FIN 301 Exam 2

Annual Percentage Rate APR

• Annual rate that is quoted by law • By definition = Period rate * periods per year (Period rate = APR / periods per year)

Municipal Bonds.

• Debt of state and local governments • Varying degrees of default risk, related similar to corporate debt • Interest received in tax-exempt at the federal level

• Constant Dividend: (zero growth)

• Firm will pay a constant dividend forever • Is like preferred stock • The price is computed using the perpetuity formula

Suppose you are offered an investment that will allow you to double your money in 6 years. You have $10,000 to invest. What is the implied rate of interest?

.122462 = 12.25%

What is the APR if the semiannual rate is .5%?

.5(2) = 1%

Suppose you need $10,000 in one year for the down payment on a new car. If you can earn 7% annually, how much do you need to invest today?

1 N 7 I/Y 10,000 FV CPT PV = -9,345.7

You ran a little short on your spring break vacation, so you put $1,000 on your credit card.•You can afford only the minimum payment of $20 per month. •The interest rate on the credit card is 1.5 percent per month. •How long will you need to pay off the $1,000?

1.5 I/Y 1,000 PV -20 PMT CPT N = 93.111 months = 7.75 years

Suppose you had a relative deposit $10 at 5.5% interest 200 years ago. How much would the investment be worth today? Simple Interest

10 + 200(10)(.055) = 120.00

APR? Semiannually EAR=11.5 Monthly EAR=12.4 Weekly EAR 10.1

11.19 11.75 9.63 12.93 EAR = 0.1150 = [1 + (APR / 2)]2 − 1 APR = 2[(1.1150)1/2 − 1] = 0.1119, or 11.19% NOM 11.19 EFF 11.5 C/Y 2

Suppose you want to buy a new computer system and the store is willing to allow you to make monthly payments. The entire computer system costs $3,500. •The loan period is for 2 years, and the interest rate is 16.9% with monthly compounding. •What is your monthly payment?

2(12) = 24 N; 16.9 / 12 = 1.408333333 I/Y; 3,500 PV; CPT PMT = -172.88

Suppose you want to buy a new computer system and the store is willing to allow you to make monthly payments. The entire computer system costs $3,500. •The loan period is for 2 years, and the interest rate is 16.9% with monthly compounding. •What is your monthly payment?

2(12) = 24 N; 16.9 / 12 = 1.408333333 I/Y; 3,500 PV; CPT PMT = -172.88

Annuity Due You are saving for a new house and you put $10,000 per year in an account paying 8%. The first payment is made today. •How much will you have at the end of 3 years?

2nd BGN 2nd Set (you should see BGN in the display) 3 N -10,000 PMT 8 I/Y CPT FV = 35,061.12 2nd BGN 2nd Set (be sure to change it back to an ordinary annuity)

You need $15,000 in 3 years for a new car. •If you can deposit money into an account that pays an APR of 5.5% based on daily compounding, how much would you need to deposit?

3(365) = 1,095 N 5.5 / 365 = .015068493 I/Y 15,000 FV CPT PV = -12,718.56

You want to purchase a new car, and you are willing to pay $20,000. •If you can invest at 10% per year and you currently have $15,000, how long will it be before you have enough money to pay cash for the car?

3.02 years

Suppose you win the Publishers Clearinghouse $10 million sweepstakes. The money is paid in equal annual end-of-year installments of $333,333.33 over 30 years. If the appropriate discount rate is 5%, how much is the sweepstakes actually worth today?

30 N; 5 I/Y; 333,333.33 PMT; CPT PV = 5,124,150.29

Suppose you deposit $50 a month into an account that has an APR of 9%, based on monthly compounding. •How much will you have in the account in 35 years?

35(12) = 420 N 9 / 12 = .75 I/Y 50 PMT CPT FV = 147,089.22

Suppose you want to borrow $20,000 for a new car. •You can borrow at 8% per year, compounded monthly (8/12 = .66667% per month). •If you take a 4-year loan, what is your monthly payment?

4(12) = 48 N; 20,000 PV; .66667 I/Y; CPT PMT = 488.26

Suppose you borrow $2,000 at 5%, and you are going to make annual payments of $734.42. •How long before you pay off the loan?

5 I/Y 2,000 PV -734.42 PMT CPT N = 3 years

What is the APR if the monthly rate is .5%?

5(12) = 6%

Suppose you borrow $10,000 from your parents to buy a car. •You agree to pay $207.58 per month for 60 months. •What is the monthly interest rate?

60 N 10,000 PV -207.58 PMT CPT I/Y = .75%

Annuity Due:

A repeating payment that is made at the beginning of each period. • All payments are in the same amount • All payments are made at the same intervals of time (Ex: once a quarter or year)

Suppose you want to earn an effective rate of 12% and you are looking at an account that compounds on a monthly basis. What APR must they pay?

APR = 12[(1+.12)^1/12 - 1] =11.39%

You are offered the opportunity to put some money away for retirement. •You will receive five annual payments of $25,000 each beginning in 40 years. •How much would you be willing to invest today if you desire an interest rate of 12%?

CF; CF0 = 0; C01 = 0; F01 = 39; C02 = 25,000; F02 = 5; NPV; I = 12; CPT NPV = 1,084.71

Is the yield to maturity on a bond the same thing as the required return? Is YTM the same thing as the coupon rate? Suppose today a 10 percent coupon bond sells at par. Two years from now, the required return on the same bond is 8 percent. What is the coupon/YTM rate on the bond?

Computers 10% YTM 8%

You are planning to make annual deposits of $4,800 into a retirement account that pays 10 percent interest compounded monthly. How large will your account balance be in 30 years?

EAR = [1 + (0.10/12)]12 − 1 = 0.1047, or 10.47% NOM=10 C/Y=12 EFF=10.47 I/Y 10.47 FV 863497.93 PMT 4800 N 30

Suppose you invest the $1,000 from the previous example for 5 years. How much would you have with simple interest?

FV = 1,000(.05)+1,000(.05)+1,000(.05)+1,000(.05)+1,000(.05)+1000 = 1,250.00

Suppose you invest the $1,000 from the previous example for 5 years How much would you have with compound interest?

FV = 1,000(1.05)5 = 1,276.28

Suppose you had a relative deposit $10 at 5.5% interest 200 years ago. How much would the investment be worth today?

FV = 10(1.055)200 = 447,189.84

You are looking at two savings accounts. One pays 5.25%, with daily compounding. The other pays 5.3% with semiannual compounding. Which account should you use?

First account:•EAR = (1 + .0525/365)365 - 1 = 5.39% Second account:•EAR = (1 + .053/2)2 - 1 = 5.37%

Suppose you want to buy a new house.•You currently have $15,000, and you figure you need to have a 10% down payment plus an additional 5% of the loan amount for closing costs. •Assume the type of house you want will cost about $150,000 and you can earn 7.5% per year. •How long will it be before you have enough money for the down payment and closing costs?

How much do you need to have in the future? Down payment = .1(150,000) = 15,000 Closing costs = .05(150,000 - 15,000) = 6,750 Total needed = 15,000 + 6,750 = 21,750 PV = -15,000, FV = 21,750, I/Y = 7.5, CPT N = 5.14 years

Although appealing to more refined tastes, art as a collectible has not always performed so profitably. During 2003, Sotheby's sold the Edgar Degas bronze sculpture Petite Danseuse de Quatorze Ans at auction for a price of $10,311,500. Unfortunately for the previous owner, he had purchased it in 1999 at a price of $12,377,500. What was his annual rate of return on this sculpture?

I/Y -4.46 PV 12377500 FV 10311500 N=4

You're trying to save to buy a new $245,000 Ferrari. You have $50,000 today that can be invested at your bank. The bank pays 4.3 percent annual interest on its accounts. How long will it be before you have enough to buy the car?

I/Y 4.3 PV 50000 FV 245000 N=37.75

At 6.1 percent interest, how long does it take to double your money?

I/Y 6.1 PV 1 FV 2 N=11.71

At 6.1 percent interest, how long does it take to quadruple it?

I/Y 6.1 PV 1 FV 4 N=23.41

You want to have $75,000 in your savings account 12 years from now, and you're prepared to make equal annual deposits into the account at the end of each year. If the account pays 6.8 percent interest, what amount must you deposit each year?

I/Y 6.8 FV 75000 PMT 4242.25 N 12

You are scheduled to receive $20,000 in two years. When you receive it, you will invest it for six more years at 6.8 percent per year. How much will you have in eight years?

I/Y 6.8 PV 20000 FV 29679.56 N=6

You have just received notification that you have won the $2 million first prize in the Centennial Lottery. However, the prize will be awarded on your 100th birthday (assuming you're around to collect), 80 years from now. What is the present value of your windfall if the appropriate discount rate is 8.4 percent?

I/Y 8.4 PV 3152.73 FV 2000000 N=80

The Relationship between a Bond's Par Value and Market Price with respect to the Yield to Maturity and Coupon Rate.

If YTM = Coupon Rate, Par Value = Bond Price If YTM > Coupon Rate, Par Value > Bond Price (Discount bond) If YTM < Coupon Rate, Par Value < Bond Price (Premium bond)

After successfully completing your corporate finance class, you feel the next challenge ahead is to serve on the board of directors of Schenkel Enterprises. Unfortunately, you will be the only person voting for you. If the company has 650,000 shares outstanding, and the stock currently sells for $43, how much will it cost you to buy a seat if the company uses straight voting? (

If the company uses straight voting, you will need to own one-half of the shares, plus one share, in order to guarantee enough votes to win the election. So, the number of shares needed to guarantee election under straight voting will be: Shares needed = (650,000 shares/2) + 1 Shares needed = 325,001 And the total cost to you will be the shares needed times the price per share, or: Total cost = 325,001 × $43 Total cost = $13,975,043

You find a zero coupon bond with a par value of $10,000 and 17 years to maturity. If the yield to maturity on this bond is 4.2 percent, what is the price of the bond? Assume semiannual compounding periods.

N 17*2 I/Y 4.2%/2 FV 10000 PV 4933.16

Even though most corporate bonds in the United States make coupon payments semiannually, bonds issued elsewhere often have annual coupon payments. Suppose a German company issues a bond with a par value of €1,000, 23 years to maturity, and a coupon rate of 3.8 percent paid annually. If the yield to maturity is 4.7 percent, what is the current price of the bond?

N 23 I/Y 4.7 PMT 38 FV 1000 PV 875.09

This question illustrates what is known as discount interest. Imagine you are discussing a loan with a somewhat unscrupulous lender. You want to borrow $25,000 for one year. The interest rate is 13 percent. You and the lender agree that the interest on the loan will be .13 × $25,000 = $3,250. So the lender deducts this interest amount from the loan up front and gives you $21,750. In this case, we say that the discount is $3,250. What is the effective interest rate?

N 1 I/Y 14.94 PV 21750 FV 25000

Yan Yan Corp. has a $2,000 par value bond outstanding with a coupon rate of 4.4 percent paid semiannually and 13 years to maturity. The yield to maturity of the bond is 4.8 percent. What is the price of the bond?

N 13*2 I/Y 4.8%/2 PV 1923.29 FV 2000 PMT -44

A Japanese company has a bond outstanding that sells for 105.43 percent of its ¥100,000 par value. The bond has a coupon rate of 3.4 percent paid annually and matures in 16 years. What is the yield to maturity of this bond?

N 16 I/Y 2.97 FV 100000 PV 105430 PMT 3400

Weismann Co. issued 15-year bonds a year ago at a coupon rate of 4.9 percent. The bonds make semiannual payments and have a par value of $1,000. If the YTM on these bonds is 4.5 percent, what is the current bond price?

N 28 I/Y 4.5%/2 PMT 49/2 FV 1000 PV 1041.22

McConnell Corporation has bonds on the market with 14.5 years to maturity, a YTM of 5.3 percent, a par value of $1,000, and a current price of $1,045. The bonds make semiannual payments. What must the coupon rate be on these bonds?

N 29 I/Y 5.3%/2 PV -1045 FV 1000 PMT 28.74

West Corp. issued 25-year bonds two years ago at a coupon rate of 5.3 percent. The bonds make semiannual payments. If these bonds currently sell for 105 percent of par value, what is the YTM?

N 46 I/Y 2.467 PMT 53/2 FV 1000 PV 1050

Suppose you are going to receive $13,500 per year for five years. The appropriate interest rate is 8.4 percent. What is the present value of the payments if they are in the form of an ordinary annuity

N 5 I/Y 8.4 PV 53338.08 PMT -13500

Suppose you are going to receive $13,500 per year for five years. The appropriate interest rate is 8.4 percent. What is the present value if the payments are an annuity due?

N 5 I/Y 8.4 PV 57818.47 PMT -13500

You want to buy a new sports car from Muscle Motors for $78,000. The contract is in the form of a 60-month annuity due at a 7.25 percent APR. What will your monthly payment be?

N 60 I/Y 7.25%/12 PV 78000 PMT 1544.98

A 15-year annuity pays $1,750 per month, and payments are made at the end of each month. If the interest rate is 10 percent compounded monthly for the first seven years, and 6 percent compounded monthly thereafter, what is the present value of the annuity?

N 84, I/Y 10%/12, PMT 1750, PV 105,414.17 N 96, I/Y 6%/12, PMT 1750, PV 133166.96 N 84, I/Y 10%/12, PV 66320.68, FV 133166.63 105,414.17 + 66320.68 = 171734.85

Gabriele Enterprises has bonds on the market making annual payments, with eight years to maturity, a par value of $1,000, and selling for $948. At this price, the bonds yield 5.1 percent. What must the coupon rate be on the bonds?

N 9 I/Y 5.1 PV 948 FV 1000 PMT 42.92

Consider a bond with a 10% annual coupon rate, 15 years to maturity, and a par value of $1,000. The current price is $928.09. Will the yield be more or less than 10%?

N = 15; PV = -928.09; FV = 1,000; PMT = 100 CPT I/Y = 11%

You are considering an investment that will pay you $1,000 in one year, $2,000 in two years, and $3,000 in three years. •If you want to earn 10% on your money, how much would you be willing to pay?

N = 1; I/Y = 10; FV = 1,000; CPT PV = -909.09 N = 2; I/Y = 10; FV = 2,000; CPT PV = -1,652.89 N = 3; I/Y = 10; FV = 3,000; CPT PV = -2,253.94 PV = 909.09 + 1,652.89 + 2,253.94 = 4,815.93

Suppose you are reviewing a bond that has a 10% annual coupon and a face value of $1000. There are 20 years to maturity, and the yield to maturity is 8%. What is the price of this bond?

N = 20; I/Y = 8; PMT = 100; FV = 1,000 CPT PV = -1,196.36

Suppose a bond with a 10% coupon rate and semiannual coupons, has a face value of $1,000, 20 years to maturity and is selling for $1,197.93. Is the YTM more or less than 10%? What is the semiannual coupon payment? How many periods are there?

N = 40; PV = -1,197.93; PMT = 50; FV = 1,000; CPT I/Y = 4% (Is this the YTM?) YTM = 4% × 2 = 8%

You are looking at an investment that will pay $1,200 in 5 years if you invest $1,000 today. What is the implied rate of interest?

N = 5 PV = -1,000 (you pay 1,000 today) FV = 1,200 (you receive 1,200 in 5 years) CPT I/Y = 3.714%

The Perfect Rose Co. has earnings of $3.18 per share. The benchmark PE for the company is 18. a. What stock price would you consider appropriate? b. What if the benchmark PE were 21?

P = 18($3.18) P = $57.24 P = 21($3.18) P = $66.78

Burnett Corp. pays a constant $8.25 dividend on its stock. The company will maintain this dividend for the next 13 years and will then cease paying dividends forever. If the required return on this stock is 11.2 percent, what is the current share price?

P0 = $8.25(PVIFA11.2%,13) P0 = $55.13

•Suppose TB Pirates, Inc., is expected to pay a $2 dividend in one year. •If the dividend is expected to grow at 5% per year and the required return is 20%, what is the price?

P0 = 2 / (.2 - .05) = $13.33

Gordon Growth Company is expected to pay a dividend of $4 next period, and dividends are expected to grow at 6% per year. The required return is 16%.

P0 = 4 / (.16 - .06) = $40

Antiques R Us is a mature manufacturing firm. The company just paid a dividend of $9.80, but management expects to reduce the payout by 4 percent per year indefinitely. If you require a return of 9.5 percent on this stock, what will you pay for a share today?

P0 = D0(1 + g)/(R − g) P0 = $9.80(1 - .04)/[(.095 - (-.04)] P0 = $69.69

Suppose Big D, Inc., just paid a dividend of $0.50 per share. •It is expected to increase its dividend by 2% per year. •If the market requires a return of 15% on assets of this risk, how much should the stock be selling for?

P0= .50(1+.02) / (.15 - .02) = $3.92

You want to begin saving for your daughter's college education and you estimate that she will need $150,000 in 17 years. If you feel confident that you can earn 8% per year, how much do you need to invest today?

PV = 150,000 / (1.08)17 = 40,540.34

Your parents set up a trust fund for you 10 years ago that is now worth $19,671.51. If the fund earned 7% per year, how much did your parents invest?

PV = 19,671.51 / (1.07)10 = 10,000

The Maybe Pay Life Insurance Co. is trying to sell you an investment policy that will pay you and your heirs $30,000 per year forever. If the required return on this investment is 5.8 percent, how much will you pay for the policy?

PV = C / r PV = $30,000 / 0.058 = $517,241.38

Par Value Coupon Coupon Rate Yield to Maturity

Par/Face Value: principal amount, repaid at maturity Coupon: Stated interest rate Coupon Rate: annual coupon divided by face value Yield to Maturity: rate of return required in the market for the bond

Suppose you buy a 7 percent coupon, 20-year bond today when it's first issued. If interest rates suddenly rise to 15 percent, what happens to the value of your bond?

Price will fall

Red, Inc., Yellow Corp., and Blue Company each will pay a dividend of $3.65 next year. The growth rate in dividends for all three companies is 4 percent. The required return for each company's stock is 8 percent, 11 percent, and 14 percent, respectively. What is the stock price for each company?

Red stock price = $3.65/(.08 - .04) = $91.25 Yellow stock price = $3.65/(.11 - .04) = $52.14 Blue stock price = $3.65/(.14 - .04) = $36.50

Effective Annual Rate

The actual rate paid (or received) after accounting for compounding that occurs during the year When comparing, need to use EAR

• Constant Dividend Growth

The firm will increase the dividend by a constant percent every period The price is computed using the growing perpetuity model

You think you will be able to deposit $4,000 at the end of each of the next three years in a bank account paying 8 percent interest. •You currently have $7,000 in the account. •How much will you have in three years? •How much will you have in four years?

Today's (year 0) CF: 3 N; 8 I/Y; -7,000 PV; CPT FV = 8817.98 Year 1 CF: 2 N; 8 I/Y; -4,000 PV; CPT FV = 4,665.60 Year 2 CF: 1 N; 8 I/Y; -4,000 PV; CPT FV = 4,320 Year 3 CF: value = 4,000 Total value in 3 years = 8,817.98 + 4,665.60 + 4,320 + 4,000 = 21,803.58 Value at year 4: 1 N; 8 I/Y; -21,803.58 PV; CPT FV = 23,547.87

Understand the characteristics associated with U.S Government Bonds in terms of risk.

Treasury Securities • Federal Government Debt • T-bills: pure discount bonds with original maturity of one year or less • T-Notes: coupon debt with original maturity between one and ten years • T-Bonds: coupon debt with original maturity greater than ten years

Investment X offers to pay you $5,200 per year for eight years, whereas Investment Y offers to pay you $7,300 per year for five years. Calculate the present value for Investment X and Y if the discount rate is 5 percent.

X= 33608.71 Y= 31605.18

Calculate the present value for Investment X and Y if the discount rate is 15 percent.

X=23334.07 Y=24470.73

Suppose you invest $500 in a mutual fund today and $600 in one year. •If the fund pays 9% annually, how much will you have in two years?

Year 0 CF: 2 N; -500 PV; 9 I/Y; CPT FV = 594.05 Year 1 CF: 1 N; -600 PV; 9 I/Y; CPT FV = 654.00 Total FV = 594.05 + 654.00 = 1,248.05

Compounding Interest:

results in earning interest on interest

Simple Interest:

results in earning interest only on the original present value amount

Ordinary Annuity

series of equal payments made at the end of consecutive periods over a fixed length of time. While the payments in an annuity can be made as frequently as every week.

Present Value:

the current value of a future sum of money or stream of cash flows given a specified rate of return

Future Value:

the value of a current asset at a specified date in the future based on an assumed rate of growth