Fin 350

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) What is Anle's expected dividend yield? Answer 9.5 %. (Round to two decimal places.) (b) What is Anle's expected capital gain rate? Answer 4.76 %. (Round to two decimal places.) (b) What is Anle's equity cost of capital? Answer 14.26 %. (Round to two decimal places.)

(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

Krell Industries has a share price of $20.50 today. If Krell is expected to pay a dividend of $1.00 this year, and its stock price is expected to grow to $25 at the end of the year, what is Krell's dividend yield and equity cost of capital? (a) Krell's dividend yield is Answer 4.88 %. (Round to two decimal places.) (b) Krell's equity cost of capital is Answer 26.83 %. (Round to two decimal places.)

(a) The dividend yield is the percentage return the investor expects to earn from the dividend paid by the stock. It is given by: DividendYield=Div1P0, where Div1 is the dividend to be paid within the year, and P0 is the current stock price. Substituting the appropriate values, we have: Dividend Yield = $1 ÷ $20.50 (b) The equity cost of capital should equal to the expected return that the investor will earn for a one-year investment in the stock. It is equal to the sum of the dividend yield and the capital gain rate: rE = Dividend Yield + Capital Gain Rate The capital gain rate is the ratio between the capital gain and the current stock price: CapitalGainRate=P1−P0P0, that is: CapitalGainRate=25.00−20.5020.50 Therefore, the Equity Cost of Capital = Dividend Yield + Capital Gain Rate

A project costs $200 million and is expected to generate cash flows of $25 million per year, starting at the end of the first year and lasting forever. What is the internal rate of return?

Note that the cash flow stream is a perpetuity. So its present value is: C / r NPV = -$200 + $25 ÷ IRR. Set NPV = 0, solve for IRR, IRR=12.5% The correct answer is: 12.5%

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 termshould equal the YTM on a risk-free bond with 3 year maturity: r3 = YTM3 = 5.45%

The prices of several bonds with face values of $1,000 are summarized in the following table: Bond A B C D Price $972.50 $1040.75 $1150.00 $1,000.00 For each bond, provide an answer for whether it trades at a discount, at par, or at a premium.

A) Discount B) Premium C) Premium D) Par

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 . (Round to the nearest cent.) (b) What will the price of the bond be if it is downgraded?

A)P=CPN/YTM×(1−1(1+YTM)N)+FV(1+YTM)N 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)3

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 28

Below is the timeline for the cash flows (which continue into perpetuity): t=0 t=1 t=2 t=3 |----------------|----------------|----------------|------ $1.40 $1.40(1+g) $1.40(1+g)2 According to the constant dividend growth model, the value of the firm depends on the current dividend level divided by the equity cost of capital adjusted by the growth rate. Then, P0=Div1rE−g, where P0 is the current stock price, Div1 is the next dividend payment, rE is the equity cost of capital, and g is the expected dividend growth rate. Substituting values, we have: P0 = $1.40 / (0.100 - 0.050)

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

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

Explain why the yield of a bond that trades at a discount exceeds the bond's coupon rate. Select one: A. The bond's coupon yield is irrelevant. It trades at a discount because investors avoid these bonds. B. The bond is trading a discount because investors don't like the bond. C. Because the value of the bond is discounted, the return on the bond is reduced and the yield exceeds the coupon. D. The bond can be purchased for a discount, which gives it an "extra return"; hence, the yield exceeds the coupon.

D. The bond can be purchased for a discount, which gives it an "extra return"; hence, the yield exceeds the coupon.

True/ False: NPV is positive only for discount rates greater than the internal rate of return.

False

A bond will make payments every six months as shown on the following timeline (using six-month periods): t=0 t=1 t=2 t=27 t=28 |----------------|----------------|--------- ··········-----|----------------| $60 $60 $60 $1,060 (a) What is the maturity of the bond (in years)? Answer 14 years. (b) What is the face value? $Answer 1,000 . (c) What is the coupon rate (in percent)? Answer 12 %. (Round to two decimal places.)

Hint: (a) To determine the maturity of the bond, find the number of periods on timeline and divided by two because there are two payments in each year. (b) The face value is the amount paid at maturity, so the last payment is made up of the semi-annual coupon payment and the face value, or $60,00 and $1,000, in this case. (c) To determine the coupon rate, use the formula: Coupon Payment= (Coupon Rate × Face Value) / Number of Payments per year. This implies: $60 = $1,000 × Coupon Rate / 2

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 $

Hint: The question is about calculating the present value of a stream of cash flows involving a perpetuity structure. The cost of building the machine is $400 paid today. It takes the machine one year to manufacture $400, so the very first cash flow (+) will arrive at t=1. The time line can be drawn as: t=0 t=1 t=2 t=3 |----------------|----------------|----------------|----- ·············· - $4,000 $400 $400 $400 The stream of cash flow above can be decomposed into two parts: a single cash flow of - $4,000 at t=0, and a standard perpetuity afterwards. Thus, PV =CF0 + PV(perpetuity) = -$4,000 + C / r = - $4,000+ $400 / 0.035

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? $

In order to justify the current price of $60, the price that the stock sells for must take into account both the cost of capital for the investment as well as the dividend that is paid out.P0=Div1+P11+rE. $60 = ($2.20 + P1) ÷ (1+19%) Expected Price = $60 × (1+0.19) - $2.20

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%

Gillette Corporation will pay an annual dividend of $0.60 one year from now. Analysts expect this dividend to grow at 11% per year thereafter until the fifth year. After that, growth will level off at 1.9% per year. According to the dividend-discount model, what is the value of a share of Gillette if the firm's equity cost of capital is 9%? The price per share is $Answer 11.37 . (Round to the nearest cent.)

P0=PVt=0(GrowingAnnuity)+PVt=5(GrowingPerpetuity)(1+rE)5 More Specifically:P0=Div1rE−g1×[1−(1+g11+rE)5]+Div6rE−g2(1+rE)5, where Div1 the dividend at t=1, which is $0.60, and Div6 equals to Div1(1+g1)4(1+g2). g1 is 11% and g2 is 1.9%. Cost of Capital rE is 9%. Substitute these values into the above formula and you will find the total present value of the dividend payments.

Year Cash Flow 0 -10,000 1 4,000 2 4,000 3 4,000 4 4,000 Assume the appropriate discount rate for this project is 15%. The payback period for this project is closest to:

Payback = 10000 / 4000 = 2.5, Round upward to 3.

Your firm is preparing to open a new retail strip mall and you have multiple businesses that would like lease space in it. Each business will pay a fixed amount of rent each month plus a percentage of the gross sales generated each month. The NPVs from each of the businesses has approximately the same amount of risk. The business names, square footage requirements, and monthly expected NPVs for each of the businesses that would like to lease space in your strip mall are provided below: Business Name Square Feet Required Expected Monthly NPV Videos Now 4,000 70,000 Gords Gym 3,500 52,500 Pizza Warehouse 2,500 52,500 Super Clips 1,500 25,500 30 1/2 Flavors 1,500 28,500 S-Mart 12,000 180,000 WalVerde Drugs 6,000 147,000 Multigular Wireless 1,000 22,250 If your new strip mall will have 15,000 square feet of retail space available to be leased, what is the maximum monthly NPVs to be generated?

So we select projects based upon their ranking until we run out of space. The optimal combination is shown below: WalVerde Drugs 6,000 147,000 24.5 1 Multigular Wireless 1,000 22,250 22.25 2 Pizza Warehouse 2,500 52,500 21 3 30 1/2 Flavors 1,500 28,500 19 4 Videos Now 4,000 70,000 17.5 5 Total 15,000 $320,250 The correct answer is: $320,250

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?

The question is about calculating the future value of a stream of cash flows involving a Growing Annuity structure. The cash flow will become 3% larger than the previous cash flow each year. The time line can be drawn as: t=0 t=1 t=2 t=3 t=45 |----------------|----------------|----------------|----- ··············------| $0 $4000 $4000×(1+g) $4000×(1+g)2 $4000×(1+g)44 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

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?

The stream of cash flow above can be decomposed into two parts: a single cash flow of $20k at t=0, and a 12-year growing annuity. 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]

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

The stream of cash flow above can be decomposed into two parts: a single cash flow of - $4,000 at t=0, and a standard perpetuity afterwards. 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 $

The stream of cash flow above can be decomposed into two parts: a single cash flow of - $9,000 at t=0, and a standard perpetuity if you stand at t=1. For the perpetuity portion, we first need to compute the present value at t=1, PVt=1. Then we will bring PVt=1 backward in time for one period, PV = PVt=1 ÷ (1+r) 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 $Answer 1204 . (Round to the nearest cent.)

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. (3) t=0 t=1 t=2 t=19 t=20 |----------------|----------------|--------- ··········-----|----------------| $55 $55 $55 $55 + $1000 Use this formula to find the price: P=CPNYTM×(1−1(1+YTM)N)+FV(1+YTM)N, where P is the price of the bond, CPN is the coupon payment, N is the number of payments, FV is the face value paid at maturity, and y is the yield to maturity. So in this case: P = $55/0.04 × (1 - 1/(1+0.04)20 ) + $1,000 / (1+0.04)20