FIN316

What is the value today of a stock that pays a dividend of $5 every year and has an expected rate of return on 10%?

P0 = 5/.10 = $50

A share of preferred stock pays an annual dividend of $1.25 per share. If the value of this preferred stock today is $30, what rate of return do investors require on this investment?

P0 = Div/r 30 = 1.25/r r = 4.16%

If market interest rates rise:

Short term bonds will rise more than long term

If a bond offers investors an 11% nominal rate of return during a year in which the rate of inflation was 4% then the investor's real rate of return is what?

1+real = 1.11/1.04 = 6.73%

Which one of the following represents additional compensation provided to bondholders to offset the possibility that the bond issuer might not pay the interest and/or principal payments as expected?

Default risk premium

What is the PV of the of the following payment stream discounted at 8% annually: 1,000 at the end of year 1, 3,000 at the end of year 2, and 5,000 at the end of year 3?

PV = 1000/(1.08)^1 + 3000/(1.08)^2 + 5000/(1.08)^3 = 7467.11

Which ONE of the following is FALSE? Bond investors get to vote for the Board of Directors Bonds are required to pay coupon payments or else they are in default Bonds represent debt for the companies selling them to investors The US government through the Treasury sells bonds to investors

Bond investors get to vote for the Board of Directors

Upon arriving in Bolivia, you decide to buy a house. The house costs $125,000 and you put $25,000 down. What are your monthly payments if you finance the house for over 30 years and the interest rate is 12%? Monthly compounding

Cash payment, annuity formula = $1028.61

Which of the following is true: Stocks selling between investors occur on the primary market If you expect interest rates to fall you want to buy short term bonds The default risk premium compensates investors for interest rate risk Common stock has the least priority in bankruptcy

Common stock has the least priority in bankruptcy

Suppose you will receive payments of 10,000 for 10 years with the first payment being received 7 years from now. If interest rates are 6% annually what is the present value of this payment stream?

Delayed annuity problem Step 1: use PV of an annuity Step 2: PV of a single cash flow where the FV is the value you got from step 1 = 51,885.71

Suppose that you win the lottery and choose to recieve annual payments of $30,000 for a period of 8 years (8 total payments). The first payment will be made 4 years from now. The interest rate is 4% what is the PV of this stream of payments?

Delayed annuity problem. Step 1: use PV of an annuity Step 2: PV of a single cash flow where the FV is the value you got from step 1 = 179,561.57

The required rate of return on the common stock of Gondry Corporation is 10%. The stocks current dividend is $2.50 and is expected to grow at a constant rate of 3% forever. What is the value of the stock today?

Discount Dividend Model Constant Growth P0 = (div0(1+g)^1)/r-g = (2.50(1+.03)^1)/.10-.03 = 36.79

Which account would be preferred by a depositor (ie you are earning money) and why? A 6% APR with monthly compounding or 6.5% APR with semi-annual compounding?

EAR = (1+r/m)^m - 1 Calculate the effective annual rate of each offer and then choose the best rate in this question you are depositing money so you can choose the higher EAR

For the next 30 years you plan to put 1000 per year into you IRA account for retirment. You expect your money to grow 10% per year. How much will you have in 30 years?

FV of an annuity FV = 1000 (((1.1)^30 - 1) /.1) = 164494.02

How long will it take to save $10,000 if you deposit $200 monthly. and earn an annual interest rate of 15% on your money? (monthly implies monthly compounding)

FV of number of years annuity

If Esther deposits $100 into a bank account which earns 10% interest compounded quarterly for 3 years, how much money does she have at the end of 3 years?

Future Value of a single Cash flow FV = PV(1+(r/m))^n*m = 100(1+(0.1/4))^12 = $134.49

If investors recieve a 10% interest rate on their bank deposits, how much will their purchasing power increase if the inflation rate over the year is 6%?

Inflation question = 1+real=1+nominal/1+inflation 1+real = 1.10/1.06 1+real = 1.0337736 =3.77%

Suppose interest rates have been at historically high levels the past two years and you therefore expect they will soon go down. A reasonable strategy for bond investors during this time period would be to:

Invest in short term. Bonds to reduce interest rate risk

A bond will sell at a discount (below par value) if:

Investors current required rate of return is above the coupon rate of the bond

What is the present value of a 30 year $1500 annuity if interest rates are 12% annually?

Multiple cash flows - PV annuity formula = 12,082.78

Suppose you want to fund a scholarship fund at the UO with the extra 1million you have. You expect the fund to earn 9% interest and begin making payments one year from now. If you instruct the UO not to touch the principle, how much will the annual scholarship be?

PV = C/R 1,000,000= C/.09 C = 90,000

What is the present value of a 10 year annuity with payments of $1000 per year if interest rates are 6% annually?

PV of an annuity = 1000(1-(1/1+0.6/1)^10*1/(0.06/1) = 7360.09

An annuity will pay you $300 per year for 25 years but the first payment does not come until 10 years from now. If interest rates are 10% what is the PV of this delayed annuity?

PV of an annuity formula = 300(1-(1/1+.10/1)^25/(.10/1) = 2723.11 is the value of the annuity at year 9. This is now a single cash flow that needs to be discounted back to present value, year 0 PV of single cash flow formula = 2723.11/(1+.10/1)^9*1 = 1154.87 is the PV of the delayed annuity

Suppose your company is deciding whether to lease a truck from a leasing company for 6 years. Payments are $8000 per year, beginning immediately. Alternatively, the company can buy a new truck for $40,000. Assume the value of the truck is worthless after 6 years under both payment options. Which is preferred if the opportunity cost of capital is 7% annually?

PV of annuity problem however you must add an additional 8000. because payments began. immediately = 40,801.60

Suppose you are looking to purchase a share of preferred stock which offers $2.50 dividends each year forever. The dividends start one year from now. If interest rates in the market for investments of similar risk are 4% what price would you be willing to pay today for this stock?

PV of perpetuity formula = 62.50

What is the present value of $100 perpetuity if interest rates are 10%?

PV perpetuity formula = $1000

You invest $500,000 today at an annual interest rate of 9%. If you want to provide a scholarship that starts today, what will the scholarship payments be?

PV perpetutiy starts today formula = 41,284.40

A local bank will pay you a level cash payment each year beginning today for your lifetime if you deposit $2500 in the bank today with a 10% rate of return. You plan to live forever

Perpetuity Question PV = (c/r) + c 2500 = (c/.10) + c c = 227.27

Suppose you are rich and want to fund a. scholarship with $1million that you have. You expect the fund to earn 7%. If you instruct the school to simply pay out the interest, not the principle, how much the annual scholarship payment be? The scholarship will begin 1 year from now.

Perpetuity problem PV=c/r = 70,000

A share of preferred stock that sells for $40 and pays $2 dividends forever (beginning 1 year from now - which is normal) is offering what rate of return?

Rate of preferred stock formula: DIV/current price = 5%

You currently have $20,000 in credit card debt which is accruing monthly interest at a 15% annual rate. You would like to pay off this debt over the next 3 years. What monthly payments will you need to make to achieve this goal?

Solve for C of an annuity = 693.31

You want to buy a car and it costs 15,000. Interest rates are 7.5% annually. You decide that you want a 5 year loan where payments are made at the end of each month. What are your monthly payments?

Solve for c of an annuity C = 15,000 / ((1-1/1+(.075/12))^60/(.075/12)) C = 15000/49.905 C = 300.57 *anytime you are buying something rather than saving money use the equation with PV in it

You buy a 6% coupon bond with a maturity of ten years that pays annual coupons. When you buy the bond, the market interest rate is 9%. You decided to sell the bond 3 years later after you've received three coupon payments, and the market interest rate is 6%. You sell the bond for $1000. What was the price of the bond when you bought it?

Step 1: Find the present value of the coupons as a $60 10 year annuity Step 2: find the present value of par ($1000) as a single cash flow Step 3: add results of step 1 and 2 N = 10 C = 60 M = 1 R = .09 = 807.47

Which one of the following is most likely true for a AAA bond compared to a CCC bond?

The AAA bond has a lower default premium than the CCC bond

John owns a corporate bond with a coupon rate of 8% that matures in 10 years. Bill owns a corporate bond with a coupon rate of 12% that matures in 25 years. If interest rates go down, then:

The value of both bonds will remain the same because they were both purchased in an earlier time period before the interest rate changed

Which of the following is true: When interest rates rise, bond prices rise When interest rates rise, long term bonds will decline in value more than short term When interest rates rise bond values do not change as they are fixed When interest rates rise coupon payments decrease

When interest rates rise, long term bonds will decline in value more than short term

A company paid a $2 per share dividend yesterday (Div0). You expect the dividend to grow steadily at a rate of 3% per year forever. a. What is the expected dividend in each of the next 3 years? b. If the discount rate for the stock is 9% what is the stock's current price?

a. Div0 = 2 Div1 = Div0 (1+g)^1 -> 2(1.03)^1 = 2.06 Div2 = Div0 (1+g)^2 -> 2(1.03)^2 = 2.1218 Div3 = Div0 (1+g)^3 -> 2(1.03)^3 = 2.1854 b. P0 = (Div0(1+g)/(r-g) = 2(1.03)/(.09-.03) = 34.33

You are considering the purchase of a 3-year bond with an annual coupon rate of 8% and a par value of $1000. The bond pays coupons annually. The discount rate for similar bonds is 9% a. Will the bond be priced at par, discount, or premium? b. What are the annual coupon payments from this bond? c. What price are you willing to pay for the bond today (beginning price)?

a. coupon rate < required rate = sells at a discount .08 > .09 = premium b. par value*coupon rate = coupon payment 1000*.08 = 80 c. Step 1: find the present value of the coupons as an $80, 3y annuity N=3 C=80 M=1 R=.09 Step 2: find the PV of par $1000 as a single cash flow Step 3: add the results of steps 1&2 = 974.68 `

Deciding what long term assets a company should invest in is referred as:

capital budgeting decisions

Which of the following appears to be the most appropriate goal for corporate management?

maximizing market value of the company's stock