The document contains examples and problems related to valuation of bonds and shares. It discusses calculating present value of bonds with different maturity periods, yields, interest rates and cash flows. It also provides examples of calculating intrinsic value of perpetual and redeemable preference shares, and value of common shares using dividend discount model and two-stage growth model. The problems cover various bond and share valuation concepts including yield to maturity, current yield and effective yield.

1. Chapter 3: Valuation of Bonds and Shares
Problem 1
(1) 1-year government bond maturity value (Rs) 1,000
Market rate of interest 8%
PV of the bond: 1,000/1.08 (Rs) 925.93
(2) Purchase price of bond (Rs) 904.98
Implied return: (1,000 – 904.98)/904.98 10.50%
Problem 2
Perpetual interest (Rs) 140
Current yield 0.13
Price of bond (B) (Rs): 140/0.13 1076.92
Required rate 0.15
New price of bond (B) (Rs) : 140/0.15 933.33
Problem 3
Face value (Rs) 1000
Annual interest (Rs) 140
Maturity (years) 10
Maturity value (Rs) 1000
Required rate 0.12 0.14 0.16
PVAF, 10 year 5.6502 5.2161 4.8332
PVF, 10 year 0.3220 0.2697 0.2267
PV of interest (Rs) 791.03 730.26 676.65
PV of maturity value (Rs): (d x g) 321.97 269.74 226.68
PV of 10-year debenture (Rs) 1113.00 1000.00 903.34
n =10
PV of 10 - year bond = ∑ (1.12)
140
t =1
t
t
+
1,000
(1 .12 )10
= 140 × PVAF .12,10 + 1,000 × PVF.12,10
= 140 × 5 .6502 + 1,000 × 0 .3220 = Rs 1,113.00
Similar calculations can be made if the required rate is 14% or 16%.
What would happen to the present value of bond if it had a maturity of 5 years? A similar procedure can be
followed. PV of a 5-year bond at 12%, 14% and 16% respectively will be as shown below:
Required rate 0.12 0.14 0.16
PVAF, 5 year 3.6048 3.4331 3.2743
PVF, 5 year 0.5674 0.5194 0.4761
PV of interest (Rs) 504.67 480.63 458.40
PV of maturity value (Rs) 567.43 519.37 476.11
PV of 5-year debenture (Rs) 1072.10 1000.00 934.51
Problem 4
Face value (Rs) 1000
Interest rate 0.16
Interest (Rs): (1,000 x 0.16) 160
Price of bond, B0 (Rs) 800 1300 1000
INT
Yield =
B 0
0.20 0.123 0.16
Problem 5
Taxco (three-year maturity): PVF PVF

2. Year Cash flow 9% PV (Rs) 12%
1 120 0.917 110.09 0.893
2 120 0.842 101.00 0.797
3 1120 0.772 864.85 0.712
1075.94
Maxco (three-year maturity):
Year Cash flow PVF 9% PV (Rs) PVF 12%
1 60 0.917 55.05 0.893
2 60 0.842 50.50 0.797
3 1060 0.772 818.51 0.712
924.06
Taxco (eight-year maturity):
Year Cash flow 9% PV (Rs) 12%
1 120 0.917 110.09 0.893
2 120 0.842 101.00 0.797
3 120 0.772 92.66 0.712
4 120 0.708 85.01 0.636
5 120 0.650 77.99 0.567
6 120 0.596 71.55 0.507
7 120 0.547 65.64 0.452
8 1120 0.502 562.09 0.404
1166.04
Maxco (eight-year maturity):
Year Cash flow PVF 9% PV (Rs) PVF 12%
1 60 0.917 55.05 0.893
2 60 0.842 50.50 0.797
3 60 0.772 46.33 0.712
4 60 0.708 42.51 0.636
5 60 0.650 39.00 0.567
6 60 0.596 35.78 0.507
7 60 0.547 32.82 0.452
8 1060 0.502 531.98 0.404
833.96
Problem 6
(1) Annual compounding: Annual interest rate 12%
Discount rate - annual 10% 12%
Period Cash flow PVF PV PVF
1 to 5* 120 3.791 454.89 3.605
5 1,000 0.621 620.92 0.567
620.92
* Annuity factor
(2) Half-yearly compounding: Half-yearly interest rate 6%
Discount rate -half-yearly 5% 6%
Period Cash flow PVF PV PVF
1 to 10* 60 7.722 463.30 7.360
10 1,000 0.614 613.91 0.558
1,077.22
* Annuity factor
(3) Quarterly compounding: Quarterly interest rate 3%
Discount rate -half-yearly 2.50% 3%
Period Cash flow PVF PV PVF
1 to 20 60 15.589 935.35 14.877

3. 20 1,000 0.610 610.27 0.554
1,545.62
* Annuity factor
Problem 7
Face value (Rs) 1,000
Maturity periods (half-yearly) 20
Half-yearly interest rate 6%
Interest payment period 10
Maturity value (Rs) 1,050
Required rate (half-yearly) 7%
Interest payment, 11 to 20 years (Rs) 60.00
Value of interest (Rs) 214.23
Value of maturity value (Rs) 271.34
Value of bond (Rs) 485.57
20
∑ (1.07)
60t 1,050
Valueof bond = t
+
t =11
(1.07)n
20(
= 60 × PVAF ,7% − PVAF ,7% + 1,050 × PVF ,7%
10 20 )
= 60 × (10.5940 − 7.0236) + 1,050 × 0.2584 = Rs 485.57
Problem 8
Bond 1 Bond 2 Bond 3 Bond 4
Interest rate 16% 14% 12% 12%
Required rate of return 15% 13% 8% 8%
Maturity period (years) 25 15 20 10
Par/maturity value (Rs) 100 100 100 100
Semi-annual interest rate 8.00% 7.00% 6.00% 6.00%
Required rate of return (half-yearly) 7.50% 6.50% 4.00% 4.00%
Compounding periods 50 30 40 20
PVAF (annuity) 12.9748 13.0587 19.7928 13.5903
Half-yearly interest (Rs) 8 7 6 6
PV of interest (Rs) 103.80 91.41 118.76 81.54
PVF (lump sum) 0.0269 0.1512 0.2083 0.4564
PV of maturity value (Rs) 2.69 15.12 20.83 45.64
Bond value (Rs) 106.49 106.53 139.59 127.18
Current market price of bonds (Rs) 95 100 110 115
Annual yields (by trial & error) 16.86% 14.00% 10.76% 9.60%
Semi-annual yield (by trial & error) 8.43% 7.00% 5.39% 4.82%
Value of a bond that pays interest half-yearly can be calculated by the following equation:
2n 1 ( INT t )
∑ 2 Bn
B0 = kd
+ k d 2n
t =1 (1 + 2
)t (1 + 2
)
Problem 9

4. 20 − year bond redeemable in 12 years : Half - yearly interes t 5%; periods 24
24
∑ (1 + YTC )
50 t 1,150
1, 000 = t
+
t =1
(1 + YTC ) n
YTC = 5 . 32 %
24
∑ (1 + YTC )
50 t 1,100
1, 000 = t
+
t =1
(1 + YTC ) n
YTC = 5 . 22 %
20 − year bond redeemable in 8 years : Half - yearly interes t 5%; periods 16
16
∑ (1 + YTC )
50 t 1,150
1, 000 = t
+
t =1
(1 + YTC ) n
YTC = 5 . 60 %
Problem 10
20 − year bond redeemable in 12 years : Half - yearly interest 5%; periods 24
24
∑ (1 + YTC )
50 t 1,150
1,000 = +
t
t =1
(1 + YTC ) n
YTC = 5 .32 %
24
∑ (1 + YTC )
50 t 1,100
1,000 = +
t
t =1
(1 + YTC ) n
YTC = 5 .22 %
20 − year bond redeemable in 8 years : Half - yearly interest 5%; periods 16
16
∑ (1 + YTC )
50 t 1,150
1,000 = +
t
t =1
(1 + YTC ) n
YTC = 5 .60 %
Problem 11
Annual interest rate 15%
Quarterly interest rate 3.75%
Market price (Rs) 875
Maturity value (Rs) 1000
Quarterly periods 60
New interest rate 12.00%
New quarterly interest rate 3.00%
Stated yield
Quarterly interest (Rs) 37.5
Market price (Rs) 875
Quarterly yield 4.34%
Expected yield
Quarterly interest (Rs) 30
Market price (Rs) 875
Quarterly yield 3.50%
Quarterly yields can be found by trial and error. You can also use the Excel formula for rate to calculate yield:
= RATE(nper,pmt,pv,[fv],[type],guess)
Problem 12
Value of perpetual preference share =12/0.10 = Rs 120 120

5. 7
∑
12 t 110
Value of redeemable preference share = t
+
t =1
(1 . 10 ) (1 . 10 ) 7
= 12 × PVAF 7 ,10 % + 110 × PVF 7 ,10 %
= 12 × 4 . 868 + 110 × 0 . 513 = Rs 114 . 87
You can use the Excel formula to calculate value of redeemable preference share: =PV(rate,nper,pmt,[fv],[type])
Problem 13
Expected DPS (Rs) 3.00
Current share price (Rs) 50.00
Share price after 1 year (Rs) 53.00
Required rate 0.10
PV of share (Rs):
DIV 1 + P1 3 + 53
P = = 50.91
(1 + k e )1 1 .1
Return on share:
DIV1 + (P1 − P0 ) 3 + 53 − 50 12%
re = = =
P0 50
Problem 14
Share price (Rs) 75.00
Capitalisation rate 0.12
Year DPS Share price (Rs) PVF PV
(Rs) at 12% (Rs)
0
1 7.50 0.8929 6.70
2 7.50 0.7972 5.98
3 9.00 0.7118 6.41
4 15.00 0.6355 9.53
4 70.00 0.6355 44.49
Value of the share 73.10
It is a desirable investment since the present value of the share is more than its current price.
Problem 15
Current share price 60.00
DPS 1.50
Growth rate 0.10
Required rate 0.12
Value of the share:
DIV 1
P0 =
k e − g
82.5
1 . 5 (1 . 1 ) 1 . 65
= = = 82 . 50
0 . 12 − 0 . 10 0 . 02
Share should be bought

6. Problem 16
Earnings growth up to 7 years 0.15
Perpetual growth after 7 years 0.09
Required rate for 7 years 0.12
Required rate after 7 years 0.10
EPS 4.00
DPS 2.00
DPS PVF PV
Year (Rs) @ 12% (Rs)
0 2.00
1 2.30 0.8929 2.05
2 2.65 0.7972 2.11
3 3.04 0.7118 2.17
4 3.50 0.6355 2.22
5 4.02 0.5674 2.28
6 4.63 0.5066 2.34
7 5.32 0.4523 2.41
15.58
Present value of dividend growing perpetually after 7 years
DIV 7 (1 + g n ) 5.32 (1.09 )
P7 = = = Rs 579.88 579.88
ke − gn 0.10 − 0.09
PV of Rs 579.88
579 . 88 1 . 10 7 = 579.88 × 0.5132 = Rs 297.57 297.57
Value of share: 15.58 + 297.57 313.16
Problem 17
(Rs)
Current EPS 5
Retention ratio, b 0.6
Current DPS, DIV0 = EPS0(1 - b) 2
Rate of return, r 0.15
Required rate, ke 0.13
Current share price (Rs) 60
Growth, g = b x r 0.09
Expected EPS (Rs): EPS1 = EPS0(1+g) = 5 x 1.09 5.45
Expected DPS (Rs): DIV1 = DIV0(1+g) = 2 x 1.09 2.18
Expected retained earnings, RE1 = EPS1 - DIV1 3.27
Value of share if g = 0
EPS 1 5 . 45
P 0 = =
k e − g 0 . 13 − 0
41.92
Value of share if g = 9%
D IV 1 2 ( 1 + .0 9 ) 2 .1 8
P0 = = =
k e − g 0 .1 3 − . 0 9 0 .0 4 54.50
Value of growth opportunities, Vg (Rs): 54.50 - 41.92 12.58
The following formula can be used to find Vg:
RE 1 (r − k e ) 3.27 (.15 − .13) .0654
Vg = = =
k e (k e − g) .13(.13 − .09 ) .0052 12.58
Problem 18

7. Total assets (Rs) 80,000
Equity (Rs) 80,000
Number of shares 10,000
Equity per share: 80,000/10,000 8
Internal rate of return, r 10%
Earnings: 10% × 80,000 8000
EPS 0.8
Capitalisation rate, k 12%
Retention ratio, b 70%
Dividend per share, DIV: 30% × 8 0.24
Growth rate, g: b × r 7%
Expected DIV: 0.240 × 1.07 0.2568
PV of share: 0.2568/(0.12 – 0.07) 5.14
Problem 19
Last year's DPS (Rs) 3
Current market price (Rs) 80
Required rate 0.1
Scenario 1: Scenario 2: Scenario 3:
No growth Perpetual growth Different
growth rates
Growth rate 0 0.06
Value of share (Rs) 3/.10= Rs 30 3(1.06)/.1 - .06 =Rs Rs 68.84 (see
79.5 below)
Scenario 3: Different growth rates
Growth rate Year DPS (Rs) PVF
1-3 years 0.12 0 3.00
4-6 years 0.07 1 3.36 0.9091
7 year and onwards 0.04 2 3.76 0.8264
3 4.21 0.7513
4 4.51 0.6830
5 4.83 0.6209
6 5.16 0.5645
PV of DPS at 10% from year 1 to 6
PV of DPS growing perpetually at the end of 6 years: 5.37 16.6667
5.16(1.04)/(.1 - .04)
PV of value of Rs 89.50 received at the end of 6th year: 0.5645
89.5 x 0.5645
Value of share (Rs): 18.32 + 50.42
Problem 20
Current DPS (Rs) 5
Current growth rate 0.05
New growth 0.1
Capitalisation rate 0.15
Share price (Rs) if g = 5%, [5(1.05)/(0.15-.05)] 52.5
Share price (Rs) if g = 10%, [5(1.1)/(0.15-0.1)] 110
When the firm’s growth increases from 5% to 10%, the share prices rises from Rs 52.50 to Rs 110. It is quite
logical since price depends on expected dividend and future growth opportunities.
Problem 21
Face value (Rs) 10

8. Market price
EPS (Rs) Dividend rate (Rs) DPS (Rs)
Bajaj 11.9 0.50 275.0 5.0
Hero Honda 10.2 0.22 135.0 2.2
Kinetic 12.0 0.25 177.5 2.5
Maharashtra. Scooters 20.1 0.25 205.0 2.5
Bajaj has the highest current share price but it also pays maximum dividend (as a percentage of its earnings). On the other hand, Maharashtra Scooters has maximu
EPS, lowest payout, lowest dividend yield and it is ranked third in terms of share price. Hero Honda has lowest EPS and lowest share price. Kinetic ranks at third p
in terms of EPS, DPS and share price. It appears that the market is giving consideration to the companies’ current performance as well as future growth prospects.
Problem 22
DPS in year 0 (Rs) 3.5
DPS in year 10, (Rs) 10.5
Period (years) 10
1/10 0.1161
Dividend growth rate: [(10.5/3.5) -1]
Share price (Rs) 75
Expected dividend yield [3.5(1.1161)/75] 0.0521
Capitalisation rate: 0.1161 + 0.0521 0.1682
Problem 23
Current EPS (Rs) 8.6
Growth 0.12
Payout 0.4
Retention ratio: 1 - .4 0.6
Capitalisation rate 0.18
DPS (Rs) 3.44
Expected EPS: 8.6 × 1.12 9.63
Expected dividend: 3.44 ×1.12 3.85
Expected retained earnings: 9.63 x 0.60 5.78
Share value (12% growth) (Rs) 64.21
Share value (no growth) (Rs) 53.51
Value of growth opportunities: 10.70
Firm's rate of return:
g = r × b 0.20
r = g / b = . 12 / .6
Value of growth opportunities: 10.70
RE1(r − ke ) 5.78(.20− .18) .1156
Vg = = =
ke (ke − g) .18(.18− .12) .0108
Problem 24
12% 14% Pref. Equity
debenture debenture share share
Face value (Rs) 1000 1000 100 100
Interest or dividend rate 12% 14% 15%
Payment frequency annual half-yearly annual annual
Maturity (years) 12 10
Compounding periods 12 20
Maturity value (Rs) 1000 1000
Principal amount (Rs crore) 50 30 100 200
Required rate of return 0.100 0.060 0.135 0.150
PVAF (annuity) 6.8137 11.4699
PVF (lump sum) 0.3186 0.3118
Interest/dividend amount (Rs) 120 70 15 12

9. Perpetual growth rate 0.08
Market value of each debenture or share (Rs) 120 x 6.8137 70 x 11.4699
+ 1000 x .3186 + 1000 x .3118 15/.135 12/(.15 - .08)
1136.27 1114.70 111.11 171.43
Total market value (Rs crore) 56.81 33.44 111.11 342.86
Problem 25
Net profit (Rs crore) 50
Number of shares (crore) 2
EPS: 50/2 25
ROE 25%
Capitalisation rate, k 12%
Payout 60%
Retention ratio, b 40%
Dividend per share, DIV: 60% × 25 15
Growth rate, g: b × r: 40% × 25% 10%
Expected DIV: 25 × 1.10 16.5
Current share price (Rs), P0 240
Expected dividend yield: DIV1/ P0 6.88%
Capitalisation rate, k = (DIV1/ P0) + g 16.88%
Problem 26
Net earnings (Rs million) 25
Paid-up capital (Rs million) 200
Par value of share (Rs) 10
Number of shares: paid-up capital/par value of share 20
(mn.)
EPS = dividend per share, DIV (assumed): 25/20 1.25
Growth (without investment) 2%
Opportunity cost of capital 10%
Share price: P0 = (1.25 × 1.02)/ (0.10 – 0.02) 15.94
Investment (Rs million) 10
Earnings from investment (Rs million) 2
Life of investment, years 15
Investment’s NPV: PV of Rs 2 million for 15 years at
10%: 2*7.6061-10 5.21
Share price (with investment): 15.94 + 5.21 (million) 21.15
Problem 27
Earnings (without project) (Rs crore) 80
Number of shares (crore) 5
EPS: 80/5 16
Required rate of return 12.50%
Share price (without project): 16/0.125 128
Earnings from project after one year (Rs crore) 20
EPS from project: 20/5 4
Growth in earnings from project after one year 8%
Required rate of return 12.50%
Value of growth opportunities: 4/(0.125 – 0.08) 88.89
Share value with project: 128 + 88.89 216.89
EPS after project 20
P/E ratio: 216.89/20 10.84
Problem 28
Number of shares (million) 10

10. Net cash profits (Rs million) 80
Cash EPS: 80/10 8
Opportunity cost of capital 20%
(a) (i) Retention ratio 40%
Return on retained earnings 20%
Growth: 40% × 20% 8%
Expected Dividend per share, DIV1: 8 × (1 – 0.40) × 1.08 5.18
Share price: 5.18/(0.20 – 0.08) 43.20
(a) (ii) Retention ratio 60%
Return on retained earnings 20%
Growth: 60% × 20% 12%
Expected Dividend per share, DIV1: 8 × (1 – 0.60) × 1.12 3.58
Share price: 3.58/(0.20 – 0.12) 44.80
(b) (i) Retention ratio 40%
Return on retained earnings 24%
Growth: 40% × 24% 9.60%
Expected Dividend per share, DIV1: 8 × (1 – 0.40) × 1.096 5.26
Share price: 5.26/(0.20 – 0.096) 50.58
(b) (ii) Retention ratio 60%
Return on retained earnings 24%
Growth: 60% × 24% 14.40%
Expected Dividend per share, DIV1: 8 × (1 – 0.60) × 1.144 3.66
Share price: 3.66/(0.20 – 0.144) 65.37
Problem 29
Year EPS DPS
Cash EPS (perpetuity) 10 0 10.00 5.00
Payout 100% 1 10.90 5.45
DIV 10 2 11.88 5.94
Opportunity cost of capital 15% 3 12.95 6.48
(a) Share price: 10/0.15 66.67 4 14.12 7.06
(b) Expansion opportunity 5 15.39 7.69
Earnings retention 50% 6 16.77 8.39
Rate of return 18% 7 18.28 9.14
Growth: 50% × 18% 9% 8 19.93 9.96
DIV1: 5 × 1.09 5.45 9 21.72 10.86
Period of growth, years 10 10 23.67 11.84
Value of growth opportunity:
 1  n 
  1 + g   
V = DIV 1 ×  × 1 −   
k − g   1 + k  
  
  10 
1   1 . 09   37.68
= 5 . 45 ×  × 1 −   
 0 . 15 − 0 . 09   1 . 15  
  
= 5 . 45 × 16 . 67 × 0 . 4148 = Rs 37.68
10 157.80
Value after growth opportunity: (10×1.09 /0.15)
PV after growth opportunity: 157.80 × 1/1.1510 39.01
Total share price with growth opportunity: 37.68 + 39.01 76.69

11. PVF

12. PV (Rs) 6% PV (Rs)
107.14 0.943 113.21
95.66 0.890 106.80
797.19 0.840 940.37
1000.00 1160.38
PV (Rs) PVF 6% PV (Rs)
53.57 0.943 56.60
47.83 0.890 53.40
754.49 0.840 890.00
855.89 1000.00
PV (Rs) 6% PV (Rs)
107.14 0.943 113.21
95.66 0.890 106.80
85.41 0.840 100.75
76.26 0.792 95.05
68.09 0.747 89.67
60.80 0.705 84.60
54.28 0.665 79.81
452.35 0.627 702.70
1000.00 1372.59
PV (Rs) PVF 6% PV (Rs)
53.57 0.943 56.60
47.83 0.890 53.40
42.71 0.840 50.38
38.13 0.792 47.53
34.05 0.747 44.84
30.40 0.705 42.30
27.14 0.665 39.90
428.12 0.627 665.06
701.94 1000.00
16%
PV PVF PV
432.57 3.274 392.92
567.43 0.476 476.11
1000.00 869.03
8%
PV PVF PV
441.61 6.710 402.60
558.39 0.463 463.19
1,000.00 865.80
4%
PV PVF PV
892.65 13.590 815.42

13. 553.68 0.456 456.39
1,446.32 1,271.81

14. 1- yearbond
(i) Annual yield
10+100
95 = = 15%
1+ y
(ii) Half- yearlyyield
5 5 +100
95 = +
1 + y (1 + y) 2
2 − yearbond
(i) Annualyield
10 10+100
100 = +
1+ y (1 + y)
(ii) Half- yearlyyield
5 5
100 = +
1+ y (1+ y)
3 − yearbond
(i) Annualyield
10 10
110 = +
1+ y (1+ y)
(ii) Half- yearlyyield
5 5
110 = +
1+ y (1+ y)
4 − yearbond
(i) Annualyield

15. 110 = +
1+ y (1+ y)
(ii) Half- yearlyyield
5 5
110 = +
1+ y (1+ y)
114.87 4 − yearbond
(i) Annual yield
10 10
115= +
1 + y (1 + y)
(ii) Half- yearlyyield
5 5
115= +
1 + y (1 + y)

17. PV (Rs)
3.05
3.11
3.17
3.08
3.00
2.91
18.32
89.50
50.52
68.84

18. Payout Earnings Dividend
yield yield
0.420 0.0433 0.0182
0.216 0.0756 0.0163
0.208 0.0676 0.0141
0.124 0.0980 0.0122
rnings). On the other hand, Maharashtra Scooters has maximum
has lowest EPS and lowest share price. Kinetic ranks at third place
nies’ current performance as well as future growth prospects.

24. 1- yearbond
(i) Annual yield
10+100
95 = = 15%
1+ y
(ii) Half- yearlyyield
5 5 +100
95 = + = 7.8%
1 + y (1 + y) 2
2 − yearbond
(i) Annualyield
10 10+100
100 = + = 10%
1+ y (1 + y) 2
(ii) Half- yearlyyield
5 5 5 5 +100
100 = + + + = 5%
1+ y (1+ y)2 (1 + y)3 (1 + y)4
3 − yearbond
(i) Annual yield
10 10 10+100
110 = + + = 6.24%
1+ y (1+ y)2 (1 + y)3
(ii) Half- yearlyyield
5 5 5 5 5 5 +100
110 = + + + + + = 3.15%
1+ y (1+ y)2 (1 + y)3 (1 + y)4 (1 + y)5 (1 + y)6
4 − yearbond
(i) Annual yield

25. 110 = + + = 6.24%
1+ y (1+ y)2 (1 + y)3
(ii) Half- yearlyyield
5 5 5 5 5 5 +100
110 = + + + + + = 3.15%
1+ y (1+ y)2 (1 + y)3 (1 + y)4 (1 + y)5 (1 + y)6
4 − yearbond
(i) Annual yield
10 10 10 10+100
115= + + + = 5.70%
1 + y (1 + y)2 (1 + y)3 (1 + y) 4
(ii) Half- yearlyyield
5 5 5 5 5 5 5 5 +100
115= + + + + + + + = 2.87%
1 + y (1 + y)2 (1 + y)3 (1 + y)4 (1 + y)5 (1 + y)6 (1 + y)7 (1 + y)8