Managerial Finance Exam #2

Perpetuity

infinite series of equal payments

What is the monthly rate if the APR is 12 % with monthly compounding

(12/12) = 1%

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

.5(12) = 6%

Find the EAR in each of the following cases APR: 9.2% Quarterly 18.2 Monthly 11.2 Infinite

9.52% 19.78% 11.85

Gerritt wants to buy a car that costs $30,250. The interest rate on his loan is 5.61 percent compounded monthly and the loan is for 5 years. What are his monthly payments?

C = $579.35 N = 60 Interest = 5.61/12 PV = -30250 PMT = 579

Coupon < Yield

Discount

Annuity Due

First payment occurs at the beginning of a period

Suppose you win the $10 million sweepstakes. Money is paid in annual installments of $333,333.33 over 30 years. If the discount rate is 5% how much is it actually worth?

PMT: $333,333.33 N : 30 years Interest: 5%

If a T-bill promises to repay $10,000 in 12 months and the market interest rate is 7 percent, how much will the bill sell for in the market

PV = 10000/ 7% Market Value = 9345.79

YTM > Coupon

Trades at discount

YTM < coupon

Trades at premium

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

Present Value : 2000 Interest Rate 5% PMT: $734.42 N : 2.61 = 3 years

Effective Annual Rate

the actual rate paid after the accounting for compounding during the year

3 Types of Interest Rates

- Stated Rate (compounded) - Periodic Rate (TVM "Per" "For") - Effective Rate (Effective)

What is the APR if the semi annual rate is .5%

.5(2) = 1%

Saving for retirement You are offered to put 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 with an desired interest rate of 12%?

0 cfj 0cfj 39 shift/cjf 25000cfj 5 shift/cfj 12 interest NPV: 1,084

Suppose the U.S. Treasury 6.25 41 are priced at 101'16. Suppose also, the bond pays coupons semi-annually. What is the yield on the bond quoted "compounded semi-annually." What does this translate to in EAY? What is the bond's Current Yield? Assume for convenience the bond's maturity date is exactly 20 years from today

101 ' 16 = 101 (16/32) = 101.5 FV = 100 PV = -101.15 N = (20 x 2) = 40 PMT = 6.25 / 2 = 3.125 I/Yr = 3.059 x 2 = 6.118962% Yield Semi = 6.118962% Current Yield = 3.125 + 3.125 / 101.5 = 6.1584% EAY = PV = -1 I = 3.059 N = 2 FV = 1.06212 = 6.212

First National Bank charges 13.8 percent compounded monthly on its business loans. First United Bank charges 14.1 percent compounded semiannually. Calculate the EAR for First National Bank and First United Bank.

13.8/12 = 1.0115 ^ 12 = 1.14 - 1 = 14.7 % 14.1/2 = 1.07^2 = 1.1459 - 1 = 14.597%

Using the Fisher equation (actual not approximate), what is the expected inflation if the nominal rate of return is 7.375% and the real rate of return is 2.5%

4.756% (1.07375/1.025 = 1.04756 -> -1 = .04756 *100 = 4.756%

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 10000PV -207.58 PMT I/Y : .75%

Microhard has issued a bond with the following characteristics: Par: $1,000 Time to maturity: 13 years Coupon rate: 8 percent Semiannual payments Calculate the price of this bond if the YTM is

8% = FV = 1000 PMT = 40 PV = ? N = 26 Interest Rate = 4%

Period Rate =

APR / number of periods per year

Friendly's Quick Loans, Inc., offers you "six for seven or I knock on your door." This means you get $6 today and repay $7 when you get your paycheck in one week (or else). If you were brave enough to ask, what APR would Friendly's say you were paying What's the EAR Friendly's earns on this lending business?

APR = PV = 6 FV =7 N = 1 Interest = 16.67% * 52 = 866.67 APR EAR: PV: -1 I = 25 N = 52 FV = 109,476.44 -> 10947644.25

You earn 3% per quarter What is the APR What is the EAR

APR = 3(4) = 12% PV = 1 Interest = 3% N = 4 FV = 1.12 EAR = 1.12 - 1 = 12.55

You earn 1% per month of $1 invested What is the APR? What is the EAR?

APR: 1(12) = 12% 1 PV 1 Interest N 12 FV = 1.126825 APR = 1.12 - 1 = 12%

Treasury bills are currently paying 7 percent and the inflation rate is 3.4 percent. What is the approximate real rate of interest? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) What is the exact real rate?

Approximate Real Rate = nominal - interest rate 7 - 3.4 = 3.6 Exact Real Rate = (1.07/1.034) - 1 = 3.5%

How much interest will you earn on $100 invested for a year at 12% compounded quarterly?

Cash Flow: $100 Interest=.12/4 = .03 N = 4 1.03^4 - 1 = Interest of 12.55

What is the value today of $100 1 year from now if the appropriate discount rate is 9% compounded monthly?

Cash Flow: $100 N: 12 Interest = .09/12 = .0075 Effective Rate = 1.0075^12 - 1 = .0938 = 1 / 1.0938 discount factor = 91.4

What is the present value of an annuity of $5,500 per year, with the first cash flow received three years from today and the last one received 25 years from today? Use a discount rate of 6 percent

Cf 0 = 0 cf 1 = 0 Nj = 2 cf 2 = 5500 nj 23 interest = 6 npv: 60,000

Hacker Software has 10.6 percent coupon bonds on the market with 17 years to maturity. The bonds make semiannual payments and currently sell for 108.1 percent of par. What is the current yield on the bonds? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) What is the YTM? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) What is the effective annual yield?

Current Yield : Annual Income / Current Price 10.6 / 108.1 x 100 = 9.81% Yield to Maturity = 5.3 + ( 108.1 - 100/34) / 108.1 + 100 / 2 = 4.86% 4.86% x 2 = 9.72% per year EAR= 10.6 / 2 = 5.3 + 1 = 1.053^2 - 1 = 10.88%

•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?

Daily Rate = .055/365 = .00015068 Number of Days = 3 * 365 = 1095 PV = 15000 / 1.00015068^ 1095 = 12718.56

Find the PV of each cash flows and add them. Year 1 CF: 200 Year 2 CF: 400 Year 3 CF: 600 Year 4 CF: 800 Discount Rate is 12%

Entry in Calculator: 0 cfj 200 cfj 400 cfj 600 cfj 800 cfj 12 I/YR NPV: 1,432

IBM 4 31 (meaning 4% coupon rate maturing in the year 2031) yielding 5% compounded semi-annually Price each bond based upon the yield. Assume that the bond matures in the current month, on the current day, in the year of maturity, and has a face value of $100. Re-price the bonds with each yield 0.1% higher than before. What is the dollar change in price? What is the percentage change in price (from the original price

FV: $100 PMT = 2 (4/2) I = 2.5 (5/2) N = 20 (10* 2) PV = 92.21 Interest goes up 1% 5/2 = 2.5 5.1/2 = 2.55 92.21 - 91.47 = -0.74 Percent Change is -.74 / 92.21 = -0.802%

What is the present value of a four year annuity of $100 per year that makes its first payment two years from today at a discount at 9%?

FV: 0 PMT: 100 Interest: 9% N : 4 Present Value: 323.97 PV/ (1.09) = $297.22

Burlington 3 24 yielding 4.8% compounded semi-annually Price each bond based upon the yield. Assume that the bond matures in the current month, on the current day, in the year of maturity, and has a face value of $100. Re-price the bonds with each yield 0.1% higher than before. What is the dollar change in price? What is the percentage change in price (from the original price)?

FV: 100 PMT: 1.5 I = 2.4 4.9/2 = 2.45 N = 6 PV = 95.03 Change in .1% = 95.03 - 94.76 = -.27 % change = 94.76 - 95.03 / 95.03 = -0.282%

GE 10½ 31 yielding 5% compounded semi-annually Price each bond based upon the yield. Assume that the bond matures in the current month, on the current day, in the year of maturity, and has a face value of $100. Re-price the bonds with each yield 0.1% higher than before. What is the dollar change in price? What is the percentage change in price (from the original price)?

FV: 100 PMT: 5.25 N = 20 Interest: 2.5 PV = 142.87 Interest = 2.51 = PV = 141.89 141.89 - 142.97 = $-0.74 change -0.98 / 142.97 = -0.684%

What does discounting mean?

Finding the present value of some future amount

Annuity

Finite series of equal payments that occur at regular intervals

Ordinary Annuity

First payment that occurs at the end of a period

What is Yield to Maturity

It is the required market interest rate on a bond.

Do long term or short term bonds have more price risk?

Long - Term Bonds

Do low or high coupon rate bonds have more price risk?

Low coupon rate bonds

Suppose you want to borrow $20,000 for a new car. You can borrow 8% per year compounded monthly. If you take a 4 year loan, what is your monthly payment?

PV: 20,000 Interest= .667% = .8/12 N = 4 years PMT: $488.26

YTM = Coupon

Par

Annual Percentage Rate

Period rate times the number of periods per year

Coupon > Yield

Premium

A 6-year annuity of twelve $10,200 semiannual payments will begin 11 years from now, with the first payment coming 11.5 years from now. If the discount rate is 8 percent compounded monthly, what is the value of this annuity five years from now?

Monthly rate .08/12 = .0067 Semi annual interest rate = 1.0067^6 -1 = 4.067%

Convert the following: 12.6825% EAY to an annual rate compounded monthly. 10.2500% EAY to an annual rate compounded semi-annually. 16.9859% EAY to an annual rate compounded quarterly.

Monthly: 1.126825 ^ 1/12 = ANS +1 *12 = 12% Semi Annually: 10% Quarterly: 16%

Find the present value (as of January 1, 2009), of a 6 3/8% coupon bond with semi-annual payments, and a maturity date of December 2013 if the YTM is 5%.

N = 10 I/Y = 2.5 PMT = 31.875 (1,000 x .06375 / 2) FV = 1000 PV = 1060.17

Suppose you want to buy a new computer system and the store is willing to sell it to allow you to make monthly payments. The entire computer system costs $3500. The loan period is for 2 years and the interest rate is 16.9% with monthly compounding. What is your monthly payment

N = 14 PV = 3500 Interest = .169/12 = 1.408 PMT = 172.88

Broker calls and tells you that if you invest $100 today you will receive $40 in one year and $75 in two years. If you require a 15% investment, should you take it.

No, you get offered less than $ 100 cfj 0 cfj 40 cfj 75 interest : 15% = $91.75

You are considering purchasing an investment that promises $250 a year for the next 5 years (with the first payment to be made 1 year from now). If the yield on the security on an annual basis is 6%, what would be the maximum you should be willing to pay? What is the future value of the security in question 8, at the end of 5 years?

PMT: 250 N: 5 Interst = 6% PV = 1053.09 1.06^ 5 = Future Value Factor Future Value Factor x PV = End of year 5

RAK Co. wants to issue new 15-year bonds for some much-needed expansion projects. The company currently has 7 percent coupon bonds on the market that sell for $1,060, have a par value of $1,000, make semiannual payments, and mature in 15 years. What coupon rate should the company set on its new bonds if it wants them to sell at par?

PV = -1060 FV = 1000 N = 30 PMT = 35 YTM = 6.37

A Japanese company has a bond outstanding that sells for 94 percent of its ¥100,000 par value. The bond has a coupon rate of 6.1 percent paid annually and matures in 17 years.

PV = 94000 FV = 100000 N = 17 PMT = 6100 I/YR = 6.70%

Suppose you begin saving for your retirement by depositing $2000 per year in an IRA. If the interest rate is 7.5%, how much will you have in 40 years

PV: 0 Interest: 7.5% N : 40 PMT: 2000 FV: 454,513

Bond Value

Present Value of Coupons + Present Value of Face Amount

An investor purchasing a British consol is entitled to receive annual payments from the British government forever. What is the price of a consol that pays $190 annually if the next payment occurs one year from today? The market rate is 5 percent.

Price of consol=annual cash flows/interest rate =(190/0.05) which is equal to =$3800

Assume you have the choice of the following investments: 8.1% compounded semi-annually 8% compounded quarterly 7.9% compounded monthly 8.2% compounded annually 7.9% continuously compounded Based solely on effective annual yield, which is best?

Semi Annually = .081 / 2 = .0405 + 1 = 1.0405 1.0405^2 = 1.0826 - 1 = 8.26% Quarterly= 8.24 Annually = 8.2% Continuously Compounded =

Treasury Securities (3 of them)

Treasury Bills - 1 year or less Treasury Notes - one to 10 years Treasury Bonds - greater than 10 years

Reinvestment Rate Risk

Uncertainty concerning rates at which cash flows can be reinvested Short term bonds have more reinvestment rate risk than long term bonds High coupon rate bonds have more reinvestment risk

Compute the future value of $1,900 continuously compounded for 7 years at an APR of 8 percent. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. Compute the future value of $1,900 continuously compounded for 5 years at an APR of 11 percent. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) c. Compute the future value of $1,900 continuously compounded for 8 years at an APR of 5 percent. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) d. Compute the future value of $1,900 continuously compounded for 5 years at an APR of 7 percent. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

a.) PV * e ^ 8 percent * 7

Net Present Value

present value of expected cash flows - cost of investment