = CF / (r - g) = 10,000 / (0.1 - 0.05) = 200,000

A common stock will pay a cash dividend of $4 next year. After that, the dividends are expected to increase indefinitely at 4% a year. If the discount rate is 14%, what is the PV of the stream of dividend payments?

PV = CF / (r - g) = 4 / (14% - 4%) = 40

What is the present value of perpetuity of $3000 per year if the interest rate is 10% per year?

PV = CF / r = 3,000 / 0.1 = 30,000

Cindy agrees to repay a loan in 12 annual installments of $20,000 each. If the interest rate on the loan is 7.5% per year, what is the present value of the loan payments? Should Cindy accept a loan of $150,000?

PV=154,705.57

You expect to receive $10,000 8 years from today. If the required return is 10% per year, what is the money worth today

PV=4,665.07

The interest rate (r) is 9% per period. Consider the NPV of the following cash flows: Time Notation Cash Flow 0 CF0 - $ 3,000 1 CF1 + $ 1,500 2 CF2 + $ 1,500 3 CF3 + $ 2,500

. PV = 1,569.13

After hearing a knock at your front door, you are surprised to see Prize Patrol from a large, well known magazine subscription company. It has arrived with good news that you are the big winner, having won $15 million. You discover that you have three options: (1) you can receive $2 million per year for the next 10 years (2) you can have $12 million today (3) you can have $3 million today and receive $1.2 million for each of the next 10 years. Your lawyer tells you that it is reasonable to expect to earn 10 percent on investments. Which option do you prefer? What factors influence your decision?

#1 1) N=10 i=10 PMT=-2 FV=0 PV=12.29 2) PV=12 3) N=10 i=10 PMT=-1.2 FV=0 PV=7.37; total PV = 3 + 7.37 = 10.37 Choose option 1)

Company X is expected to pay an end-of-year dividend of $5 a share. After paying the dividend, its stock is expected to sell at $110. If the market capitalization rate is 8%, what is the current stock price?

(Div1+P1) /(1+r) = (5+110)/(1+8%) = 106.48

What's the PV of $100 received in: A. year 10 (at a discount rate of 1%)? B. year 10 (at a discount rate of 13%)? C. year 15 (at a discount rate of 25%)? D. Each of years 1 through 3 (at a discount rate of 12%)?

A. N=10 i=1 FV=100 PMT=0 PV=(-)90.53, B. N=10 i=13 FV=100 PMT=0 PV=(-)29.46, C. N=15 i=25 FV=100 PMT=0 PV=(-)3.52, D. N=3 i=12 FV=0 PMT=100 PV=(-)240.18,

A. The cost of a new car is $10,000. if the interest rate is 5%, how much would you have to set aside now to provide this sum in five years? B. You have to pay $12,000 a year in school fees at the end of each of the next six years. If the interest rate is 8%, how much do you need to set aside today to cover these bills? C. You have invested $60,476 at 8%. After paying the above school fees how much would remain at the end of the six years?

A. N=5 i=5 FV=10,000 PMT=0 PV=(-)7835.26, B. N=6 i=8 FV=0 PMT=12,000 PV=(-)55,474.56, C. PV of money left = 60,476-55,474.56 = 5,001.44 N=6 i=8 PV= 5,001.44 PMT=0 FV=(-)7,936.66,

As winner of a breakfast cereal competition, you can choose one of the following prizes: A. $100,000 now. B. $180,000 at the end of five years. C. $11,400 a year forever. D. $19,000 for each of the 10 years. E. $6,500 next year and increasing thereafter by 5% a year forever. If the interest rate is 12%, which is the most valuable prize?

A. PV = 100,000; B. N=5 i=12 FV=180,000 PMT=0 PV=(-)102,136.83, C. PV = CF / r = 11,400 / 12% = 95,000 D. N=10 i=12 FV=0 PMT=19,000 PV=(-)107,354.24, E. PV = CF / (r-g) = 6,500 / (12%-5%) = 92857.14 Choose D as it is the most valuable

Assume the risk-free interest rate is 7% and the market return is 12%. If the beta of a stock is 1.4, according to CAPM, what is the required rate of return on the stock?

According to CAPM, the required stock return is 7 + (12 - 7) x 1.4 = 14%.

Northwest Natural Gas stock was selling for $48 per share at the start of 2015. Dividend payments for the next year were expected to be $2.00 a share. What is the expected return on equity, assuming a growth rate of 8%?

Expected return = 𝑟𝑟 = 2.00 /48 + .08 = 12.18%

A factory costs $800,000. You reckon that it will produce an inflow after operating costs of $170,000 a year for 10 years. If the opportunity cost of capital is 14%, what is the NPV of the factory?

C0 = -800,000, C1 = 170,000, F1 = 10, i=14, NPV = 86,739.66

A project produces a cash flow of $432 in year 1, $137 in year 2, and 797 in year 3. if the cost of capital is 15%, what is the project's PV? If the project requires an initial investment of $1200, what is its NPV?

C0=0, C01=432, F01=1, C02=137, F02=1, C03=797, F03=1, i=15, NPV= 1,003.28; NPV above is the PV of the future CFs. NPV = -1,200 + 1,003.28 =-196.72

A machine costs $380,000 and is expected to produce the following cash flows Year 1 2 3 4 5 6 7 8 9 10 CF ($000) 50 57 75 80 85 92 92 80 68 50 If the cost of capital is 12%, what is the machine's NPV?

C0=380, C01=50, F01=1, C02=57, F02=1, C03=75, F03=1, C04=80, F04=1, C05=85, F05=1, C06=92, F06=1, C07=92, F07=1, C08=80, F08=1, C09=68, F09=1, C10=50, F10=1, i=12, NPV= $23,696.15

In November 2014 you purchase a 2 year US Government bond with a $1,000 par. The bond has an annual coupon rate of 3%, paid semi-annually. If investors demand a 1% annual return, what is the price of the bond?

Divide both interest rate and cash flow by 2 (semiannual compounding from Ch2) N=4 i=0.5 FV=1000 PMT=15 PV=(-)1,039.50,

Northwest Natural Gas stock was selling for $48 per share at the start of 2015. Dividend payments for the next year were expected to be $2.00 a share. What is the dividend yield, assuming no growth?

Dividend yield = 𝑟 = 2.00 /48 = 4.17%

If Fledgling Electronics is selling for $200 per share today and is expected to sell for $210 one year from now, what is the expected return if the dividend one year from now is forecasted to be $8.00?

Expected return = 8 + 210 − 200/ 200 = 0.09

A bond increases in price from $1065.80 to $1,280.50 and pays a coupon of $21.5 during the same period. What is the rate of return?

Rate of return = (21.5+(1280.50−1065.80) / 1065.80 = .2216 = 22.16%

Consider a 10-year project with the following cash flows: Initial investment: -$5,000. Cash flows in Years 1-6: $900. Cash flows in Year 7-10: $1,000. Cash flow in Year 11: $1,200. Compute the IRR, NPV@10%, and NPV@12%.

answer = $1,129.63 answer = $584.05 IRR: answer = 14.51%

If interest rate rise, do bond prices rise or fall?

fall

Everything else equal, do high coupon bonds sell at higher or lower prices than low coupon bonds?

higher