FIN 350

Assume Evco, Inc., has a current stock price of $60 and will pay a $2.20 dividend in one year; its equity cost of capital is 19%. What price must you expect Evco stock to sell for immediately after the firm pays the dividend in one year to justify its current price?

$60 = ($2.20 + P1) ÷ (1+19%) Expected Price = $60 × (1+0.19) - $2.20

Anle Corporation has a current price of $21, is expected to pay a dividend of $2 in one year, and its expected price right after paying that dividend is $22.

(a) Anle's expected dividend yield is: Dividend⋅yield=Div1P0, where Div1 is the dividend and P0 is the current share price. Dividend yield = $2 / $21 (b) Anle's expected capital gain rate is: Capital⋅gain⋅rate=P1−P0P0, where P1 is the expected share price in one year and P0 is the current share price. Capital Gain Rate = ($22 - $21) / $21 (c) Anle's equity cost of capital is: Equity Cost of Capital = Dividend yield + Capital gain rate

Andrew Industries is contemplating issuing a 30-year bond with a coupon rate of 7.50% (annual coupon payments) and a face value of $1,000. Andrew believes it can get a rating of A from Standard Poor's. However, due to recent financial difficulties at the company, Standard and Poor's is warning that it may downgrade Andrew Industries bonds to BBB. Yields on A-rated long-term bonds are currently 7.00%, and yields on BBB-rated bonds are 7.40%. (a) What is the price of the bond if Andrew maintains the A rating for the bond issue? $Answer 1062 . (Round to the nearest cent.) (b) What will the price of the bond be if it is downgraded? $Answer

(a) If Andrew Industries maintains a rating of A, it should have a YTM = 7%. With an 7.5% coupon rate and annual coupons, the coupon payment per year is: CPN = FV × Coupon Rate / Number of Payments per year = $1,000 × 7.5% / 1 = $75. YTM is 7% per year. N = 30 years. P = $75/0.07 × (1 - 1/(1+0.07)30 ) + $1,000 / (1+0.07)30 b) If Andrew Industries maintains a rating of BBB, it should have a YTM = 7.4%. So in this case: P = $75/0.074 × (1 - 1/(1+0.074)30 ) + $1,000 / (1+0.074)30

The last four years of returns for a stock are as follows: 1 2 3 4 -3.5% +28.5% +12.5% +4.5%

(a) The average return is:(RT) =1/4 × (-3.5% + 28.5% + 12.5% + 4.5%) (b) VAR(R) = 1/ 3 × [ (-3.5% - 10.50%)2 + (28.5% - 10.50%)2 + (12.5% - 10.50%)2 + (4.5% - 10.50%)2 ] (c) The standard deviation is: SD(R) = ( VAR(R) )0.5

Suppose the current, zero-coupon, yield curve for risk-free bonds is as follows: Maturity (years) 1 2 3 4 5 Yield to Maturity 4.70% 5.20% 5.45% 5.65% 5.80% (a) What is the price per $100 face value of a 3-year, zero-coupon risk-free bond? The price is $Answer 85.28 . (Round to two decimal places.) (b) What is the price per $100 face value of a 5-year, zero-coupon, risk-free bond? The price is $Answer 75.43 . (Round to two decimal places.) (c) What is the risk-free interest rate for 3-year term? The risk-free interest rate for 3-year maturity is Answer 5.45 %. (Round to two decimal places.)

(a) The formula for the price of a zero-coupon bond is as follows: P=FV(1+YTMn)n, where FV is the face value of $100, YTM is the yield to maturity and n is the number of periods. Therefore: P = $100 ÷ (1+5.45%)3 (b) The formula for the price of a zero-coupon bond is as follows: P=FV(1+YTMn)n, where FV is the face value of $100, YTM is the yield to maturity and n is the number of periods. Therefore: P = $100 ÷ (1+5.80%)5 (c) The risk-free interest rate for a 3-year term should equal the YTM on a risk-free bond with 3 year maturity: r3 = YTM3 = 5.45%

You are 20 years old and decide to start saving for your retirement. You plan to save $4,000 at the end of the first year and then increase your savings by 3% per year until you make the very last deposit at age 65. Suppose you earn 6% per year on your retirement savings. How much will you have saved for retirement right at age 65?

C = $4,000 r = 0.06 g = 0.03 n = 45 Thus, PV =C / (r-g) * [ 1 - (1+g)n / (1+r)n ] FV = PV * (1+r)n

You are 22 years old and decide to start saving for your retirement. You plan to save $6,000 at the end of each year (so the first deposit will be one year from now), and will make the last deposit when you retire at age 65. Suppose you earn 6% per year on your retirement savings. How much will you have saved for retirement right at age 65?

Constant Cash Flow: C = $6,000. Annual Interest Rate: r = 0.06. n = 65 - 22 = 43. FV = PV * (1+r)^n = 6000 / 0.06 * [ 1 - 1 / (1+0.06)^43 ] * (1+0.06)^43

The table below shows the one-year return distribution for RCS stocks. Possible Return Ri Probability pi -40% 0.10 -20% 0.20 0% 0.15 20% 0.25 40% 0.30 (a) The expected return is: Answer 9 (b) The standard deviation is Answer 27.18

Expected Return rate E(R) = 0.10 × (-40%) + 0.20 × (-20%) +0.15 × (0%) +0.25 × (20%) +0.30 × (40%) Standard Deviation VAR(R) = 0.10 × (-40% - 9%)2 + 0.20 × (-20% - 9%)2 + 0.15 × (0% - 9%)2 + 0.25 × (20% - 9%)2 +0.30 × (40% - 9%)2

Your oldest daughter is about start kindergarten in a private school. Tuition is $20,000 per year, payable at the beginning of the school year. You expect to keep your daughter in private school through high school. You expect tuition to increase at a rate of 3% over the 13 years of her schooling. What is the present value of your tuition payments if the interest rate is 8% per year? That is, you would need to have $Answer 198730 (Round to the nearest dollar) in the bank now to fund all 13 years of tuition.

For the 12-year growing annuity, C, the cash flow at t=1, is $20k×(1+g), not $20k. Remember, C is always referring to the cash flow at t=1; r = 8%; g = 3%. Therefore, PV = $20,000 + PV(growing annuity) = $20,000 + [$20,000 ×(1+0.03)] ÷ (0.08 - 0.03) × [1 - (1.03/1.08)12]

Total risk is measured using volatility and Miney has the highest volatility, hence the most total risk.

Market risk is measured using beta and Eenie has the lowest beta, hence the lowest market risk.

Consider a project with the following cash flows: Year Cash Flow 0 -10,000 1 14,000 Assume the appropriate discount rate for this project is 15%. The IRR for this project is closest to:

NPV = -$10,000 + $14,000÷ (1+IRR), solve for IRR, IRR = 40% The correct answer is: 40%

Summit Systems will pay a dividend of $1.40 in one year. If you expect Summit's dividend to grow by 5.0% per year, what is its share price if its equity cost of capital is 10%? The price per share is $Answer

P0 = $1.40 / (0.100 - 0.050)

Your lender now offers you a 30-year fixed-rate home mortgage with 3.6% interest per year. If you can afford a monthly payment of $3,000, what is maximum price of a house that you can afford? The maximum house price is $Answer

The maximum monthly payment C = $3,000. the monthly interest rate can be derived from annual rate: rm= r ÷ 12 = 3.6% ÷ 12 = 0.3% =0.003. n = 30 years × 12 = 360 month. Apply the PV formula for annuity and you can figure out the max affordable loan. PV = $3000 / 0.003 * [1 - 1 / (1+0.003)^360]

A rich relative has bequeathed you a growing perpetuity. The first payment will occur in one year and will be $4,000 each. Each year after that, you will receive a payment on the anniversary of the last payment that is 4% larger than the last payment. This pattern of payments will go on forever. If the interest rate is 11% per year, what is the present value of the bequest? The PV of the growing perpetuity is

Thus, PV =C / (r-g) = $4,000 ÷ (0.11- 0.04)

Your buddy in mechanical engineering has invested a machine. It takes one year for the machine to manufacture $400 worth of goods. Once built, the machine will last forever and will require no maintenance. The machine can be built immediately and will cost $4,000 to build. If the interest rate is 3.5%, the NPV of the machine is

Thus, PV =CF0 + PV(perpetuity) = -$4,000 + C / r = - $4,000+ $400 / 0.035

Your buddy in mechanical engineering has invested a machine. It takes one year for the machine to manufacture $900 worth of goods. Once built, the machine will last forever and will require no maintenance. The machine will take one year to build and will cost $9,000 today. If the interest rate is 11%, the NPV of the machine is $

Thus, PV =CF0 + PVt=1(perpetuity) ÷ (1+r) = -$9000 + (C / r) ÷ (1+r) = - $9,000+ ($900 / 0.11) ÷ (1+0.11)

A 10-year bond, $1,000 face value bond with a 11% coupon rate and semi-annual coupons has a yield to maturity of 8%. The bond should be trading at a price of $

With an 11% coupon rate and semiannual coupons, the coupon payment per six months is: CPN = FV × Coupon Rate / Number of Payments per year = $1,000 × 11% / 2 = $55. (2) YTM is 8% per year, so YTM per six months is 4%. N = 10 years × 2 =20. P = $55/0.04 × (1 - 1/(1+0.04)20 ) + $1,000 / (1+0.04)20

FV = PV × (1+r)n

Your daughter is currently 6 years old. You anticipate that she will be going to college in 12 years. You would like to have $144,000 in a savings account to fund her education at that time. If the account promises to pay a fixed interest rate of 7% per year, how much money do you need to put into the account today to ensure that you will have $144,000 in 12 years? Your deposit today should be

Wyatt Oil has a bond issue outstanding with seven years to maturity, a yield to maturity of 7.0%, and a BBB rating. The bondholders expected loss rate in the event of default is 70%. Assuming a normal economy the expected return on Wyatt Oil's debt is closest to:

rd = ytm - prob(default) × loss rate = 7% - 0.4%(70%) = 6.72%

Wyatt Oil has a bond issue outstanding with seven years to maturity, a yield to maturity of 7.0%, and a BBB rating. The bondholders expected loss rate in the event of default is 70%. Assuming the economy is in recession, then the expected return on Wyatt Oil's debt is closest to:

rd = ytm - prob(default) × loss rate = 7% - 3.0%(70%) = 5.53%

What is the present value of $5,000 paid at the end of each of the next 78 years if the interest rate is 9% per year? The present value is $Answer

the stream of cash flows described above is a standard Annuity. Therefore, you can apply directly the Present Value formula for Annuity. Identify C, r and n, and use PV = C/r × [ 1 - 1/(1+r)n ].