FINC 301 Exam 2 (Ch 5-7)

PV of annuity due

(PV of annuity) x (1 + r)

At a compound annual interest rate of 12%, how long will it take to double your investment?

6 years

The real rate of interest is 5%. and the nominal rate of interest is 11%. According to the Fisher Effect, what is the rate of inflation?

6%

If an investment doubles in 10 years, what is the approximate compound annual rate of interest?

7.2%

What is a "fallen angel"?

A bond which devolves from investment grade to junk status

What is the "yield curve"?

A plot of the interest rates of bonds (which have equal credit quality) against different maturity dates

What is a "covenant"?

A required action placed on the company by the bondholders, in order to protect their interests

Annual Percentage Rate (APR)

APR = (Stated Rate) x (365/Actual Days)

You are considering a payday loan for $100, which you will repay in 19 days when you will receive your next monthly salary payment. The loan company wants a post-dated check for $120 dated 19 days in the future. What is the actual annual percentage rate (APR) that you will be paying?

APR = Nominal Interest x (365 / Actual Days)\ = .20 x (365 / 19) = .20 x 19.2 = 384%

A new credit card is advertising a monthly rate of 1.3%. What is the actual annual percentage rate (APR) on this credit card?

APR = Nominal Rate x (365/Actual Days) = .013 x (365/30) = 15.8%

Good Deal Pawn Shop charges an interest rate of 20% every 17 days on loans to its customers. Like all lenders, Good Deal must report an APR to consumers. What rate should the shop report?

APR = Stated Interest Rate x Conversion Factor = .20 x (365 / 17) = .20 x 21.47 = 4.2941 = 429.41%

What are the Standard & Poor's ratings just above/just below the line that divides investment grade from speculative grade?

BBB- and BB+

An investment will generate $6,100 per year for 15 years, with the first payment occurring one year from now. If this stream of payments will be invested at 6%, what will be the value of the investment at the end of 15 years?

FV = C x (FV factor from Table A.4 for 15 years at 6%) = $6,100 x 23.276 = $141,983.60

If you deposit $5,000 at the end of each of the next 20 years into an account paying 12%, how much money will you have in the account in 20 years?

FV = C x (FV factor from Table A.4 for 20 years at 12%) = $5,000 x 72.052 = $360,260

FV of annuity

FV = C x (Factor of t and r)

A lottery winner will receive $1 million at the end of each of the next ten years. What is the future value (FV) of her winnings at the time of her final payment, given that the interest rate is 9.0% per year?

FV = C x FACTOR (t = 10, r = 9) = $1,000,000 x 15.193 = $15,193,000

Every year, for the past 20 years, your grandfather has been putting $20,000 into an investment fund for you. The fund has grown to $632,000 today. What has been the average annual compound growth rate on these funds?

FV = C x FACTOR (t = 20, r = ?) $632,000 = $20,000 x FACTOR FACTOR = $632,000/$20,000 = 31.600 33.066 5.00% 3.288 1.822 31.600 ? X 1.0 29.778 4.00% 1.822 / 3.288 = X / 1.00 3.288X = 1.822 X = .554 The compound growth rate was 4.000% + .554% = 4.55%

What is the future value of $12,000 a year for 25 years at 12 percent interest?

FV = C x FACTOR (t = 25, r = 12) = $12,000 x 133.33 = $1,599,960

At age 25, you will begin saving for your retirement, which you plan to take at age 75. How much would you have to save each year in order to have $5,000,000 waiting for you at age 75, assuming that interest rates will average 7% over the period?

FV = C x FACTOR (t = 50, r = 7) $5,000,000 = C x 406.53 C = $12,299.22

FV of $1

FV = PV x (Factor of t and r)

You are depositing $3,000 in a retirement account today. How much money would you have if you were to invest it at seven percent for 50 years?

FV = PV x FACTOR (t = 50, r = 7) = $3,000 x 29.457 = $88,371

An investment which costs $100 today will grow to $300 in seven years. What is the rate of return?

FV = PV x FACTOR (t = 7, r = ?) $300 = $100 x FACTOR FACTOR = $300 / $100 = 3.0000 3.1855 18% .3593 .1738 3.0000 ? X 2.0 2.8262 16% X / 2.0 = .1738 / .3593 .3593X = .3476 X = .9674 The rate is 16.00% + .9674%, or 16.97%.

You have just made your first $5,000 contribution to your retirement account. Assuming that you earn a 10% compound annual rate of return, and assuming that you make no more contributions, what will your account b worth when you retire in 50 years? What will it be worth when you retire if you wait 10 years to make the same single initial contribution, which will earn the same 10% compound annual rate of return (but for only 40 years)?

FV = PV x Factor (A.1) FV= $5,000 x 117.39 FV= $586,950.00 FV= $5,000 x 45.259 FV= $226,295.00

Your coin collection contains fifty 2020 silver dollars. If you purchased the for face value of $1 each in 2020, and if the silver dollars have been appreciating, and will continue to appreciate, at a 5% compound annual rate, what will the collection be worth in 2030?

FV= PV x Factor (A.1) FV= $50 x 1.6289 FV= $81.45

Find the FV Years= 6 Interest rate= 5% PV= $14,334

FV=PV x Factor (A.1) FV= $19,181.75

Find the FV Years= 20 Interest rate= 8% PV= $100,000

FV=PV x Factor (A.1) FV= $466,100.00

Nominal Rate

Nominal Rate= Real Rate + Inflation

--- are unsecured bonds with maturities of ten years or less, and --- are unsecured bonds with maturities of 10 years or more.

Notes, debentures

You own a lake house that you are looking to sell. You have received two offers for it. The first offer is for $150,000 cash today. The second offer is from a potential buyer who will pay you $35,000 down now, $70,000 at the end of one year, and another $70,000 at the end of two years, for a total of $175,000. You're tempted to take the second offer, because it appears to be more money. If your discount rate is 8%, what are the present values for the two offers?

PRESENT VALUE OF FIRST OFFER = $150,000 PRESENT VALUE OF SECOND OFFER @ 8.0%: Year: 0 1 2 Amount: $35,000 $70,000 $70,000 PV Factor 1.0000 .9259 .8573 Present Value $35,000 $64,813 $60,011 = $159,824

Perpetuity

PV = C / r

PV of annuity

PV = C x (Factor of t and r)

An investment offers to pay you $7,300 per year for five years. If your discount rate is 15%, what is the present value of this investment?

PV = C x (PV factor from Table A.3 for 5 years at 15%) = $7,300 x 3.3522 = $24,471.06

Your company will generate $68,000 in net income each year for the next seven years. If the appropriate interest rate is 9%, then what is the present value of this income stream?

PV = C x (PV factor from Table A.3 for 7 years at 9%) = $68,000 x 5.0330 = $342,244

What would be the annual payments on a fixed payment amount loan of $10,000 for seven years at 9%?

PV = C x (Present value factor from Table A.3 for 7 years and 9%) $10,000 = C x (5.033) $10,000 = 5.033C C = $10,000 / 5.033 C = $1,986.89

A potential tenant for your factory building is offering to pay you $50,000 in advance each year for the next 10 years, with the first payment on signing of the lease. Your discount rate is 12%. What is the present value of this stream of payments?

PV = C x FACTOR (t = 10, r = 12) = $50,000 x 5.6502 = $282,510 Now, converting to annuity due: $282,510 x (1 + r) = $282,510 x 1.12 = $316,411

If your discount rate is 8%, what is the present value of a stream of payments of $4,000 each year over the next 10 years?

PV = C x FACTOR (t = 10, r = 8) = $4,000 x 6.710 = $26,840.40

An annuity pays $100 per year for 5 years. What is the present value (PV) of this annuity given that the interest rate is 6% and the annuity is compounded annually?

PV = C x FACTOR (t = 5, r = 6) = $100 x 4.2124 = $421.24

PV of $1

PV = FV x (Factor of t and r)

How much would you pay today for a $10,000 Treasury note maturing at the end of three-years, if the market interest rate were 3%?

PV = FV x (Present value factor from Table A.2 for 3 years and 3%) = $10,000 x (.9151) = $9,151

What is the present value of $150,000 to be received in 10 years if the discount rate is 12%?

PV = FV x FACTOR (t = 10, r = 12) = $150,000 x .3220 = $48,300

Fourteen years ago, your parents set aside $7,500 to help fund your college education. Today, that fund is valued at $26,180. What rate of interest has been earned on this account?

PV = FV x FACTOR (t = 14, r = ?) $7,500 = $26,180 x FACTOR FACTOR = $7,500 / $26,180 = .2865 .2992 9% .0359 .0232 .2865 ? X --1.0 .2633 10% .0232 / .0359 = X / --1.0 .0359X = --.0232 X = --.646 The rate was 10% -- .646% = 9.35%

Imprudential, Inc. has an unfunded pension liability of $850 million that must be paid in 25 years. To assess the value of the firm's stock, financial analysts want to discount this liability back to the present at a discount rate of 7 percent. What is the present value of this liability?

PV = FV x FACTOR (t = 25, r = 7) = $850,000,000 x .1842 = $156,570,000

You have just won the $1,000,000 first prize in the Centennial Lottery. However, the prize will be awarded on your 70th birthday, which will be 50 years from now (you are 20 years old). What is the present value of your windfall if the appropriate discount rate is 9%?

PV= FV x Factor (A.2) PV= $1,000,000 x 0.0134 PV= $13,400.00

Find the PV Years= 13 Interest rate= 7% FV= $15,451

PV=FV x Factor (A.2) PV = $6,412.17

Find the PV Years= 4 Interest rate= 10% FV= $51,557

PV=FV x Factor (A.2) PV= $35,213.43

Travis invested $9,250 in an account that pays 6 percent simple interest. How much more could he have earned over a 7-year period if the interest had compounded annually?

SIMPLE INTEREST: I = P x R x T I = $9,250 x .06 x 7 years = $3,885.00 COMPOUND INTEREST: FV = PV x FACTOR (t = 7, r = 6) = $9,250 x 1.5036 = $13,908.30 Deduct principal: $13,908.30 - $9,250 = $4,658.30 DIFFERENCE: $ 773.30

True or false. Fixed-principal amount loans generally are used for corporate purposes, while fixed payment amount loans generally are used for retail purposes.

True

True or false. Over the life of a bond, the par/face value, the coupon, and the coupon rate never change.

True

True or false. The interest rates on speculative grade bonds are higher than the interest rates on investment grade bonds.

True

True or false. There can be a fairly large difference in average interest rates between investment grade bonds and speculative grade bonds.

True

The right of a company to buy back its bonds before maturity is a ---, and the amount that it pays the bondholders above par for this feature is a ---

call provision, call premium

A bond that can be swapped for a certain number of shares of common stock is said to be a --- bond

convertible

A bond selling in the market for less than par, or face, value is called a --- bond; a bond selling in the market for more than the par, or face, value is called a --- bond

discount, premium

With a --- loan, a pre-set amount of principal is paid each period, along with varying amounts of interest, while with a --- loan, a pre-set total amount, consisting of varying amounts of principal and of interest, is paid each period.

fixed principal amount, fixed payment amount

bonds may be issued in one of two forms:

registered, bearer

A company which carries a rating of A- from one ratings agency and a rating of BBB+ from another ratings agency is said to be ---

split-rated

a bond which has been placed in a lower level of the repayment cascade, junior to other debt which is senior, is called a --- bond

subordinated

The bondholders are represented by a ---

trustee

As interest rates go ---, bond prices go ---, and as interest rates go ---, bond prices go ---

up, down, down, up

What are the three types of loans?

· Interest-only · Amortizing · Pure discount loans

What five items may be found in a bond indenture?

· Par value, coupon, etc. · Repayment arrangements · Security · Call provisions · Covenants

All other things equal, interest rate risk is greater under what two conditions

· The longer the time to maturity · The lower the coupon rate

Nuclear Engineering Associates Inc. has a bond outstanding with an initial maturity of 20 years and a par value of $1,000, which bond now sells for $891.68. The bond has a coupon rate of 5.0%, paid annually, and now has 18 years remaining to maturity. What is the yield to maturity of this bond?

PV of Bond = PV of Coupons + PV of Par Value Finding yield to maturity is an iterative process. First, we find the coupon: $1,000 x .05 = $50 annually Now, the iteration begins. Since the price is less that par value, this is a discount bond. Since bond prices and interest rates move inversely to each other, the yield to maturity must be higher than the original coupon rate of 5%. Let's start with a rate of 7%. Calculation of PV of Coupons PV = C x (Factor from Table A.3 for 7% and 18 years) PV = $50 x 10.0591 PV = $502.96 Calculation of PV of Par Value PV = FV x (Factor from Table A.2 for 7%, 18 years) PV = $1,000 x .2959 PV = $295.90 Addition $502.96 + $295.90 = $798.86 OK, so 7% produces a value of $798.86, which is below the price of $891.68. So, we have to try a rate lower than 7 % to get a higher price nearer $891.68. So, let's try 6%. Calculation of PV of Coupons PV = C x (Factor from Table A.3 for 6% and 18 years) PV = $50 x 10.8276 PV = $541.38 Calculation of PV of Par Value PV = FV x (Factor from Table A.2 for 6% and 18 years) PV = $1,000 x .3503 present value PV = $350.30 Addition $541.38 + $350.30 = $891.68 SUCCESS!! The YTM is 6.0%.

Ten years ago, LaSalle Global Inc. issued a 20-year, $1,000 par value bond, with a coupon rate of 6.00%, paid annually. Today, the bond has ten years remaining to maturity, and the bond is currently selling in the market for $1,162.25. What is the bond's yield to maturity (YTM)?

PV of Bond = PV of Coupons + PV of Par Value Finding yield to maturity is an iterative process. First, we find the coupon: $1,000 x .06 = $60 annually Now, the iteration begins. Since the price is more that par value, this is a premium bond. Since bond prices and interest rates move inversely to each other, the yield to maturity must be lower than the original coupon rate of 6%. Let's start with a rate of 5%. Calculation of PV of Coupons PV = C x (Factor from Table A.3 for 5% and 10 years) PV = $60 x7.7217 PV = $463.30 Calculation of PV of Par Value PV = FV x (Factor from Table A.2 for 5%, 10 years) PV = $1,000 x.6139 PV = $613.90 Addition $463.30 + $613.90 = $1,077.20 OK, so 5% produces a value of $1,077.20, which is more than par, but still less than $1,162.25. So, we have to try a rate lower than 5% to get a higher price. So, let's try 4%. Calculation of PV of Coupons PV = C x (Factor from Table A.3 for 4% and 10 years) PV = $60 x 8.1109 PV = $486.65 Calculation of PV of Par Value PV = FV x (Factor from Table A.2 for 4% and 10 years) PV = $1,000 x .6756 PV = $675.60 Addition $486.65 + $675.60 = $1,162.25 SUCCESS!! The yield to maturity is exactly 4.0%.

Five years ago, Atlas Industries sold a bond with a par value of $1,000, with 30 years to maturity, and with a coupon rate of 6.0%, paid annually. Today, with 25 years remaining to maturity, the yield to maturity is 8.0%. What is the price of this bond?

PV of Bond = PV of Coupons + PV of Par Value First, we find the coupon: $1,000 x .06 = $60 per annum Calculation of PV of Coupons PV = C x (Factor from Table A.3 for 8% and 25 years) PV = $60 x 10.6748 PV = $640.49 Calculation of PV of Par Value PV = FV x (Factor from Table A.2 for 8% and 25 years) PV = $1,000 x .1460 PV = $146.00 Addition Price = $640.49 + $146.00 = $786.49

Ten years ago, Excelsior Manufacturing sold a 30-year bond issue, with a par value of $1,000, and a coupon rate of 9%, paid annually. Today, with 20 years remaining until maturity, the yield to maturity is 5.0%. What is the price of this bond?

PV of Bond = PV of Coupons + PV of Par Value First, we find the coupon: $1,000 x .09 = $90 per annum Calculation of PV of Coupons PV = C x (Factor from Table A.3 for 5% and 20 years) PV = $90 x12.4622 PV = $1,121.60 Calculation of PV of Par Value PV = FV x (Factor from Table A.2 for 5% and 20 years) PV = $1,000 x .3769 PV = $376.90 Addition Price = $1,121.60 + $376.90 = $1,498.50

Years ago, your grandfather won a lottery. The value of his winnings at the time was $50,000. He invested the entire amount such that it will provide annual payments of $2,400 a year to his heirs forever. What is the rate of return?

PV of Perpetuity = C / r $50,000 = $2,400 / r $50,000r = $2,400 r = .048 or 4.8%

Your firm just signed a contract to a receive annual royalties forever. The royalties are estimated to be $1 million every year, starting a year from now. If the discount rate is 12%, what is the present value of the royalties from this contract?

PV of Perpetuity = C / r = $1,000,000 / .12 = $8,333,333

What is the present value of an infinite stream of payments of $10,000 per year if your discount rate is 10%?

PV of Perpetuity = C / r = $10,000 / .10 = $100,000

The Excelsior Life Insurance Co. is trying to sell you an investment policy that will pay you and your heirs $30,000 per year forever. If your required return on this investment is 6%, how much would you be willing to pay for this policy?

PV of a Perpetuity = Annual Cash Flow/Discount Rate = $30,000 / .06 = $500,000

First City Bank pays 7% simple interest on its savings accounts and makes you withdraw the interest every year, whereas Second City Bank pays 7% compound interest. If you made a $6,000 deposit in each bank how much more would you have earned from your Second City Bank account at the end of 9 years?

Simple Interest-First City Bank $6,000 x 0.07 x 9 years = $3,780 Compound Interest-Second City Bank FV=$6,000 x 1.8385 (Table A.) FV=$11,031-$6,000 FV=$5,031 $5,031-$3,780=$1,251

You are a commercial property owner. A prospective customer offers to rent your property for ten years, with equal annual payments of $10,000, starting immediately. Assuming that your discount rate is 10%, what is the present value of this proposal?

This is an annuity due problem, with payments made at the beginning of each year. First, we calculate the answer as a normal annuity problem: PV = C x (Present value factor from Table A.3 for 10 years and 10%) = $10,000 x (6.1446) = $61,446 Next, we solve for the annuity due value: PV of Annuity Due = (PV of Ordinary Annuity) x (1.00 + .10) = $61,446 x 1.10 = $67,591

You are a consultant. A prospective client offers to sign a $100,000 contract for your services, with payment as follows: Immediate down payment $10,000 Payable at the end of year one 30,000 Payable at the end of year two 30,000 Payable at the end of year three 30,000 At a discount rate of 12%, what is the present value of your prospective client's proposal?

This is the "quarterback" problem, with multiple single amounts. We will use Table A.2 to solve. First, we set up the schedule of cash flows: Immediate Year 1 Year 2 Year 3 Cash Inflow $10,000 $30,000 $30,000 $30,000 Next, we find the present value factors for years 1, 2, and 3 in the column for 12% in Table A.2. The present value factor for money received in the present is always 1.0000. Immediate Year 1 Year 2 Year 3 Cash Inflow $10,000 $30,000 $30,000 $30,000 PV Factor 12% 1.0000 .8929 .7972 .7118 Next, we multiply each cash inflow by its present value factor. Immediate Year 1 Year 2 Year 3 Cash Inflow $10,000 $30,000 $30,000 $30,000 PV Factor 12% 1.0000 .8929 .7972 .7118 Present Value $10,000 $26,787 $23,916 $21,354 We then add the found present values to find the combined present value: $10,000 + $26,787 + $23,916 + $21,354 = $82,057

In January 2010, the average house price in the United States was $283,400. In January 2000, the average house price in the United States was $200,300. What was the annual compounded rate of increase, to the nearest tenth of one percent, in the average house price from 2000 to 2010?

To answer this question, we can use either the FV or the PV formula. We will use the FV formula, that is: FV = PV x FACTOR Next, we fill in the information that we have: $283,400 = $200,300 x FACTOR Then, we calculate the factor: $283,400/$200,300, or 1.4149. Next, we go to Table A.1, the future value table. In the "Period" column, we find the line for 10 years, then move right until we find two factors that bracket 1.4149. Those are 1.3439 for 3% and 1.4802 for 4%. So, we know that our interest rate is between 3% and 4%. Next, we interpolate to find the exact rate: 1.4802 4.00% 1.4149 ? % 1.3439 3.00% (1.4149 - 1.3439)/(1.4802 - 1.3439) = x/(4.0000 - 3.0000) .0710 / .1363 = x / 1.0000 .1363 x = .0710 x = .0710 / .1363 x = .5209 So, the rate is 3.0000% + .5209%, or 3.52% Rounding to the nearest tenth of a percentage point, our answer is 3.5%