1. Find the present value of the following:

a. (10) A preferred stock with dividend = $4.50, if r = 5%.

b10) A contract that pays $10,000/year each year for the first 10 years; then $20,000/year for the following 10 years. Assume the required return is 10%, and all payments are made at the end of each year.

2. Three friends each own portfolios consisting of a diversified stock index fund and short term risk-free Treasury bills. The risk-free rate of return is R_f = 4% and the stock market index fund has an expected return of R_mbar = 10% with a standard deviation of _m = 6%.

For each friend, find the portfolio weights for each investment (w_m and w_rf ), the expected portfolio rate of return, and the portfolio standard deviation of return.

a (12). Tanya has $50,000 to invest. She purchases $30,000 in stocks, and puts the rest into T-bills.

b. (12) Bruce has $25,000 to invest. He borrows an extra $20,000 from his broker at the risk-free rate, and puts all the funds into stocks.

c. (12) Camille has $9000 to invest. She puts all her funds in risk-free T-bills.

d. (14) Suppose after the friends invest, a recession occurs and the actual stock market return is -20%. What rate of return will each friend actually earn in this circumstance? Whose portfolio performed best?

5. Steve owns shares of stock in Spectron Corp., a manufacturer of microscopes. Spectron has a beta value of b_s = 1.9. Currently the overall stock markets expected rate of return is R_m= 10%, and the risk-free rate of return is R_f = 4%.

a. (5) What is the market risk premium at this time?

b.(10) What is the required rate of return on Spectron Corp. stock?

c. (15) If the stocks most recent dividend was $1.50 and its growth in dividends is expected to remain constant at 4%, what is the stocks market price?

d. (20) Steve learns that Spectrons management plans to begin marketing its product line in China. Steve believes that this change in marketing strategy will cause Spectrons beta value to rise to b_s = 2.2, and its growth rate in dividends to rise to 7%. If he is correct, what is the new required rate of return for this stock? What will the new stock price be? Should he sell his shares now before this marketing change occurs, or buy more shares ?

6. Branford Foods has the following capital structure: $140,000,000 common stock (equity)

20,000,000 preferred stock

40,000,000 long term bonds (debt)

The firm's beta value, estimated from market data, is 1.2

The risk-free rate is 1%, and the market risk premium is 9%

Investors' required rate of return on the preferred stock is 7%, and the required rate of return on the bonds is 7.5%. The firm's marginal tax rate is 25%.

a. (6) Find the weights we, wps and wd that reflect this firm's capital structure.

b. (32) Find the firm's weighted average cost of capital (W.A.C. C.)

c. (12) The firm is considering purchasing a mixing machine that costs $50,000 today. This asset will yield an annual cash flow of $7,000 per year, at the end of each year, for 10 years. Find the NPV of this asset, using your answer from part b as needed. Should the firm proceed with purchasing this asset?

SECTION B. 50 points each 1. Find the present value of the following: a. (10) A preferred stock with dividend = $4.50, if r = 5%. b 10) A contract that pays $10,000/year each year for the first 10 years; then $20,000/year for the following 10 years. Assume the required return is 10%, and all payments are made at the end of each year. 2. Three friends each own portfolios consisting of a diversified stock index fund and short term risk-free Treasury bills. The risk-free rate of return is Rf = 4% and the stock market index fund has an expected return of Rmbar = 10% with a standard deviation of m = 6%. For each friend, find the portfolio weights for each investment (w m and wrf ), the expected portfolio rate of return, and the portfolio standard deviation of return. a (12). Tanya has $50,000 to invest. She purchases $30,000 in stocks, and puts the rest into Tbills. b. (12) Bruce has $25,000 to invest. He borrows an extra $20,000 from his broker at the risk-free rate, and puts all the funds into stocks. c. (12) Camille has $9000 to invest. She puts all her funds in risk-free T-bills. d. (14) Suppose after the friends invest, a recession occurs and the actual stock market return is -20%. What rate of return will each friend actually earn in this circumstance? Whose portfolio performed best? 5. Steve owns shares of stock in Spectron Corp., a manufacturer of microscopes. Spectron has a beta value of s = 1.9. Currently the overall stock market's expected rate of return is R m= 10%, and the risk-free rate of return is Rf = 4%. a. (5) What is the market risk premium at this time? b.(10) What is the required rate of return on Spectron Corp. stock? c. (15) If the stock's most recent dividend was $1.50 and its growth in dividends is expected to remain constant at 4%, what is the stock's market price? d. (20) Steve learns that Spectron's management plans to begin marketing its product line in China. Steve believes that this change in marketing strategy will cause Spectron's beta value to rise to s = 2.2, and its growth rate in dividends to rise to 7%. If he is correct, what is the new required rate of return for this stock? What will the new stock price be? Should he sell his shares now before this marketing change occurs, or buy more shares ? 6. Branford Foods has the following capital structure: $140,000,000 common stock (equity) 20,000,000 preferred stock 40,000,000 long term bonds (debt) The firm's beta value, estimated from market data, is 1.2 The risk-free rate is 1%, and the market risk premium is 9% Investors' required rate of return on the preferred stock is 7%, and the required rate of return on the bonds is 7.5%. The firm's marginal tax rate is 25%. a. (6) Find the weights we, wps and wd that reflect this firm's capital structure. b. (32) Find the firm's weighted average cost of capital (W.A.C. C.) c. (12) The firm is considering purchasing a mixing machine that costs $50,000 today. This asset will yield an annual cash flow of $7,000 per year, at the end of each year, for 10 years. Find the NPV of this asset, using your answer from part b as needed. Should the firm proceed with purchasing this asset? SECTION B. 50 points each 1. Find the present value of the following: a. (10) A preferred stock with dividend = $4.50, if r = 5%. Solution: PV of preferred stock = D / r = $4.50 / 0.05 = $90.00 b 10) A contract that pays $10,000/year each year for the first 10 years; then $20,000/year for the following 10 years. Assume the required return is 10%, and all payments are made at the end of each year. Solution: PV of $10,000 paid each year = $10,000 x PVIFA10%,10 = $10,000 x 6.1446 = $61,446 PV of $20,000 paid each year = $20,000 x PVIFA10%,10 x PVIF10%,10 = $20,000 x 6.1446 x 0.3855 = $47,375 Total value of contract = $61,446 + $47,375 = $108,821 2. Three friends each own portfolios consisting of a diversified stock index fund and short term risk-free Treasury bills. The risk-free rate of return is Rf = 4% and the stock market index fund has an expected return of Rmbar = 10% with a standard deviation of m = 6%. For each friend, find the portfolio weights for each investment (w m and wrf ), the expected portfolio rate of return, and the portfolio standard deviation of return. a (12). Tanya has $50,000 to invest. She purchases $30,000 in stocks, and puts the rest into Tbills. Solution: wm = 30,000 / 50,000 = 0.6 wrf = (50,000 - 30,000) / 50,000 = 0.4 Expected portfolio rate of return = wm x Rmbar + wrf x Rf = 0.6 x 0.10 + 0.4 x 0.04 = 0.06 + 0.016 = 0 .076 or 7.6% Portfolio standard deviation = wm x m (as standard deviation of treasury bills is zero) Portfolio standard deviation = 0.6 x 6% = 0.036 or 3.6% b. (12) Bruce has $25,000 to invest. He borrows an extra $20,000 from his broker at the risk-free rate, and puts all the funds into stocks. Solution: wm = (25,000 + 20,000) / 25,000 = 45,000 / 25,000 = 1.8 wrf = -20,000 / 25,000 = -0.8 Expected portfolio rate of return = wm x Rmbar + wrf x Rf = 1.8 x 0.10 - 0.8 x 0.04 = 0.18 - 0.032 = 0 .148 or 14.8% Portfolio standard deviation = wm x m (as standard deviation of treasury bills is zero) Portfolio standard deviation = 1.8 x 6% = 10.8% c. (12) Camille has $9000 to invest. She puts all her funds in risk-free T-bills. Solution: wm = 0 wrf = 9,000 / 9,000 = 1 Expected portfolio rate of return = wm x Rmbar + wrf x Rf = 0 + 1 x 0.04 = 0.04 or 4% =0 d. (14) Suppose after the friends invest, a recession occurs and the actual stock market return is -20%. What rate of return will each friend actually earn in this circumstance? Whose portfolio performed best? Solution: Tanya: Expected portfolio rate of return = wm x Rmbar + wrf x Rf = 0.6 x -0.20 + 0.4 x 0.04 = -0.12 + 0.016 = -0.136 or -13.6% Bruce: Expected portfolio rate of return = wm x Rmbar + wrf x Rf = 1.8 x -0.20 - 0.8 x 0.04 = -0.36 - 0.032 = -0.392 or -39.2% Camille: Expected portfolio rate of return = wm x Rmbar + wrf x Rf = 0 + 1 x 0.04 = 0.04 or 4% Camille's portfolio performed the best in this circumstance. 5. Steve owns shares of stock in Spectron Corp., a manufacturer of microscopes. Spectron has a beta value of s = 1.9. Currently the overall stock market's expected rate of return is R m= 10%, and the risk-free rate of return is Rf = 4%. a. (5) What is the market risk premium at this time? Solution: Market risk premium Rmrp = Rm - Rf = 0.10 - 0.04 = 0.06 or 6% b.(10) What is the required rate of return on Spectron Corp. stock? Solution: Required rate of return on Spectron Corp. stock = Rf + Rmrp x s = 0.04 + 0.06 x 1.9 = 0.04 + 0.114 = 0.154 or 15.4% c. (15) If the stock's most recent dividend was $1.50 and its growth in dividends is expected to remain constant at 4%, what is the stock's market price? Solution: D0 = $1.50 g = 4% Rs = 15.4% D1 = D0 x (1 + g) = $1.50 x 1.04 = $1.56 Ps = D1 / Rs - g = 1.56 / 0.154 - 0.04 = 1.56 / 0.114 = $13.68 d. (20) Steve learns that Spectron's management plans to begin marketing its product line in China. Steve believes that this change in marketing strategy will cause Spectron's beta value to rise to s = 2.2, and its growth rate in dividends to rise to 7%. If he is correct, what is the new required rate of return for this stock? What will the new stock price be? Should he sell his shares now before this marketing change occurs, or buy more shares ? Solution: New required rate of return on Spectron Corp. stock = Rf + Rmrp x s = 0.04 + 0.06 x 2.2 = 0.04 + 0.132 = 0.172 or 17.2% D1 = D0 x (1 + g) = $1.50 x 1.07 = $1.605 Ps = D1 / Rs - g = 1.605 / 0.172 - 0.07 = 1.605 / 0.102 = $15.74 6. Branford Foods has the following capital structure: $140,000,000 common stock (equity) 20,000,000 preferred stock 40,000,000 long term bonds (debt) The firm's beta value, estimated from market data, is 1.2 The risk-free rate is 1%, and the market risk premium is 9% Investors' required rate of return on the preferred stock is 7%, and the required rate of return on the bonds is 7.5%. The firm's marginal tax rate is 25%. a. (6) Find the weights we, wps and wd that reflect this firm's capital structure. Solution: Capital structure Common stock Preferred stock Bonds Total value Value $140,000,00 0 20,000,000 40,000,000 $200,000,00 0 Weight we = 140,000,000/200,000,000 = 0.7 wps = 20,000,000/200,000,000 = 0.1 wd = 40,000,000/200,000,000 = 0.2 b. (32) Find the firm's weighted average cost of capital (W.A.C. C.) Solution: ke = Rf + Rmrp x e = 0.01 + 0.09 x 1.2 = 0.01 + 0.108 = 0.118 or 11.8% kpf = 7% kd = 0.075 x (1 - T) = 0.075 x (1 - 0.25) = 0.05625 or 5.63% Capital structure Common stock Preferred stock Bonds Weight w 0.7 0.1 0.2 Cost k 0.1180 0.0700 0.0563 WACC = wxk 0.0826 0.0070 0.0113 0.1009 WACC = 10.09% or 10% approx. c. (12) The firm is considering purchasing a mixing machine that costs $50,000 today. This asset will yield an annual cash flow of $7,000 per year, at the end of each year, for 10 years. Find the NPV of this asset, using your answer from part b as needed. Should the firm proceed with purchasing this asset? Solution: Cost = $50,000 Annual cash flow = $7,000 per year Time period = 10 years PV of annual cash flows = $7,000 x PVIFA10%, 10 = $7,000 x 6.1446 = $43,012 NPV = PV of cash flows - Cost = $43,012 - 50,000 = -$6,988 The firm should not purchase this asset as NPV associated with it is negative. SECTION B. 50 points each 1. Find the present value of the following: a. (10) A preferred stock with dividend = $4.50, if r = 5%. Solution: PV of preferred stock = D / r = $4.50 / 0.05 = $90.00 b 10) A contract that pays $10,000/year each year for the first 10 years; then $20,000/year for the following 10 years. Assume the required return is 10%, and all payments are made at the end of each year. Solution: PV of $10,000 paid each year = $10,000 x PVIFA10%,10 = $10,000 x 6.1446 = $61,446 PV of $20,000 paid each year = $20,000 x PVIFA10%,10 x PVIF10%,10 = $20,000 x 6.1446 x 0.3855 = $47,375 Total value of contract = $61,446 + $47,375 = $108,821 2. Three friends each own portfolios consisting of a diversified stock index fund and short term risk-free Treasury bills. The risk-free rate of return is Rf = 4% and the stock market index fund has an expected return of Rmbar = 10% with a standard deviation of m = 6%. For each friend, find the portfolio weights for each investment (w m and wrf ), the expected portfolio rate of return, and the portfolio standard deviation of return. a (12). Tanya has $50,000 to invest. She purchases $30,000 in stocks, and puts the rest into Tbills. Solution: wm = 30,000 / 50,000 = 0.6 wrf = (50,000 - 30,000) / 50,000 = 0.4 Expected portfolio rate of return = wm x Rmbar + wrf x Rf = 0.6 x 0.10 + 0.4 x 0.04 = 0.06 + 0.016 = 0 .076 or 7.6% Portfolio standard deviation = wm x m (as standard deviation of treasury bills is zero) Portfolio standard deviation = 0.6 x 6% = 0.036 or 3.6% b. (12) Bruce has $25,000 to invest. He borrows an extra $20,000 from his broker at the risk-free rate, and puts all the funds into stocks. Solution: wm = (25,000 + 20,000) / 25,000 = 45,000 / 25,000 = 1.8 wrf = -20,000 / 25,000 = -0.8 Expected portfolio rate of return = wm x Rmbar + wrf x Rf = 1.8 x 0.10 - 0.8 x 0.04 = 0.18 - 0.032 = 0 .148 or 14.8% Portfolio standard deviation = wm x m (as standard deviation of treasury bills is zero) Portfolio standard deviation = 1.8 x 6% = 10.8% c. (12) Camille has $9000 to invest. She puts all her funds in risk-free T-bills. Solution: wm = 0 wrf = 9,000 / 9,000 = 1 Expected portfolio rate of return = wm x Rmbar + wrf x Rf = 0 + 1 x 0.04 = 0.04 or 4% =0 d. (14) Suppose after the friends invest, a recession occurs and the actual stock market return is -20%. What rate of return will each friend actually earn in this circumstance? Whose portfolio performed best? Solution: Tanya: Expected portfolio rate of return = wm x Rmbar + wrf x Rf = 0.6 x -0.20 + 0.4 x 0.04 = -0.12 + 0.016 = -0.136 or -13.6% Bruce: Expected portfolio rate of return = wm x Rmbar + wrf x Rf = 1.8 x -0.20 - 0.8 x 0.04 = -0.36 - 0.032 = -0.392 or -39.2% Camille: Expected portfolio rate of return = wm x Rmbar + wrf x Rf = 0 + 1 x 0.04 = 0.04 or 4% Camille's portfolio performed the best in this circumstance. 5. Steve owns shares of stock in Spectron Corp., a manufacturer of microscopes. Spectron has a beta value of s = 1.9. Currently the overall stock market's expected rate of return is R m= 10%, and the risk-free rate of return is Rf = 4%. a. (5) What is the market risk premium at this time? Solution: Market risk premium Rmrp = Rm - Rf = 0.10 - 0.04 = 0.06 or 6% b.(10) What is the required rate of return on Spectron Corp. stock? Solution: Required rate of return on Spectron Corp. stock = Rf + Rmrp x s = 0.04 + 0.06 x 1.9 = 0.04 + 0.114 = 0.154 or 15.4% c. (15) If the stock's most recent dividend was $1.50 and its growth in dividends is expected to remain constant at 4%, what is the stock's market price? Solution: D0 = $1.50 g = 4% Rs = 15.4% D1 = D0 x (1 + g) = $1.50 x 1.04 = $1.56 Ps = D1 / Rs - g = 1.56 / 0.154 - 0.04 = 1.56 / 0.114 = $13.68 d. (20) Steve learns that Spectron's management plans to begin marketing its product line in China. Steve believes that this change in marketing strategy will cause Spectron's beta value to rise to s = 2.2, and its growth rate in dividends to rise to 7%. If he is correct, what is the new required rate of return for this stock? What will the new stock price be? Should he sell his shares now before this marketing change occurs, or buy more shares ? Solution: New required rate of return on Spectron Corp. stock = Rf + Rmrp x s = 0.04 + 0.06 x 2.2 = 0.04 + 0.132 = 0.172 or 17.2% D1 = D0 x (1 + g) = $1.50 x 1.07 = $1.605 Ps = D1 / Rs - g = 1.605 / 0.172 - 0.07 = 1.605 / 0.102 = $15.74 6. Branford Foods has the following capital structure: $140,000,000 common stock (equity) 20,000,000 preferred stock 40,000,000 long term bonds (debt) The firm's beta value, estimated from market data, is 1.2 The risk-free rate is 1%, and the market risk premium is 9% Investors' required rate of return on the preferred stock is 7%, and the required rate of return on the bonds is 7.5%. The firm's marginal tax rate is 25%. a. (6) Find the weights we, wps and wd that reflect this firm's capital structure. Solution: Capital structure Common stock Preferred stock Bonds Total value Value $140,000,00 0 20,000,000 40,000,000 $200,000,00 0 Weight we = 140,000,000/200,000,000 = 0.7 wps = 20,000,000/200,000,000 = 0.1 wd = 40,000,000/200,000,000 = 0.2 b. (32) Find the firm's weighted average cost of capital (W.A.C. C.) Solution: ke = Rf + Rmrp x e = 0.01 + 0.09 x 1.2 = 0.01 + 0.108 = 0.118 or 11.8% kpf = 7% kd = 0.075 x (1 - T) = 0.075 x (1 - 0.25) = 0.05625 or 5.63% Capital structure Common stock Preferred stock Bonds Weight w 0.7 0.1 0.2 Cost k 0.1180 0.0700 0.0563 WACC = wxk 0.0826 0.0070 0.0113 0.1009 WACC = 10.09% or 10% approx. c. (12) The firm is considering purchasing a mixing machine that costs $50,000 today. This asset will yield an annual cash flow of $7,000 per year, at the end of each year, for 10 years. Find the NPV of this asset, using your answer from part b as needed. Should the firm proceed with purchasing this asset? Solution: Cost = $50,000 Annual cash flow = $7,000 per year Time period = 10 years PV of annual cash flows = $7,000 x PVIFA10%, 10 = $7,000 x 6.1446 = $43,012 NPV = PV of cash flows - Cost = $43,012 - 50,000 = -$6,988 The firm should not purchase this asset as NPV associated with it is negative