FINN 3222 – Final Exam Study Guide - SolutionsDr. Judson Russell

1. The monthly returns for securities A, B, C, and the Market (S&P 500) are shown below.

Month A, % B, % C, % Market (S&P), %1 14.03 25.12 12.98 12.022 -12.04 -6.09 7.12 -14.863 19.32 14.51 9.12 9.234 8.53 24.09 7.12 23.945 -7.49 -12.62 -8.94 -15.72

You should know how to calculate the arithmetic and geometric returns, variance, standard deviation, correlation coefficient, covariance, and beta for each.

2. Using a two-stage dividend discount model determine the present value of a stock with a current dividend (D0) of $3 per share, expected growth of 20% for the next two years, and growth at 3% thereafter. The risk-free rate is 4%, the stock’s beta with the market is 1.1 and the expected return on the market is 10%.

3. Company XYZ has a target capital structure of 40 percent debt and 60 percent equity. Its bonds pay 10 percent coupon (semi-annual payout), mature in 20 years, and sell for $849.54 per $1,000 in face value. The company stock beta is 1.2 versus the market. The risk-free rate of interest is 10 percent and the market risk premium is 5 percent. The company is a mature, constant growth firm that just paid a dividend of $2.00 and has a stock price of $27.00 per share. The growth rate in earnings and dividends is 8 percent while the marginal tax rate is 40 percent. What is the after-tax cost of debt, the cost of equity using the CAPM approach, and the cost of equity using the discounted cash flow approach?

4. What is the modified duration for a three-year, semi-annual pay, $1,000 par value, 6.35% coupon bond that is currently priced to yield 1.98%?

5. You should make sure you practice the bonus problem---three-stage stock model. Very important that you can do that.

6. A company requires capital market financing to build a new factory in Brazil. The firm is considering two bonds---one callable, one non-callable. Both bonds pay a semi-annual coupon and have a par value of $1,000 (continued on next page)

Non-Callable CallableYears to Maturity 10 10Years to First Call na 5Coupon 7.15% 7.35%Par 100 100Call Premium na 102Price 100.71 100.71

Using the information above, calculate the Yield to Maturity on the non-callable bond. Using the information above, calculate the Yield to First Call for the callable bond.

Make sure you review the quizzes, concept checks, your midterm exam, and CFA questions for the new material since the midterm. The exam will be rigorous, but fair.

I will send the answers to the six study problems here next Wednesday. Practice these without the answers and see if you can get them correct. That way when you see the answers you’ll either be very confident or know where you made a mistake.

Formulas:

Geometric = ((1+Ri)^1/n)-1 Arthimetic = (Ri)/n = E(r)

2 = Ri – E(ri))2]/n 2

Beta = covariance / 2market Covariance = [(Ri – E(ri))(Rj – E(rj))]]/n

Covariance ab Coefficient of variation = /E(r)

E(rp) = waRa + wbRb 2p=wa22

a+ wb22

b+ 2*cov*wa*wb

Rc = yrp + (1-y)rf S = (E(rp) – rf)/p

y* (E(rp) – rf)/0.01A2p U = E(r) - 0.005A2

CAPM = rf + (E(rm) – rf) min var : wa = (2b – cov)/(2

a + 2b – 2cov)

P0 = [D1/(ke – g)] WACC = ka = wdkd(1-t)+weke

P0 = [D1/(1+ke)1 + D2/(1+ke)2 + … + (Dn+1/(ke-g)) /(1+ke)n]

Solutions:

1. The monthly returns for securities A, B, C, and the Market (S&P 500) are shown below.

Month A, % B, % C, % Market (S&P), %1 14.03 25.12 12.98 12.022 -12.04 -6.09 7.12 -14.863 19.32 14.51 9.12 9.234 8.53 24.09 7.12 23.945 -7.49 -12.62 -8.94 -15.72

You should know how to calculate the arithmetic and geometric returns, variance, standard deviation, correlation coefficient, covariance, and beta for each.

Month A, % B, % C, %Market,

%1 14.03 25.12 12.98 12.022 -12.04 -6.09 7.12 -14.863 19.32 14.51 9.12 9.234 8.53 24.09 7.12 23.945 -7.49 -12.62 -8.94 -15.72

Arithmetic 4.47 9.00 5.48 2.92Geometric 3.74 7.85 5.19 1.70Variance 148.80 242.61 56.56 245.61Standard Deviation 12.20 15.58 7.52 15.67

Correlation A B C MktA 1 0.847252 0.605601 0.818648B 0.847252 1 0.772921 0.958561C 0.605601 0.772921 1 0.619892

MKT 0.818648 0.958561 0.619892 1

Covariance A B C MktA 148.8043 160.9814 55.55984 156.5046B 160.9814 242.611 90.54336 233.9898C 55.55984 90.54336 56.56304 73.06416

MKT 156.5046 233.9898 73.06416 245.6089

beta A B C Mkt0.637211 0.952693 0.297482 1

2. Using a two-stage dividend discount model determine the present value of a stock with a current dividend (D0) of $3 per share, expected growth of 20% for the next

two years, and growth at 3% thereafter. The risk-free rate is 4%, the stock’s beta with the market is 1.1 and the expected return on the market is 10%.

k=10.6% PV 1 2 3dividends 3.6 4.32 4.4496PV d1 3.254973PV d2 3.531616 p2 = 58.54737PV P2 47.86269

P0 54.64928

3. Company XYZ has a target capital structure of 40 percent debt and 60 percent equity. Its bonds pay 10 percent coupon (semi-annual payout), mature in 20 years, and sell for $849.54 per $1,000 in face value. The company stock beta is 1.2 versus the market. The risk-free rate of interest is 10 percent and the market risk premium is 5 percent. The company is a mature, constant growth firm that just paid a dividend of $2.00 and has a stock price of $27.00 per share. The growth rate in earnings and dividends is 8 percent while the marginal tax rate is 40 percent. What is the after-tax cost of debt, the cost of equity using the CAPM approach, and the cost of equity using the discounted cash flow approach?

wd 40% kd = 12%we 60% after-tax 7.2 %

beta 1.2rf 10%MRP 5%CAPM, ke 16 %

D0 2 DCF, ke 16.00%P0 27g 8%t 40%

4. What is the modified duration for a three-year, semi-annual pay, $1,000 par value, 6.35% coupon bond that is currently priced to yield 1.98%?

t cf pvcf t*pvcf1 3.175 3.143876 3.1438762 3.175 3.113056 6.2261133 3.175 3.082539 9.2476184 3.175 3.052321 12.209295 3.175 3.022399 15.1126 103.175 97.25328 583.5197

price 112.6675 629.4586

Macaulay 5.58687Macaulay 2.793435Modified 2.766051

5. You should make sure you practice the bonus problem---three-stage stock model. Very important that you can do that. Practice…you will see one of these on final. Replicate the example I gave you in class.

6. A company requires capital market financing to build a new factory in Brazil. The firm is considering two bonds---one callable, one non-callable. Both bonds pay a semi-annual coupon and have a par value of $1,000 (continued on next page)

Non-Callable CallableYears to Maturity 10 10Years to First Call na 5Coupon 7.15% 7.35%Par 100 100Call Premium na 102Price 100.71 100.71

Using the information above, calculate the Yield to Maturity on the non-callable bond. Using the information above, calculate the Yield to First Call for the callable bond.

non-call callN 20 10i 7.04986 7.51397PV 100.71 100.71PMT 3.575 3.675FV 100 102