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Analysis of Investment Activities - Practice Question bank
(Please bring to every class a scientific calculator and this booklet.)
Topics covered
1. Efficient Markets
2. Portfolio Theory
3. CAPM and APT
4. Valuation of Bonds
5. Duration and Immunisation
6. Active Bond Management
7. Futures
8. Options
9. Portfolio hedging: Futures and Options
10. Portfolio Management
Appendices
Useful formulae
Tables
KVShenai-pq IA03
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(1) Efficient Markets
(1) If the EMH is valid:
(i) How are shares priced?
(ii) How are price changes on a share explained?
(iii) Can security Prices be forecast accurately?
(iv) What types of information can be accounted for in the different forms of efficiency?
(2) Explain which of the following announcements are likely to change share price
in an efficient market and give full reasons for why or why not:
(i) The Chairman announces at the Annual General Meeting that the previous year was a highly
successful one.
(ii) A company changes its depreciation policy and reports a higher profit.
(iii) A competitor receives approval from the patents office for a new health drug.
(iv) The Central Bank cuts interest rates by half a percent.
(v) The government revises its estimates of economic growth for the next quarter by half a
percent.
(vi) The company’s Finance Director decides to make a provision for the value of the
brands owned by the company on the asset side of the balance sheet.
(vii) The President of a successful company, who has been responsible for marketing strategy,
suddenly passes away.
(3) On the 1st May the share prices of Aggressive plc ( which has 1m shares outstanding) and
Techno plc (which has 4m shares outstanding ) are
£10.0 and £1.50/share respectively.
Assume the management of Aggressive plc following a Board meeting
on the 1st May, 1998 enter into an agreement with the management of
Techno plc to take over its shares at £2.00 per share but do not make this
information public
On the 3rd May, Aggressive plc publicly offers £2.00 per share of Techno.
On the 10th May, it emerges in published newsletters that as a result of the takeover of
Agressive by Techno the management of Agressive expected at their Board meeting of the 1st
May that the post acquisition value of Agressive would increase by
£ 9m.
Ignoring taxation, advise what you would expect the market price of the shares
of the two companies would be on May 1, May 3, May 10 if the market is
(a) semi-strong efficient
(b) strong efficient
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(2) Portfolio Theory
(1) (1) Stock X and Stock Y have an expected return of 10% and 20%, while the standard
deviation of the stocks are 5% and 15%, respectively. The correlation coefficient of the two
stocks is zero.
(a) Calculate the expected return and standard deviation of a portfolio that is composed of 90
percent X and 10 percent Y.
(b) Suppose you are risk averse would you hold 100 percent of stock X or 100% of stock Y?
(2) Share P has an expected return of 15% and a standard deviation of 12%. Share Q has an
expected rate of return of 13% and a standard deviation of 10%. Securities P and Q are
perfectly negatively correlated.
(a) What are the weights of A and B in the minimum variance portfolio?
(b) What is the return on the minimum variance portfolio?
(3) The returns on securities A and B over the last few years have been as follows:
1996
1997
1998
1999
2000
2001
A
6
4
8
11
7
10
B
20
12
12
20
18
16
(a) Calculate the mean and standard deviation of the returns of securities A and B.
(b) Calculate the covariance of returns of the two securities
(c) Calculate the correlation coefficient of the returns of the two securities.
(d) Calculate the risk and return of portfolios with the following weightings
and sketch these on a graph.
A
(i) 90%
(ii) 50%
(iii) 10%
B
10%
50%
90%
(e) If the weight of B in the minimum variance portfolio is given by the expression
w(B) = (S(A)2 – Cov AB) / ((S(A)2 + S(B)2 – 2 CovAB)
where S(A), S(B), Cov AB are the standard deviation of the returns of A, B and
Cov AB is the covariance of returns of securities A and B.
Find the minimum risk portfolio and its return.
Sketch the combinations of risk/return for the portfolios in (d) and (e) on a chart and
Identify the efficient frontier.
(3) CAPM and APT
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(1) Kaybee owns a portfolio composed of three securities. The betas of the securities
and the amounts invested are as follows. What is the beta of Kaybee’s portfolio?
Security
Beta
Amount
A
0.90
£ 450,000
B
1.30
£ 150,000
C
1.05
£ 900,000
(2) Securities X, Y, the market portfolio and t-bills have the following characteristics;:
Security
Expected Return Correlation with
Standard
market portfolio
deviation
X
17.2 %
0.90
20%
Y
8.8 %
0.80
9%
Market Portfolio
12.0 %
1.00
12%
t-bills
5.0%
(i) What are the betas of the securities?
(ii) Advise which security you would consider purchasing
(3) Mercury fund has the following portfolio
Share
proportion
Return Beta
X
0.3
18.0
1.2
Y
0.3
16.0
1.1
Z
0.4
9.0
0.6
The risk free rate of interest is 7% and the market reurn is 13%.
(a) What is the Beta of the portfolio?
(b) What is the excess return for each of the shares in the porfolio?
(c) Is Mercury Fund performing better than a synthetic portfolio on the SML with the same
Beta?
(4 ) Market model regression results for annual returns on shares A and B based on monthly data
for five years are as follows:
Stock
Market model =n
R2
Standard deviation of
residual
A
Ra=1.2+0.8Rm
0.48
10%
B
Rb=-0.8+1.2Rm
0.72
9%
The risk free rate is now 6% per annum and market returns average 14% per annum, while
market risk is 12% on the same basis.
(a) What is meant by the alpha of a stock? What are the alphas of the two stocks?
(b) What is the market risk of each stock?
(c) What is the total risk of each stock?
(d) What returns are the stocks expected to generate in the next year, assuming the market
reaches equilibrium in terms of the CAPM?
(5) Assume the returns in a market can be described in terms of a three factor model.
The risk free rate is 6%. The information available on the sensitivity
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of three stocks X,Y and Z to the various factors is as follows:
GNP
Inflation
Interest rate
Expected return
X
0.5
-1.50
–0.7
9.04%
Y
0.7
-1
-1.5
12.0%
Z
1.5
-2
1
17.3%
Factor Premium
8%
0.5%
0.3%
(a) What is the equilibrium return of each stock? Which stocks are mispriced?
(b) Discuss the market mechanism which is likely to work on mispriced stocks.
(6) Assuming a one factor model of the form, and a factor premium of 8%:
Ri = 4% + bi . F + ei
consider the following three well diversified portfolios:
Portfolio
Factor sensitivity
Expected return
A
0.80
10.4%
B
1.00
10.0%
C
1.20
13.6%
(a) Which portfolio’s expected return is not in line with the factor model relationship?
(b) What conditions must an arbitrage portfolio satisfy?
(c) Advise if an arbitrage portfolio can be constructed by investors.
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(4) Yield Curve and Valuation of Bonds
(1) Current one and two year spot yields are 10% and 8% respectively.
(a) What is the fair price for two bonds: Bond A with a 13% coupon and Bond B with a 6%
coupon, each with a two year maturity?
(b) What is their YTM?
(2) Price the strips on a 6% coupon £100 gilt with three years to redemption.
Assume interest is paid annually. Current spot rates for 1, 2 and 3 years are
8%,10% and 12% respectively.
What is the present value of the gilt?
What is its ytm?
(3) A perpetual Bond has just gone ex-int. It pays £10.00 a year. If the ytm is
8%, what is its fair price? If instead of a perpetuity it is an annuity which will be redeemed at
face value (£100) at the end of 5 years , what would be its fair price? Assume ytm is the same.
(4) You are given the following information about Gilt prices, coupon rates and maturities.
Gilt
Coupon
Market Price
Maturity
A
14%
£ 102.70
1 year
B
10%
£100.00
2 years
C
12.5%
£107.52
3 years
D
8.5%
£ 97.58
4 years
Calculate upto two decimal places, for years 1-4:
(i) the YTMs
(ii) Spot rates
(iii) Forward rates.
Plot the yield curve and offer explanations for the shape of the yield curve.
(5) Current Spot rates for one and two years are 8% and 10% respectively,
at which there are there are unlimited number of borrowers and lenders.
A lender is prepared to accept 11% for a £1,000 loan to you between years 1 and 2. Ignoring
transaction costs, work out an arbitrage strategy. What do you expect will happen in due
course?
(6) Current Spot rates for one and two years are 8% and 10% respectively.
What is the fair price for a 10% coupon bond maturing in two years’ time?
Advise any arbitrage strategy which could be applied if the bond was priced at
(a) £98-00 (b) £ 102-00 if lending, borrowing rates are the same.
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(5) Duration and Immunisation
(1) What is meant by duration ?
What is meant by convexity?
(2) For a 10% coupon bond at par value with 3 years left to maturity
(a) Calculate the duration and convexity.
(b) Estimate the price change of the bond using its duration if yields fall or rise by 1%.
(c) What is the effect of convexity on the price changes on the bond?
(3) A pension fund has a liability to payout £ 1million at the end of the fourth year.
It has the opportunity to buy the following bonds:
Bond A ; 6% coupon, redeemable at par in one year’s time.
Bond B; Zero coupon bond redeemable at par in five years’ time.
If the ytm for all periods is 8%(a) Calculate the durations of the two bonds
(b) What proportions of Bonds A and B are to be purchased to immunise the portfolio?
(ii) What is the effect of (a) a 1% increase in ytms (b) a 1% decrease in ytms. Assume flat
yield curves.
(4) A fund manager has to payout $1 million at the end of 10 years. Current yields
are 5%. Two bonds are available to immunise the position :
- a 5 year zero coupon bond
- a level perpetuity
(a) Calculate the investment required in the two bonds to completely immunise the position.
(b) What is the position at the end of the year?
(6) Active Bond Management
Riding the yield curve
The following three bonds of 3 years maturity are available:
Bond A: Zero coupon bond ,
Bond B: 8% coupon bond,
Bond C: 10% coupon bond.
The one year yield on zero coupon bond is 4%, the yield on zero coupon bonds of two years is 5%
and the yield on zero coupon bonds of three years and more is 6%. If the yield curve is expected
to remain the same shape in the foreseeable future which bond will you buy over a one year
investment period?
Horizon matching
Current ytms are 8% on all bonds.
The following three bonds are available:
Bond A: Zero coupon bond of 10 years maturity,
Bond B: 6% coupon bond of 6 years maturity,
Bond C: 10% coupon bond of two years maturity.
(i) what are their prices?
(ii If you expect the ytm one year from now to be 8%, which bond will you buy?
(iii) If you expect the ytm one year from now to be 7%, which bond will you buy?
(7) Futures
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(1) An investor buys one FTSE index contract at 5500 for delivery in December .
Contracts are valued at £10 per point.
Calculate the outcome at expiry if the index has value (i) 5250 (ii) 5850
(2) An investor sells one FTSE index contract at 5500 for delivery in December .
Contracts are valued at £10 per point.
Calculate the outcome at expiry if the index has value (i) 5350 (ii) 5950
(3) A non dividend paying stock is now quoted at $100. The t-bill rate is 6%.
(a) If the futures contract with a one year maturity on the stock is now quoted at $106, is the
futures correctly priced? Show workings.
(b) If the stock price drops by 5%, but the futures remains at $106, write out the arbitrage
strategy that can be applied.
(c) ) If the stock price drops by 5%, and the futures falls to $97, write out the arbitrage strategy
that can be applied.
(4) A share is now trading at $70. It is expected to pay a dividend of $3.50 at the end of one
year. Interest rates are 12% pa.
(a) What is the fair price of the stock at the end of one year?
(b) Suggest arbitrage strategies if the price of the one year futures on the stock is
(i) $73 (ii) $77.
(5) You are now in September. Interest costs are 6.5% pa, expected dividend
income is 3.00 % pa.
(a) If the index is trading today at 5,450
determine the fair price of the March Index future.
(b) Advise any arbitrage strategies if(i) If the March future is priced at 5600.
(8) Options
(1) Find the value of the options at their expiration dates:
Option
Market price at expiry Exercise price of Option
Calls A
12
18
B
35
25
Puts C
45
25
D
32
45
(2) On 30th September, Plastics plc shares are trading at 380p. Prices for their
traded call options are as below. Identify any arbitrage possibilities. Interest rates are 5% per
annum.
Exercise Price(p)
350
375
400
May
25
10
15
Aug
20
18
25
(3) December end puts and calls are available as below:
KVShenai-pq IA03
8
Strike
price
3800
Premia (£10 per point)
Calls
649
Puts
344
4000
4080
4200
484
370
470
400
344
420
Identify any arbitrage possibilities. Interest rates are 5% per annum.
(4) Portfolio hedging: Futures and options
It is now January 200X, the FTSE-100 index is currently at 4000. Short term interest rates are
at 5.0% per annum; the expected dividend yield on FTSE stocks is 3.0%. A Fund manager has a
well diversified portfolio of shares and a current value of £1 m. The fund has a beta of 1.0. He
feels the market may fall substantially over the next year. He is now exploring alternative
strategies to hedge his portfolio upto the end of December, 200X. December end FTSE 100
futures are priced at 4080, £10 per point.
The value of one contract =strike price x£10.
(a) Is the futures correctly priced? How many contracts are required?
(b) Are the options correctly priced? How many contracts are required if the strike price is the
forward price. The premium for puts is 400p and for calls 470p.
(b) Examine the outcomes for the fund in each of the following strategies if at the end of
December, the FTSE is
(i) 2000 (ii) 3000 (iii) 4000 (iv) 5000 (v) 6000
(1) Do nothing strategy
(2) Hedging using futures
(3) Hedging using options (at a strike price equal to the forward price)
Tabulate your results discuss the merits of each strategy. Taxes may be ignored.
(5) With the data as in question 4, examine the results of a `collar’ strategy involving purchase
of contracts of put options at an exercise price of 3800 for the full value of the portfolio and
sale of an equal number of call option contracts at an exercise price of 4200.
KVShenai-pq IA03
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(10) Portfolio Management and Performance evaluation.
(1) Star mutual fund is a well diversified fund. It generated a return of 16.8%
annually over the last four years. Its beta in this period was 1.1. The riskfree rate averaged 7.4%
pa in this period, while the return on the market averaged 15.2%pa. On the basis of the
information available, advise an investor on the relative performance of Star portfolio.
(2) Apollo fund is a common stock mutual fund and its performance compares with the Market
Index over a ten year period as below:
Apollo Fund
Market Index
Average excess monthly return
0.25
0.20
S. d. of monthly excess returns
6.3%
5.3%
Beta
1.20
1.0
Advise an investor on which fund he should invest in if he is a believer in
Mean Variance theory.
(3) Norwesco fund is a fully diversified fund with a beta of 1.1 and an actual return of
15%. TR Fund also has a return of 15%. Its beta is 1.1 and it has a specific risk of 13.33% .
The risk free return is 7% and the market return and risk are 13% and 11% respectively.
Investors can invest in the Market portfolio, Norwesco Fund, TR Fund or the risk free asset.
Advise an investor who is prepared to take on a risk of 10% of the fund he should in for the best
return-risk payoff.
(4) The beta of portfolio X is 0.8; and the expected rate of return is 12% pa, and its standard
deviation is 12% pa. The beta of portfolio Y is 1.4 ; and the expected rate of return is 17% pa
and its standard deviation is 22% pa. The t-bill rate is 4% while the return on the All Share
Index is 14% pa and its standard deviation is 12% pa.
Required:
(a) What are the Jensen, Treynor and Sharpe ratios of the three portfolios.
(b) Which measure would you consider is the most appropriate way of evaluating portfolio
performance? Why?
(c) An investor is interested in a portfolio with a risk of 10%. If you could invest in a
combination of the t-bill and one of the above portfolios, which would you choose? What
would be its expected return per annum?
(4) Sun Bond portfolio has the following characteristics, and performance:
Bond
X
Y
Z
% holding
40
30
30
Return
10
12
13
 sp
14
12
10
Duration
5
7
9
The market portfolio of bonds had a return of 12%, risk of 11% and a duration of
10 years. The return on t-bills was 6 %.
(a) What is the equation of the expost Bond Market Line?
(b) Assess the performance of the Bond Fund manager, in terms of
(i) the BML (ii) the Sharpe ratio.
KVShenai-pq IA03
10
Formulas for AIA
A. NPV and Internal Rate of Return (IRR)
NPV =

CFt
( 1 + k) t
`CFt’ is the cash inflow/(outflow) in time `t’
`k’ is the required rate of return
The `k’ which makes the NPV =0, is the IRR.
IRR= R1+((NPV(R1)/(NPV(R1)-NPV(R2))(R2-R1),
where R1 and R2 are rates of return used to discoiunt the cash flows
B. Portfolios (two asset case)
(i) Expected return on a portfolio:
E(R) = w1 R1 + w2R2,
(ii) Standard deviation of a portfolio :
p =  (w12 12 + w2 22 + 2 w1w212 12 )
(iii) Covariance = 12 12
where
w1, w2 are the relative weights invested in securities 1 and 2; w1 + w2 = 1.
R1, R2 are the returns on securities 1,2 respectively
12 is the coefficient of correlation for returns on securities 1,2
p, 1, 2 are the variances of the return on the portfolio, security 1 and security 2
respectively.
C. CML/SML
(i) Capital Market Line equation: Rp = Rf + ( Rm-Rf ) p/m
Rp is the return and p is the risk of the pth portfolio along the CML;
Rf is the riskfree rate and m is the risk of the market portfolio.
(ii) Security Market Line (SML): Rj = Rf + j ( Rm-Rf)
Where
`Rf’ is the risk free rate, `Rm’ is the return on the market portfolio
`Rj’ is the expected return on security `j,’ ` Rm,’ is the mean return on the market
portfolio; Rj is the mean return on the security;
`j’ is the market sensitivity of the security
= Covariance (j,m) / Variance (m)
=  p (Rj- Rj ) ( Rm- Rm) / ( p (Rm-Rm)2 ) = j m j / m
 p =1
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11
D. Cost of Capital Relationships (with taxation), asset and equity beta
(i) Cost of Equity Capital:
(ii) Value of Geared Firm :
Keg = Ku + ( Ku-Kd) (l - T) (B/VS)
Vg = Vu + TB (with perpetual debt)
(iii) WACC=Ku(1-TL); L=B/Vg
(iv) eg = u + (u -d)(1-T)(B/Vs)
`Ku’ is the cost of capital for the all equity firm
`Kd’ is the cost of debt
`T’ is the rate of taxation
`B’ is the value of debt
`Vs’ is the value of equity
eg is the equity beta; u is the asset beta and d is the debt beta
E. Dividend Valuation Models
General formula:
P =  ( Dt / (1+k)t )
Where `P’ is the Price of the share,
`Dt’ is the dividend in time t
Return `k’ is required by shareholders
Special cases:
(i) When the perpetual growth rate in dividends is `g,’ then
P = D1 / (k-g)
(ii) With constant dividends;
P = D1/ k
F. Forward
Fair price: Fo= So(1+CC.t)
Where Fo,So are forward and spot prices at time `o’; `CC is the carry cost
and t is the time.
G. Options
`So ’ is the value of the share at the beginning of the option period;
`P,’ ` C’ are the prices of the put and call options respectively
`u’ and `d’ are the upward and downward multipliers for the share price
at the end of the option period. Lower case letters relate to the state.
`X’ is the exercise price; `T’ is the unexpired time
`e’ is 2.71828; `rf’ is the riskfree rate of return
`’ is the variance of the return on the share
N(') = Cumulative probability under normal curve
(i) Binomial Option Pricing
(So –m Co) (1+rf) = uS - mCu = dS- mCd ;
Hedge ratio `m’ = S(u-d) / (Cu-Cd)
(ii)
Put-Call Parity:
S + P – C = PV(X)= X/ (1+rf)
(iii) B-S Option Pricing Formula
C0 = So N(d1) – Xo e-rft N(d2)
`d1’ = ln(So / Xo) + [ rf + (2 /2)]T
/  T
`d2’ = d1 - /  T
KVShenai-pq IA03
12
PRESENT VALUE TABLES
Present value of 1$ received at the end of n years (=1/(1+r)^n)
YEAR/r
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
1%
0.990
0.980
0.971
0.961
0.951
0.942
0.933
0.923
0.914
0.905
0.896
0.887
0.879
0.870
0.861
0.853
0.844
0.836
0.828
0.820
2%
0.980
0.961
0.942
0.924
0.906
0.888
0.871
0.853
0.837
0.820
0.804
0.788
0.773
0.758
0.743
0.728
0.714
0.700
0.686
0.673
3%
0.971
0.943
0.915
0.888
0.863
0.837
0.813
0.789
0.766
0.744
0.722
0.701
0.681
0.661
0.642
0.623
0.605
0.587
0.570
0.554
4%
0.962
0.925
0.889
0.855
0.822
0.790
0.760
0.731
0.703
0.676
0.650
0.625
0.601
0.577
0.555
0.534
0.513
0.494
0.475
0.456
5%
0.952
0.907
0.864
0.823
0.784
0.746
0.711
0.677
0.645
0.614
0.585
0.557
0.530
0.505
0.481
0.458
0.436
0.416
0.396
0.377
6%
0.943
0.890
0.840
0.792
0.747
0.705
0.665
0.627
0.592
0.558
0.527
0.497
0.469
0.442
0.417
0.394
0.371
0.350
0.331
0.312
7%
0.935
0.873
0.816
0.763
0.713
0.666
0.623
0.582
0.544
0.508
0.475
0.444
0.415
0.388
0.362
0.339
0.317
0.296
0.277
0.258
8%
0.926
0.857
0.794
0.735
0.681
0.630
0.583
0.540
0.500
0.463
0.429
0.397
0.368
0.340
0.315
0.292
0.270
0.250
0.232
0.215
9%
0.917
0.842
0.772
0.708
0.650
0.596
0.547
0.502
0.460
0.422
0.388
0.356
0.326
0.299
0.275
0.252
0.231
0.212
0.194
0.178
10%
0.909
0.826
0.751
0.683
0.621
0.564
0.513
0.467
0.424
0.386
0.350
0.319
0.290
0.263
0.239
0.218
0.198
0.180
0.164
0.149
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
11%
0.901
0.812
0.731
0.659
0.593
0.535
0.482
0.434
0.391
0.352
0.317
0.286
0.258
0.232
0.209
0.188
0.170
0.153
0.138
0.124
12%
0.893
0.797
0.712
0.636
0.567
0.507
0.452
0.404
0.361
0.322
0.287
0.257
0.229
0.205
0.183
0.163
0.146
0.130
0.116
0.104
13%
0.885
0.783
0.693
0.613
0.543
0.480
0.425
0.376
0.333
0.295
0.261
0.231
0.204
0.181
0.160
0.141
0.125
0.111
0.098
0.087
14%
0.877
0.769
0.675
0.592
0.519
0.456
0.400
0.351
0.308
0.270
0.237
0.208
0.182
0.160
0.140
0.123
0.108
0.095
0.083
0.073
15%
0.870
0.756
0.658
0.572
0.497
0.432
0.376
0.327
0.284
0.247
0.215
0.187
0.163
0.141
0.123
0.107
0.093
0.081
0.070
0.061
16%
0.862
0.743
0.641
0.552
0.476
0.410
0.354
0.305
0.263
0.227
0.195
0.168
0.145
0.125
0.108
0.093
0.080
0.069
0.060
0.051
17%
0.855
0.731
0.624
0.534
0.456
0.390
0.333
0.285
0.243
0.208
0.178
0.152
0.130
0.111
0.095
0.081
0.069
0.059
0.051
0.043
18%
0.847
0.718
0.609
0.516
0.437
0.370
0.314
0.266
0.225
0.191
0.162
0.137
0.116
0.099
0.084
0.071
0.060
0.051
0.043
0.037
19%
0.840
0.706
0.593
0.499
0.419
0.352
0.296
0.249
0.209
0.176
0.148
0.124
0.104
0.088
0.074
0.062
0.052
0.044
0.037
0.031
20%
0.833
0.694
0.579
0.482
0.402
0.335
0.279
0.233
0.194
0.162
0.135
0.112
0.093
0.078
0.065
0.054
0.045
0.038
0.031
0.026
YEAR/r
KVShenai-pq IA03
13
ANNUITY TABLES
Present value of 1$ received every year at the end of n years (=1/r(1- 1/(1+r)^n))
YEAR/r
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
1%
0.990
1.970
2.941
3.902
4.853
5.795
6.728
7.652
8.566
9.471
10.368
11.255
12.134
13.004
13.865
14.718
15.562
16.398
17.226
18.046
2%
0.980
1.942
2.884
3.808
4.713
5.601
6.472
7.325
8.162
8.983
9.787
10.575
11.348
12.106
12.849
13.578
14.292
14.992
15.678
16.351
3%
0.971
1.913
2.829
3.717
4.580
5.417
6.230
7.020
7.786
8.530
9.253
9.954
10.635
11.296
11.938
12.561
13.166
13.754
14.324
14.877
4%
0.962
1.886
2.775
3.630
4.452
5.242
6.002
6.733
7.435
8.111
8.760
9.385
9.986
10.563
11.118
11.652
12.166
12.659
13.134
13.590
5%
0.952
1.859
2.723
3.546
4.329
5.076
5.786
6.463
7.108
7.722
8.306
8.863
9.394
9.899
10.380
10.838
11.274
11.690
12.085
12.462
YEAR/r
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
11%
0.901
1.713
2.444
3.102
3.696
4.231
4.712
5.146
5.537
5.889
6.207
6.492
6.750
6.982
7.191
7.379
7.549
7.702
7.839
7.963
12%
0.893
1.690
2.402
3.037
3.605
4.111
4.564
4.968
5.328
5.650
5.938
6.194
6.424
6.628
6.811
6.974
7.120
7.250
7.366
7.469
13%
0.885
1.668
2.361
2.974
3.517
3.998
4.423
4.799
5.132
5.426
5.687
5.918
6.122
6.302
6.462
6.604
6.729
6.840
6.938
7.025
14%
0.877
1.647
2.322
2.914
3.433
3.889
4.288
4.639
4.946
5.216
5.453
5.660
5.842
6.002
6.142
6.265
6.373
6.467
6.550
6.623
15%
0.870
1.626
2.283
2.855
3.352
3.784
4.160
4.487
4.772
5.019
5.234
5.421
5.583
5.724
5.847
5.954
6.047
6.128
6.198
6.259
KVShenai-pq IA03
6%
7%
0.943 0.935
1.833 1.808
2.673 2.624
3.465 3.387
4.212 4.100
4.917 4.767
5.582 5.389
6.210 5.971
6.802 6.515
7.360 7.024
7.887 7.499
8.384 7.943
8.853 8.358
9.295 8.745
9.712 9.108
10.106 9.447
10.477 9.763
10.828 10.059
11.158 10.336
11.470 10.594
16%
0.862
1.605
2.246
2.798
3.274
3.685
4.039
4.344
4.607
4.833
5.029
5.197
5.342
5.468
5.575
5.668
5.749
5.818
5.877
5.929
17%
0.855
1.585
2.210
2.743
3.199
3.589
3.922
4.207
4.451
4.659
4.836
4.988
5.118
5.229
5.324
5.405
5.475
5.534
5.584
5.628
8%
0.926
1.783
2.577
3.312
3.993
4.623
5.206
5.747
6.247
6.710
7.139
7.536
7.904
8.244
8.559
8.851
9.122
9.372
9.604
9.818
9%
0.917
1.759
2.531
3.240
3.890
4.486
5.033
5.535
5.995
6.418
6.805
7.161
7.487
7.786
8.061
8.313
8.544
8.756
8.950
9.129
10%
0.909
1.736
2.487
3.170
3.791
4.355
4.868
5.335
5.759
6.145
6.495
6.814
7.103
7.367
7.606
7.824
8.022
8.201
8.365
8.514
18%
0.847
1.566
2.174
2.690
3.127
3.498
3.812
4.078
4.303
4.494
4.656
4.793
4.910
5.008
5.092
5.162
5.222
5.273
5.316
5.353
19%
0.840
1.547
2.140
2.639
3.058
3.410
3.706
3.954
4.163
4.339
4.486
4.611
4.715
4.802
4.876
4.938
4.990
5.033
5.070
5.101
20%
0.833
1.528
2.106
2.589
2.991
3.326
3.605
3.837
4.031
4.192
4.327
4.439
4.533
4.611
4.675
4.730
4.775
4.812
4.843
4.870
14