BUSI 370 Business Finance

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Henry Kennedy
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1 Review Session 2 February 7 th, 2016 Road Map 1. BONDS 2. COMMON SHARES 3. PREFERRED SHARES 4. TREASURY BILLS (T Bills) ANSWER KEY WITH COMMENTS

2 1. BONDS // Calculate the price of a ten-year annual pay bond with a par value of $1,000 and a 5% percent annual coupon and yield to maturity of 6.1%. Round to the nearest cent. $50 $50 $50 $ Without doing any calcula[on we know that PV < 1,000 since YTM>5% N = 10 I/Y = 4.3% PMT = 0.05 x 1,000 = 50 FV = 1,000 Solve for PV, PV =

3 2. BONDS // An investor bought a bond at par and held it for one year. If the coupon rate is 5 percent, residual maturity of the bond is 8 years, and the yield to maturity of the bond when it was sold was 6 percent. What is the holding period return of the bond? State as a decimal to four decimal places. PAR $ PV of the bond at [me 1 (sells at a discount to par: YTM is now equal to 6%, it was 5% one year ago (bonds were selling at par, therefore YTM = 5% then)). N = 8 I/Y = 6 PMT = $50 FV = $1,000 solve for PV, PV = Holding period return = (50 + ( ,000)) / 1,000 = %

4 3. BONDS // A 8 year annual pay bond is quoted at with a market yield of 4.3%. What is the coupon rate? State as a decimal and round to four decimal places. $50 $50 $50. $50 + 1, N = 8 I/Y = 4.3% PV* = FV = 1,000 Solve for PMT, PMT = or 27.6$ Coupon payment = $1,000 x coupon rate = 27.6$ => coupon rate = 2.76% * Bonds are quoted as a percentage of their face value: means 89.74% of $1,000.

5 4. BONDS // A 7-year bond paying 7 percent semi-annual-pay coupon is trading on the market at a yield of 5.39 percent. What is the percentage change in price if the market yield increases by 50 basis points? State as a decimal and round to four decimal places. N = 14 I/Y = 5.39 / 2 = effec[ve semi annual rate PMT = 0.07x1,000/2 = 35$ FV = 1,000 solve for PV => PV = - 1, N = 14 I/Y = ( ) / 2 = new effec[ve semi annual rate PMT = 0.07x1,000/2 = 35$ FV = 1,000 solve for PV => PV = - 1, % change in price = (1, ,092.85) / 1, = %

6 5. BONDS // What is current yield of a 8-year semi-annual pay bond with a par value of $1,000 and a 9.9 percent coupon rate when the bond is priced at $ ? State as a decimal and round to four decimal places. Current Yield = Annual interest $ / Bond price $99 per year / 1, = 9.57% = 6. BONDS // What is the YTM of a 9-year semi-annual pay bond with a par value of $1,000 and a 4 percent coupon rate when the bond is priced at $958.92? State as a decimal and round to four decimal places. N = 18 PV = PMT = 0.04 x 1,000/2 = 20$ FV = 1,000 solve for I/Y=> I/Y = 2.28 = effec[ve semi-annual rate => YTM = 2.28 x 2 = 4.56%

7 7. Common shares // Harbor Inc. just paid a dividend of 1.20 per share. the dividends are expected to grow at an annual rate of 3.2 percent indefinitely. What's today's stock price if the required return is 10.5 percent? Round to the nearest cent and do not include dollar signs. D0 = $1.20 per share => D1 = 1.20 x ( ) = K = 10.5% g = 3.2% P0 = D1 / (k-g) = / ( ) = $ Remember: P n = D n+1 / (k g)

8 8. Common Shares // Anna purchased a share for $53 a year ago. She received $4.76 in dividends and sold the stock for $56 one year later. If the infla[on rate over the year was 2.1, what is her exact real rate of return? State as a decimal to four decimal places. Holding period return = ( (56 53)) / 53 = [ 4.76 / 53 ] + [ (56 53] / 53 ] = dividend yield + capital gain yield = 14.64% Remember: (1+Nominal Rate) = (1+ Expected Infla[on rate) x (1+ Real rate)** ( ) = ( ) x (1 + real rate) => Real rate = ( / 1.021) 1 = 12.28% We expect to know this formula

9 9. Common Shares // Harbor Inc. is expected to pay a dividend of $1.30 per share in one year. If the dividend growth rate is 5.6 percent (g) forever and the required return is 11.5 percent, what should the stock be sold for 6 years from now? Do not include dollar signs and round to the nearest cent. DIV (1) = 1.30 DIV (2) = 1.30 x DIV(3) = 1.30 x DIV (7) = 1.30 x = * or N = 6 i/y = 5.6 PV = 1.3 PMT = 0 solve for FV => PV(6) = PV at [me 6 of Dividends 7, 8, 9 etc = / ( ) = $30.55

10 10. Common Shares // Harbor Inc's present value of growth opportuni[es per share is $6 and its current share price is $ What is the company's required rate of return if its expected EPS is $1.60? State as a decimal and round to four decimal places. P 0 = EPS 1 k + PVGO P0 = = (1.6/k) + 6 => k = 1.60 / ( ) = 9.73% EPS1: all other things being equal, assuming no growth (EPS constant) and that 100% of earnings are paid out as dividends (i.e. D1 = EPS1) EPS1 / k = PV of the stock if no growth (in this example: EPS1/k = 1.6/ = $16.444) If investors are willing to pay $22.45 per share today (instead of ) it is because they expect to benefit from future growth opportuni[es worth at least $6 per share today.

11 11. Common Shares // Harbor Inc. has just announced a dividend of $1.20 per share for this year and $1.25 for the next year. Dividends are expected to grow at a constant rate indefinitely (for the foreseeable future). What is the current stock price if the required rate of return is 14 percent? Do not include dollar signs and round to the nearest cent. P 0 = D 1 k g P0 = 1.25 / (0.14 g) =? D1 = D0 x (1+g) = 1.25 = 1.20 x (1+g) => g = (1.25/1.20) 1 = 4.167% P0 = 1.25 / ( ) = $12.71

12 12. Common Shares // Common shares Harbor Inc. has just paid a dividend of $0.72. Dividends are expected to grow at 15% for years one and two, 16% for years three and four, 7% for years five and six, and 12% therearer. What is the expected dividend for year 10 if the required return is 6%? Do not include dollar signs and round to the nearest cent. DIV(1) = 0.72 x 1.15 DIV(6)= 0.72 x x x DIV(2) = 0.72 x DIV(7)= 0.72 x x x x1.12 DIV(3) = 0.72 x x1.16 DIV(4) = 0.72 x x DIV(5) = 0.72 x x x1.07 DIV(10) = 0.72 x ( 1.15 ) 2 x ( 1.16 ) 2 x ( 1.07 ) 2 x ( 1.12 ) 4 = $2.3083

13 13. Common Shares // Harbor Inc's has just reported an EPS of $2.66 and expects to maintain a dividend payout of 35%. What is the company's price-earnings ra[o if its return on equity is 7% and the required return is 7.6%? Round to two decimals. P/E ra[o = P 0 / EPS 1 (1) g = ( 1 Payout Ra[o) x ROE = (1 0.35) x 7% = 4.55% (2) EPS 1 = EPS 0 x (1 + g) = 2.66 x = $ (3) P0 = ( x 0.35 ) / ( ) = $ (4) P/E ra[o = P 0 / EPS 1 = / = [mes P 0 = D 1 k g

14 14. Common shares // Harbor Inc's price earnings ra[o is 13. It expects to pay a dividend of $3.10 per share next year and to maintain a 45% payout ra[o. What is the company's required return if its return on equity is 8.3%? State as a decimal and round to four decimal places (1) g = ( ) x = or 4.565% (2) EPS1 x 0.45 = DIV1 = $3.10 (3) EPS 1 = 3.10 / 0.45 = $6.90 (4) P0 = 13 x EPS1 = $89.70 (5) P0 = = 3.10 / (k ) = > k = [3.10 / 89.70] = 8.021%

15 15. Preferred shares // Magic Co. has 1 million preferred shares issued at a par value of $36. The preferred shares are currently selling at $25.70 per share and the required rate is 8.4 percent. What is the dividend rate? State as a decimal to four decimal places. P pref. = $25.70 = DIV1 / => DIV1 = x = = dividend rate x $36 => dividend rate = or 6%

16 16. Preferred shares // The 2 million preferred shares of Magic Co., which pay a dividend rate of 8.3 percent on a stated value of $22, are currently worth $29,688,000. What is the risk premium associated with these preferred shares if the risk free rate is 5.9 percent? State as a decimal to four decimal places. DIV per preferred share = x $22 = $ P0 = price per share = $29,688,000 / 2,000,000 = = DIV / k = / k Therefore, k = / = or 12.30% = risk free rate + risk premium = risk premium => risk premium = = 6.4%

17 17. Preferred shares // Tri-Step Company's preferred stock is selling for $33 per share. What is the expected dividend of year 7 if the required rate of return is 8.2 percent? Do not include dollar signs and round to the nearest cent. P pref = $33 = DIV / DIV = $ per share or $2.71 Remember: preferred shares dividend is fixed

18 18. Common shares // How much would you pay for a share of stock today, if you expect it will pay a dividend of $3.80 and will sell for $30 one year from now? Assume your required rate of return on this stock is 8.7 percent. P0 =? D1 = $3.80 P1 = $30 k = 8.7% k = 8.7% = ( P0) / P0 = Dividend yield + Capital Gain Yield Therefore P0 = ( ) / = $

19 19.Common shares // How much would you pay for a share of stock today, if you expect it will pay a dividend of $2.4 each year during five years star[ng in 2 years from now and will sell for $49 in six years? Assume your required rate of return on this stock is 12.6 percent. D1 = 0 D2 = D3 = D4 = D5 = $2.40 D6 = $2.40 P6 = PV at [me 6 of D7, D8, D9 etc = $49 Use the CF func[on Enter CF0 = 0 CF1 = 0 CF2 = CF3 = CF4 = CF5 = 2.4 CF6 = D6 + P6 = = then solve for PV (using NPV key stroke) and arer entering 12.6 percent for I/YR => NPV = $31.6

20 20. T Bills // Suppose you observed that one-year T-bills are trading at a YTM of 3.2 percent. The yield spread between AAA- and BBB-rated corporate bonds is 150 basis points. The maturity yield differen[al between the one-year T-bills and the five-year government bonds is 75 basis points. What yield would you expect to observe on BBB-rated corporate bonds with a five-year maturity? State as a decimal to 4 decimal points. 1 year T bills (AAA credit ra[ng) 3.2% 5 year Canadian Government Bonds (AAA credit ra[ng) = 3.95% 5 year Corporate bond (BBB credit ra[ng) 3.95% = 5.45%

21 21. T Bills // What is the price of a 60-day Canadian T-bill with a par value of $9600 that has a quoted yield of 7.8 percent? Round to the nearest cent and do not include dollar signs. P = F / [ 1 + k BEY x n/365 ] = 9,600 / [ x 60/365 ] = $9,478.67

Section 8.3 Compound Interest

Section 8.3 Compound Interest Objectives 1. Use the compound interest formulas. 2. Calculate present value. 3. Understand and compute effective annual yield. 4/24/2013 Section 8.3 1 Compound interest is