1. What is the price of the following quarterly bond? Is it is premium, discount or par value bond? face value: maturity: coupon rate: discount rate:
1,000 10 years 10% 8%
2. What is the price of the following semi-annual bond? Is it is premium, discount or par value bond? face value: maturity: coupon rate: discount rate:
$1,000 10 years 8% 9%
Bond Returns 3. What is the yield to maturity (YTM) and the yield to call (YTC) of the following annual bond? face value: maturity: coupon rate: price: call price: years to call:
$1,000 10 years 8% $925 $1,150 5
4. What is the yield to maturity and the yield to call of the following annual bond? face value: maturity: coupon rate: price: call price: years to call:
$1,000 50 years 10% $850 $1,100 10
5. What is the yield to maturity and the yield to call of the following semi-annual bond? face value: maturity: coupon rate: price: call price: years to call:
$1,000 10 years 10% $1,000 $1,150 4
6. What is the yield to maturity and the yield to call of the following semi-annual bond? face value: maturity: coupon rate: price: call price: years to call:
$1,000 9.5 years 7% $1,020 $1,150 3
7. What is the yield to maturity and the yield to call of the following quarterly bond? face value: maturity: coupon rate: price: call price: years to call:
1,000 10 years 10% $1,100 $1,200 5
Common Stock 8. KKL Enterprises pays a dividend of $1.50, and you expect the dividend to remain constant. How much would you pay for the stock, if your required rate of return were 11%? 9. GBS Enterprises has just paid a dividend of $2.00, and you expect the dividend to increase at 3% forever. How much would you pay for the stock, if your required rate of return were 9%?
10. GHI Corporation has just paid a dividend of $1.00, and it is expected to increase for four years at 8%. Thereafter, it will increase at 2% and r = 7%? 11. What is the price of XZZ common stock? d0 = $2.00 and is expected to increase for three years at 10%. Thereafter, it will increase at 2% and r = 7%. 12. GEF Corporation is expected to pay a constant dividend for the next three years. In the fourth year, the dividends will begin to grow constantly by 1.3%. If this year's dividend was $3.00 and the appropriate discount rate is 7%, what is the current price of GEF stock? 13. JKH Corporation is expected to pay the following dividends, d1 =$1.34; d2 = $1.78; d3 = $2.01, for the next three years. The dividends will to grow constantly by 2.4%, and the appropriate discount rate is 7%, what is the current price of JKH stock? 14. YHT Corporation is expected to pay a dividend growing at 30% for the next three years. In the fourth year, the dividends will begin to grow constantly by 1.5%. If this year's dividend was $5.00 and the appropriate discount rate is 13%, what is the current price of YHT stock?
Preferred Stock 15. A firm pays a preferred dividend of $5.50, and the required rate of return is 10.2%. What should be the price of the preferred share? 16. A firm pays a preferred dividend of $6.20, and the required rate of return is 8.9%. What should be the price of the preferred share? 17. A firm pays a preferred dividend of $3.30, and the required rate of return is 10.7%. What should be the price of the preferred share? 18. A firm pays a preferred dividend of $7.60, and the required rate of return is 8.3%. What should be the price of the preferred share?
19. A firm pays a preferred dividend of $7.45, and the required rate of return is 11.2%. What should be the price of the preferred share?
Implied Rate of Return and Growth 20. HJJ Enterprises has just paid a dividend of $1.50. If you expect the dividend to increase at 4% forever, and you are now willing to pay $27.50 for the stock. What is the implied required rate of return? 21. GII Enterprises will pay a dividend of $1.50 next year, and your required rate of return is 12%. If you expect the dividend to grow forever (at a constant rate), and you are now willing to pay $30.00 to purchase GII stock. What must the implied growth rate? 22. IIL has pays a constant dividend of $1.50, and you are now to pay $30.00 for the stock. What is the implied required rate of return? 23. IKI Enterprises has just paid a dividend of $4.50. You expect the dividend to increase at 3.2% forever, and you are now willing to pay $55.54 for the stock. What is the implied required rate of return? 24. A firm will pay a dividend of $3.31 next year, and your required rate of return is 15.7%. If you expect the dividend to grow forever (at a constant rate), and you are now willing to pay $30.00 to purchase the stock. What must the implied growth rate? 25. A firm pays a preferred dividend of $3.45 on a share currently selling for $45.33. What is the implied required rate of return?
Solutions NOTE: I include the formulae solutions but you only need to know how to do this on a financial calculator.
Bond Valuation 1. What is the price of the following annual bond? Is it is premium, discount or par value bond? face value: maturity: coupon rate: discount rate: 80.00
$1,000 10 years 8% 9%
1,000 1 VD 10 1.09 10 0.09 1.09 VD $935.82 1
P/Y = 1; N = 10; I/Y = 9; PV = $935.82; PMT = -80; FV = -1,000 PMT = 1,000 x 0.08 = 80 Discount bond, since the price is less than the par value. 2. What is the price of the following annual bond? Is it is premium, discount or par value bond? face value: maturity: coupon rate: discount rate: VD
$1,000 50 years 10% 12%
100.00
1,000 1 1 50 50 0.12 1.12 1.12
VD $833.91
P/Y = 1; N = 50; I/Y = 12; PV = $833.91; PMT = -100; FV = -1,000 PMT = 1,000 x 0.10 = 100 Discount bond, since the price is less than the par value.
3. What is the value of the following semi-annual bond? Is it is premium, discount or par value bond? face value: maturity: coupon rate: discount rate:
$1,000 10 years 10% 9%
50.00 1 1,000 VD 1 102 10 2 0.09 0.09 0.09 1 1 2 2 2 VD $1,065.04 P/Y = 2; N = 20; I/Y = 9; PV = $1,065.04; PMT = -50; FV = -1,000 PMT = (1,000 x 0.10)/2 = 50 N = 10 x 2 = 20 Premium bond, since the price is greater than the par value. 4. What is the value of the following semi-annual bond? Is it is premium, discount or par value bond? face value: maturity: coupon rate: discount rate:
$1,000 9.5 years 7% 7%
NOTE: Since coupon rate = discount rate, this must be a par value bond, and the price is $1,000, or…
35.00 1 1,000 VD 1 9.52 0.07 9.52 0.07 0.07 1 1 2 2 2 VD $1,000.00 P/Y = 2; N = 19; I/Y = 7; PV = $1,000.00; PMT = -35; FV = -1,000 PMT = (1,000 x 0.07)/2 = 35 N = 9.5 x 2 = 19 Par value bond, since the price equals the par value.
5. What is the value of the following semi-annual bond? Is it is premium, discount or par value bond? face value: maturity: coupon rate: discount rate:
$1,000 20 years 9% 10%
45.00 1 1,000 VD 1 202 20 2 0.10 0.10 0.10 1 1 2 2 2 VD $914.20 P/Y = 2; N = 40; I/Y = 10; PV = $914.20; PMT = -45; FV = -1,000 PMT = (1,000 x 0.09)/2 = 45 N = 20 x 2 = 40 Discount bond, since the price is less than the par value. 6. What is the price of the following quarterly bond? Is it is premium, discount or par value bond? face value: maturity: coupon rate: discount rate:
1,000 10 years 10% 8%
25.00 1 1,000 VD 1 10 4 10 4 0.08 0.08 0.08 1 1 4 4 4 VD $1,136.78 P/Y = 4; N = 40; I/Y = 8; PV = $1,136.78; PMT = -25; FV = -1,000 PMT = (1,000 x 0.10)/4 = 45 N = 10 x 4 = 40 Premium bond, since the price is greater than the par value.
7. What is the price of the following semi-annual bond? Is it is premium, discount or par value bond? face value: maturity: coupon rate: discount rate:
$1,000 10 years 8% 9%
40.00 1 1,000 VD 1 102 10 2 0.09 0.09 0.09 1 1 2 2 2 VD $934.96 P/Y = 2; N = 20; I/Y = 9; PV = $934.96; PMT = -40; FV = -1,000 PMT = (1,000 x 0.08)/2 = 40 N = 10 x 2 = 20 Discount bond, since the price is less than the par value.
Bond Returns 8. What is the yield to maturity (YTM) and the yield to call (YTC) of the following annual bond? face value: maturity: coupon rate: price: call price: years to call:
$1,000 10 years 8% $925 $1,150 5
YTM: P/Y = 1; N = 10; I/Y = 9.18%; PV = 925; PMT = -80; FV = -1,000 PMT = 1,000 x 0.08 = 80 YTC: P/Y = 1; N = 5; I/Y = 12.44%; PV = 925; PMT = -80; FV = -1,150 PMT = 1,000 x 0.08 = 80
9. What is the yield to maturity and the yield to call of the following annual bond? face value:
$1,000
maturity: coupon rate: price: call price: years to call:
50 years 10% $850 $1,100 10
YTM: P/Y = 1; N = 50; I/Y = 11.77%; PV = 850; PMT = -100; FV = -1,000 PMT = 1,000 x 0.10 = 100 YTC: P/Y = 1; N = 10; I/Y = 13.34%; PV = 850; PMT = -100; FV = -1,100 PMT = 1,000 x 0.10 = 100
10. What is the yield to maturity and the yield to call of the following semi-annual bond? face value: maturity: coupon rate: price: call price: years to call:
$1,000 10 years 10% $1,000 $1,150 4
YTM: P/Y = 2; N = 20; I/Y = 10%; PV = 1,000; PMT = -50; FV = -1,000 PMT = (1,000 x 0.10)/2 = 50 N = 10 x 2 = 20 YTC: P/Y = 2; N = 8; I/Y = 12.98%; PV = 1,000; PMT = -50; FV = -1,150 PMT = (1,000 x 0.10)/2 = 50 N=4x2=8
11. What is the yield to maturity and the yield to call of the following semi-annual bond? face value: maturity: coupon rate: price: call price: years to call:
$1,000 9.5 years 7% $1,020 $1,150 3
YTM: P/Y = 2; N = 19; I/Y = 6.71%; PV = 1,020; PMT = -35; FV = -1,000 PMT = (1,000 x 0.07)/2 = 35 N = 9.5 x 2 = 19
YTC: P/Y = 2 ; N = 6; I/Y = 10.58%; PV = 1,020; PMT = -35; FV = -1,150 PMT = (1,000 x 0.07)/2 = 35 N=3x2=6
12. What is the yield to maturity and the yield to call of the following quarterly bond? face value: maturity: coupon rate: price: call price: years to call:
1,000 10 years 10% $1,100 $1,200 5
YTM: P/Y = 4; N = 40; I/Y = 8.51%; PV = 1,100; PMT = -25; FV = -1,000 PMT = (1,000 x 0.10)/4 = 45 N = 10 x 4 = 40 YTC: P/Y = 4; N = 20; I/Y = 10.50%; PV = 1,100; PMT = -25; FV = -1,200 PMT = (1,000 x 0.10)/4 = 45 N = 5 x 4 = 20
Common Stock 13. KKL Enterprises pays a dividend of $1.50, and you expect the dividend to remain constant. How much would you pay for the stock, if your required rate of return were 11%? 1.50
VCE
VCE
0.11
$13.64
14. GBS Enterprises has just paid a dividend of $2.00, and you expect the dividend to increase at 3% forever. How much would you pay for the stock, if your required rate of return were 9%? VCE VCE
2.00 1.03
0.09
0.03
$34.33
15. GHI Corporation has just paid a dividend of $1.00, and it is expected to increase for four years at 8%. Thereafter, it will increase at 2% and r = 7%? d0 = $1.00; d1 = $1.08; d 2 = $1.17; d3 = $1.26; d4 = $1.36; d5 = $1.39 VCE
1.08 1.07
1.17
1.07
2
1.26
1.07
3
1.36
1.07
4
1.39 0.07 0.02 4 1.07
VCE $25.30
16. What is the price of XZZ common stock? d0 = $2.00 and is expected to increase for three years at 10%. Thereafter, it will increase at 2% and r = 7%. d0 = $2.00; d1 = $2.20; d 2 = $2.42; d3 = $2.66; d4 = $2.71 VCE
VCE
2.20 1.07
2.42
1.07
2
2.66
1.07
3
2.71 0.07 0.02 3 1.07
$50.59
17. GEF Corporation is expected to pay a constant dividend for the next three years. In the fourth year, the dividends will begin to grow constantly by 1.3%. If this year's dividend was $3.00 and the appropriate discount rate is 7%, what is the current price of GEF stock? d0 = $3.00; d1 = $3.00; d2 = $3.00; d3 = $3.00; d4 = $3.04 3.04
VCE VCE
3.00 1 0.07 0.013 1 3 3 0.07 1.07 1.07 $51.41
18. JKH Corporation is expected to pay the following dividends, d1 =$1.34; d2 = $1.78; d3 = $2.01, for the next three years. The dividends
will to grow constantly by 2.4%, and the appropriate discount rate is 7%, what is the current price of JKH stock?
d1 = $1.34; d 2 = $1.78; d3 = $2.01; d4 = $2.06 VCE
1.34 1.78 1.07 1.072
2.01
1.07
3
2.06 0.07 0.024 3 1.07
VCE $40.97 19. YHT Corporation is expected to pay a dividend growing at 30% for the next three years. In the fourth year, the dividends will begin to grow constantly by 1.5%. If this year's dividend was $5.00 and the appropriate discount rate is 13%, what is the current price of YHT stock? d0 = $5.00;d1 = $6.50; d2 = $8.45; d3 = $10.99; d4 = $11.15 VCE
VCE
6.50
8.45
10.99
1.13 1.132 1.133
11.15 0.13 0.015 3 1.13
$87.18
Preferred Stock 20. A firm pays a preferred dividend of $5.50, and the required rate of return is 10.2%. What should be the price of the preferred share? 5.50
VPS
VPS
0.102
$53.92
21. A firm pays a preferred dividend of $6.20, and the required rate of return is 8.9%. What should be the price of the preferred share?
VPS VPS
6.20
0.089
$69.66
22. A firm pays a preferred dividend of $3.30, and the required rate of return is 10.7%. What should be the price of the preferred share? 3.30
VPS
VPS
0.107
$30.84
23. A firm pays a preferred dividend of $7.60, and the required rate of return is 8.3%. What should be the price of the preferred share?
VPS VPS
7.60
0.083
$91.57
24. A firm pays a preferred dividend of $7.45, and the required rate of return is 11.2%. What should be the price of the preferred share?
VPS VPS
7.45
0.112
$66.52
Implied Rate of Return and Growth 25. HJJ Enterprises has just paid a dividend of $1.50. If you expect the dividend to increase at 4% forever, and you are now willing to pay $27.50 for the stock. What is the implied required rate of return? 27.50
1.50 1.04 0.04 1.50 1.04
r r
0.04
27.50 1.50 1.04 r 0.04 27.50 Implied Return 9.67%
26. GII Enterprises will pay a dividend of $1.50 next year, and your required rate of return is 12%. If you expect the dividend to grow
forever (at a constant rate), and you are now willing to pay $30.00 to purchase GII stock. What must the implied growth rate?
30.00 0.12 g g
1.50 0.12 g 1.50
30.00
1.50 30.00 1.50
0.12
0.12 30.00 Implied Growth Rate 7.00%
g
27. IIL has pays a constant dividend of $1.50, and you are now to pay $30.00 for the stock. What is the implied required rate of return?
30.00
1.59
r r
1.59
30.00 Implied Return 5.3%
28. IKI Enterprises has just paid a dividend of $4.50. You expect the dividend to increase at 3.2% forever, and you are now willing to pay $55.54 for the stock. What is the implied required rate of return? 55.54
4.50 1.032 0.032 4.50 1.032
r r
0.032
55.54 4.50 1.032 0.032 r 55.54 Implied Return 11.56%
29. A firm will pay a dividend of $3.31 next year, and your required rate of return is 15.7%. If you expect the dividend to grow forever (at a constant rate), and you are now willing to pay $30.00 to purchase the stock. What must the implied growth rate?
30.00
3.31 0.157 g
0.157 g g
3.31 30.00 3.31
3.31 30.00
0.157
0.157 30.00 Implied Growth Rate 4.67%
g
30. A firm pays a preferred dividend of $3.45 on a share currently selling for $45.33. What is the implied required rate of return?
45.33
3.45 r
3.45 45.33 Implied Return 7.61% r
