A zero-coupon bond has a principal of $100 and matures in four years. The market price for the bond is $72. Calculate the yield to maturity, duration and convexity of the bond.

(Please provide a well detailed answer with the equations that are being used. Thank you!)

A monopoly faces the demand curve P = 100 -.01Q, where P is price and Q is weekly production measured in cents per unit. The firm’s cost function is C = 50Q + 20,000. Assuming the firm maximizes profit,a. What is the level of production, price, and total profit per week?b. If the government decides to put a tax of 20 cents per unit ON THE BUYERS of this product, what will be the new level of production, price the buyer pays, price the monopoly receives, and profit per week?c. What is the incidence of the tax on the buyers and on the monopoly?

Last year, Alpha Company sold 3,600 units of a single product at a price of $100 per unit. The company variable cost per unit was $75, its fixed cost for the year were $40,000.

A. How many units must ALPHA sell to break even?

B. What is ALPHA’s operating leverage? How much will ALPHA need to sell in sales dollars to earn a target profit of $80,000?

C. If ALPHA spends $18,000 and a proposed marketing campaign, it expects that sales would increase by 15%.

D. Should ALPHA approve the proposed marketing campaign (YES or NO) Why or Why not?

E. If ALPHA drops the unit price to $90, variable costs increase to $80, and fixed costs are reduced by $10,000, how many units will ALPHA need to sell to break even?

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1. Given the demand function Q = 100 - 10P, where P corresponds to price, do the following:

1. Plot the respective demand function. Be sure to label your axes. For what price will Q = 0? When P = 0, what is Q?
2. Derive the expression for the own-price elasticity. Is the own-price elasticity constant along all points on the demand curve? What price range insures that the demand for Q is inelastic?
3. Derive the inverse demand function. That is, rewrite the demand function such that

Company ABC has 10,000 shares outstanding and the stock price is $100. The company is expected to pay a dividend of $10 per share next year and thereafter the dividend is expected to grow indefinitely by 6% a year. The company now makes an announcement: It will repurchase shares next year instead of issuing cash dividends. But from year 2 on the payout policy stays the same. (8 points) a. What is the expected rate of return on the stock? b. At what price will the company repurchase shares next year? How many shares will be repurchased? c. After the payout, what is the percentage ownership of an investor who holds 1% of the shares before the payout and does not sell shares during the repurchase? d. What is the present value of all future dividends to this investor?

1. Stock Valuation: A stock has an initial price of $100 per share, paid a dividend of $2.00 per share during the year, and had an ending share price of $125. Compute the percentage total return, capital gains yield, and dividend yield.

Capital Gains = 125-100 = 25 and Dividend Yield = $2

            Total return percent = (25+2)/100 = 27/100 = 27%

            Capital Gain return = 25/100 = 25%

            Dividend Yield = 2/100 = 2%

2. Total Return: You bought a share of 4% preferred stock for $100 last year. The market price for your stock is now $120. What was your total return for last year?

Dividend = 4% of 100 = $4. The capital gain = 120-100 = 20

Total return for last year = $24 = 24%

3. CAPM - A stock has a beta of 1.20, the expected market rate of return is 12%, and a risk-free rate of 5 percent. What is the expected rate of return of the stock?

CAPM - Expected return of Stock = Rf + beta*(Rm - Rf) = 5 +1.2*(12-5) = 13.4%

4. WACC: The Corporation has a targeted capital structure of 80% common stock and 20% debt. The cost of equity is 12% and the cost of debt is 7%. The tax rate is 30%. What is the company's weighted average cost of capital (WACC)?

We*Re + Wd*Rd*(1-T) = 0.8*12 + 0.2*7*(1-0.3) = 10.58%

5. Flotation Costs: Medina Corp. has a debt-equity ratio of .75. The company is considering a new plant that will cost $125 million to build. When the company issues new equity, it incurs a flotation cost of 10%. The flotation cost on new debt is 4%. What is the initial cost of the plant if the company raises all equity externally?

125 million will be raised by issuing both debt and equity so that D/E remains 0.75.

D = 0.75E

E + 0.75E = 125

E = 71.43, D =125- 71.43 = 53.57

Initial cost of the plant will be = 125 + 71.43*0.10 + 53.57*0.04 = 125 + 9.2858 = 134.2858

1. Stock Valuation: A stock has an initial price of $100 per share, paid a dividend of $2.00 per share during the year, and had an ending share price of $125. Compute the percentage total return, capital gains yield, and dividend yield.

Capital Gains = 125-100 = 25 and Dividend Yield = $2

            Total return percent = (25+2)/100 = 27/100 = 27%

            Capital Gain return = 25/100 = 25%

            Dividend Yield = 2/100 = 2%

2. Total Return: You bought a share of 4% preferred stock for $100 last year. The market price for your stock is now $120. What was your total return for last year?

Dividend = 4% of 100 = $4. The capital gain = 120-100 = 20

Total return for last year = $24 = 24%

3. CAPM - A stock has a beta of 1.20, the expected market rate of return is 12%, and a risk-free rate of 5 percent. What is the expected rate of return of the stock?

CAPM - Expected return of Stock = Rf + beta*(Rm - Rf) = 5 +1.2*(12-5) = 13.4%

4. WACC: The Corporation has a targeted capital structure of 80% common stock and 20% debt. The cost of equity is 12% and the cost of debt is 7%. The tax rate is 30%. What is the company's weighted average cost of capital (WACC)?

We*Re + Wd*Rd*(1-T) = 0.8*12 + 0.2*7*(1-0.3) = 10.58%

5. Flotation Costs: Medina Corp. has a debt-equity ratio of .75. The company is considering a new plant that will cost $125 million to build. When the company issues new equity, it incurs a flotation cost of 10%. The flotation cost on new debt is 4%. What is the initial cost of the plant if the company raises all equity externally?

125 million will be raised by issuing both debt and equity so that D/E remains 0.75.

D = 0.75E

E + 0.75E = 125

E = 71.43, D =125- 71.43 = 53.57

Initial cost of the plant will be = 125 + 71.43*0.10 + 53.57*0.04 = 125 + 9.2858 = 134.2858

Based on the above answers explain how companies make financial decisions

What is the price of a four-year zero-coupon (or pure discount) bond with a $100 face value and yield to maturity (YTM) of 5.95%?

The Japanese government issued a zero-coupon bond with maturity of 2054 and face value of ?50,000. The current price of this bond is ?42,690. Find its YTM in percentage

Suppose we have a seven-year bond with face value of $1000, a coupon rate of 7%, quarterly coupon payments, and a yield to maturity of 5% APR. Find its price.

The current market price of a two-year 25% coupon bond, paying annual coupons with $100 face value is trading at $121.97. The current market price of a one year zero coupon bond with $100 face value is $89.28.  

1. What must the price of a two-year zero coupon bond with a $100 face value be in order to avoid arbitrage? (6 points)

(Hint: Let P be the value of a two year zero coupon bond with $100 face value if needed.)

2. Suppose the price of the two year zero coupon bond with a face value of $100 is $76. Is there an arbitrage opportunity? If yes, describe in details the transactions you will put together in order to capture the profits upfront.  (9 points)
3. Practically, what are the constraints you might face when executing the trade you proposed in b.  (5 points)