# Review

.xlsx
12acbf867ee728420f1d8f758dd503cc1cf8da4d.xlsx Problem 1 N 7 coupon 9% Price0 \$1,240.00 1 yr later: YTM 7% PVFA 4.76653965976411 Price1 \$1,095.33 cap gain -11.67% This is the Percent Change in price cy 7.26% Total return -4.41% 1-year return = coupon pmt+price1/Price0-1 Problem 2 Nonconstant growth 0 \$1.8000 1 \$2.0700 15% 1 \$2.0700 \$1.82 2 \$2.3805 15% 2 \$2.3805 \$1.83 3 \$2.7376 15% 3 \$2.7376 \$1.85 4 \$3.0113 10% 4 \$34.3292 \$20.33 5 \$3.1318 4% constant \$25.82 Terminal p4 \$31.32 r 14% P0 \$25.8209 P1 \$27.37 Problem 3 Cap Gains rate= G DY 6.50% . = D1/ P0 Div Yield = D1/P0 r 15% r = Div Yield + Cap Gains rate P3 \$85.00 P1=P0 * (1+g) g 8.50% P2=P1 * (1+g) P2 \$78.3410 P1 \$72.2037 P0 \$66.5472 Problem 4 TIPS coupon 5% Year PMT infl1 6% 1 \$50.0000 infl2 3% 2 \$1,050.0000 PMT in Y2 \$1,146.39 Problem 5 N 10 coupon 9% YTM 7% PVFA 7.02 Price 0 \$1,140.4716 If YTM is: 8% 9% 11% PVFA = 6.25 5.53 4.71 Price 1 \$1,062.4689 \$1,000.0000 \$905.7561 return 1.05% -4.43% -12.69% Problem 6 D1 1.2 D1 1.2 DY 6% Div Yield = D1/P0 P0 \$20.0000 Problem 7 Problem 1 . 1 year ago you purchased a 7 year, 9% coupon bond for \$1,240. Today, you sell the bond when the YTM is 7%. (a) What is your percent capital gain on this investment? (b) What is the current yield on the bond when you purchase it? (c) What is your total return on the investment over the year? BDS Corp. just paid a dividend of \$1.80 per share. You expect dividends to grow 15% per year for the next 3 years, 10% per year the year after that, and then grow at 4% per forever. (a) If the required return on this stock is 14%, what is the price today? (b) What is the expected price next year? You estimate that the growth rate in dividends for a company will be constant for the foreseeable future. How much should you pay for a share of the stock TODAY if the dividend yield is 6.50%, the required return is 15%, and you think the stock will sell for \$85 three years from now? Suppose you purchase a 2 year TIPS bond with a coupon rate of 5% and a Par value of \$1,000. If inflation in the first year is 6% and inflation in the second year is 3%, how much will the bond pay you in the second year? Suppose you buy an 10 year, 9% coupon bond when the YTM is 7%. What is your rate of return if you sell the bond next year when the YTM is: (a) 8% (b) 9% (c) 11%? Consider the following stock investment: A stock is expected to pay a dividend of \$1.20 next year, and its dividend yield is 6%. What is the price of the stock? The growth rate in the dividend payments of a manufacturing company is constant at -4% per year (The dividends are getting smaller). The stock just paid a dividend of \$4.50 per share. Investors require a return of 18% to invest in the company. (a) What is the price of a share of the stock today? (b) What is the expected price next year? (c) What is your rate of return for a 1 year investment in this stock?
12acbf867ee728420f1d8f758dd503cc1cf8da4d.xlsx g -4% g is the growth in dividends AND the capital gains rate because it is CONSTANT D0 4.5 r 18% P0 \$19.6364 P0 = D1/(r-g) P1 \$18.8509 r 18.00% one year return = (div+sale)/pruchase-1 Problem 8. Year Cash Flows PV 1 \$1.2000 1 \$1.2000 \$1.05 2 \$1.4000 2 \$1.4000 \$1.08 3 \$1.4500 3 \$1.4500 \$0.98 4 \$2.1000 4 \$2.1000 \$1.24 5 \$3.6000 \$63.5000 5 \$67.1000 \$34.85 \$39.20 r 14% P0 \$39.20 P1 \$43.49 I expect a 14% return Problem 9 P0 50 D1 2 P1 45 DY 4.00% CG -10.00% total ret -6.00% Problem 10 Buy it today, everyone thinks g = 5% D1 3.2 One year goes by, I collect \$3.20 D1 announce good news g 5% g is now 7% r 12% P0 \$45.7143 after 1 year, g = 7% P = next D/(r-g) Expected D2 \$3.4240 P1 \$68.48 1-yr return 56.80% Problem 11 This is a 1 Day investment (So no Coupon is Paid) N 12 coupon 9% YTM0 6% YTM1 7% PVFA0 8.38384394038333 Price0 \$1,251.5153 PVFA1 7.94268629656092 Price1 \$1,158.8537 1-day return -7.40% Problem 12 Annual Semi Annual N 10 20 coupon 9% 4.5% YTM 12% 6.0% semi-annual payments PVFA 5.65022302841087 11.469921219 Price \$827.9512 You expect a stock to pay dividends of \$1.20, \$1.40, \$1.45, \$2.10 and \$3.60 over the next 5 years. You will receive the first dividend exactly 1 year from now. You expect the stock to sell for a price of \$63.50 five years from now. (a) If the required return is 14% , what is the price of the stock today? (b) What is the expected price next year? You buy a share of ABC Inc today for \$50. One year later, the stock pays a dividend of \$2/share and you sell the share for \$45. (a) What was your dividend yield? (b) What was your capital gain yield? (c) What was your total return on this investment? ABC stock is expected to pay a dividend of \$3.20 per share 1 year from now. Investors expect dividends to grow 5% per year forever, and the required return on this stock is 12%. (a)What is the price of the stock today? (b) Suppose that after one year the stock pays the expected dividend, but investors now expect a growth rate of 7% per year forever from this stock. How much could you sell the stock for immediately after the new growth rate is known? (c) What is your rate of return on a one-year investment in this stock? In the morning, you purchase a 12-year, 9% coupon bond at a YTM of 6%. Later in the day, you sell the bond at a YTM of 7%. What is your 1-day rate of return on this investment? What is the price of a 10-year, 9% coupon bond that makes semi-annual coupon payments? The YTM is 12%.
12acbf867ee728420f1d8f758dd503cc1cf8da4d.xlsx Problem 1 N 7 coupon 9% Price0 \$1,240.00 1 yr later: YTM 7% PVFA 4.76653965976411 Price1 \$1,095.33 cap gain -11.67% cy 7.26% Total return -4.41% -4.41% Problem 2 0 \$1.8000 15% 1 \$2.0700 15% 2 \$2.3805 15% 3 \$2.7376 10% 4 \$3.0113 4% P4 \$31.3179 5 \$3.1318 r 14% P0 \$25.8209 P1 \$27.37 Problem 3 DY 6.50% r 15% P3 \$85.00 g 8.500% P2 \$78.3410 P1 \$72.2037 P0 \$66.5472 Problem 4 TIPS coupon 5% Year PMT infl1 6% 1 \$53.0000 infl2 3% 2 \$1,146.3900 Problem 5 N 10 coupon 9% YTM 7% PVFA 7.02 Price 0 \$1,140.4716 If YTM is: 8% 9% 11% PVFA = 6.24688791085676 5.9952468943 5.53704753 Price 1 \$1,062.4689 \$1,000.0000 \$889.2590 return 1.05% -4.43% -14.14% Problem 6 D1 1.2 DY 6% P0 \$20.0000