MBA Corporate Finance - Question Bank

1. Separation theorem
What is the separation theorem? Discuss its relevance in the context of  a company which has two shareholders X and Y who have equal shareholdings of 50% in a company whose present resources are £100,000. The company has a  project which can deliver a return of  20% with certainty at the end of the next year. Shareholder X requires his share of the company’s wealth for immediate expenditure; Shareholder Y is indifferent. The market rate of interest is 15%. 

2. Portfolio theory
(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  P  and Q in the minimum variance portfolio?
(b) What is the return on the minimum variance portfolio?
Formula for minimum variance portfolio:  
wa =  (b^2 - a b a b) / (b^2 + a^2 - 2 a b a b)

3. Capital Asset Pricing Model
(1) Assume the return on the market is 14% (Rm) and the risk free rate is 6% (rf). 
(i) What is the return expected from shares with the following betas:
(a) 0.4 (b) 1.2
(b) Suppose all shares in the market are in equilibrium, what is the beta of a company which has an expected return of  (a) 12%? (b) 18%? 

(2) Denbond  Corporation  is analyzing several investments for its portfolio.
 The expected returns and beta of each are given below. 
Investment		Expected return			Beta
			From Fundamental Analysis
     A			       15.0%				1.10
     B			       16.0%				1.30
     C			       10.0%				0.70
     D			         9.2%				0.40
The current rate of long-term government bonds is 6% the expected return for the market  portfolio is 14%. 
(i) Draw the SML and locate the expected return and required return from the CAPM. Which investment(s) should the firm accept?
(ii) Suppose a portfolio is made up of the above investments, what will be its Beta? What will be its equilibrium return?
. 
4. Valuing Bonds and Shares
(1) Bentex’s  perpetual bond pays $ 40 coupon annually. 
(a) What is its current market value if the yield to maturity is 10%?
(b) If the market price of the bond changes to $450, what is the new ytm?

(2) The Lemmings Corporation has just issued a bond for $96, on which it will pay $6 interest annually for the next 10 years. The bond will be redeemed at its face value of  $100. The issue cost of the bond is 3% and interest paid is tax deductible. The rate of  taxation is 40%. What is the after tax cost of the bond to the company? 

(3) Stock A is expected to provide a dividend of  $1 forever.
Stock B is expected to pay a dividend of $0.8 next year. Thereafter dividend growth is expected to be 4% a year forever.
Stock C is expected to pay a dividend of  $1.0 next year. Thereafter dividend is expected to grow by 50% a year for the next two years and then level off.
Stock D is expected to pay no dividend next year. A dividend of  $0.75 will be paid at the end of the second year. Thereafter dividend is expected to grow by 5% a year forever.
Which stock has the highest price if the required rate of return is 10%.

(4) Kemp Limited is issuing new ordinary shares at a market price of $6.00. Dividends last year were 50 cents and are expected to grow at an annual rate of 6% forever. Issue costs will be 8% of market price. 
What will be the firm’s cost of equity?
Suppose the dividends estimates are revised so that the growth rate is 0, then what will happen to the share price?

(5) Divgro Limited’s dividend payment pattern per share has been as below for the past five years-
t(-4)		18.0p
t(-3)		10.0p
t(-2)		12.0p
t(-1)		20.5p
t(0)		25.0p
The company’s share is now quoted at £1.50. 
(i) What is its cost of equity capital? 
(ii) What will be its value today if dividends are expected to grow at the same rate as in the past for the next three years, then level off.

(6) Baxter Limited is a company  in the  utilities  industry which has had no growth for several years. Data on the company has averaged as below:
Sales	£ 5,000,000
Profit after tax	£ 600,000
Share capital and reserves	£ 3,500,000
No of shares	1,500,000
Loans	£ 2,000,000
The company has been declaring all its earnings as dividends for several years.  The company holds patents which are estimated to have a market value of £ 1 million. The share is now quoted at £ 3.33 on the Market for small companies. Industry average figures are as below:
Price earnings ratio	14  times
Market to Book ratio	2.5 times
Required
(a) Value the shares of  Baxter limited by two different methods and offer explanations for any differences resulting from the valuation.
(b) The project department of  Baxter Limited has identified two potential projects, which are expected to result in the following:
Project A:  next year’s dividend will fall to 35p/share but it is expected that dividends will grow at 6% a year thereafter for ever.
Project B: the dividend will grow by 20% for the next two years and level off after that. 
Estimate the cost of equity capital of the company from the information above and advise which if any of the above projects the company should accept.

(7) Fengro Limited’s earnings over the last five years are as follows:
Profit after tax:	(£’000)
20X1			120
20X2			125
20X3			130
20X4			135
20X5			140
The share capital of the company is made up  of  500,000 shares.
The market risk premium is 8% and the risk free rate is 6%.  The company has a beta of 1.2. Calculate the expected share price and P/e ratio of the company if 
(a) Analyst A expects the existing growth in earnings will continue and all earnings will be paid out as dividends.  
(b) Analyst B estimates the company’s growth prospects are limited and cannot continue any further.

5.  Financing the Corporation

Rights issues
Hampton Hotels Limited is considering raising £12 million equity capital through
a rights issue. Each rights share will be priced at £15. It has 2.4 million shares of 
common stock outstanding and these are currently traded at £18 
(a) How many  new shares must HHL issue?
(b) How many rights will be required to purchase one share?
(c) What is the expected post rights price of the share?
(d) Discuss wealth and control effects for shareholders who do and do not take up rights shares.

Bond finance versus Bank finance
Filtex Corporation has decided to raise £10m of  debt finance for a new project. 
The finance is required for a ten year period.  As the Finance Manager of the 
company you have had detailed discussions with the company’s bankers and also a
broking firm which advises its clients on raising finance from the markets for their operations. 
(a) The following  two alternatives have been identified:
(i) Finance from the bank: this will carry an interest of  9% per annum.
(ii) Finance from a bond issue: this will have a face value of  £100 and carry a coupon of  8%. It will be redeemed at its face value at maturity. The broker estimates that investors will pay £95 at issue per £100 face value. Issue costs are estimated at 3%.
The rate of corporate taxation is 30%. Ignoring taxes, which source of finance is lower in cost?
(b) Calculate the effective cost to the company if another broking firm estimates that the bond will be taken up at £98 per face value of  £100. Issue costs are estimated at 2.0%.

Convertible Bond
Felton limited has 6,000 9% convertible bonds in its capital structure. The bonds have a face value of £100. The holder of a bond may convert each bond into 60 ordinary shares three years from now or 54 shares at the end of four years from now. The share of the company is now trading at 
£2-00 and is expected to increase by 10% a year for the next four years. The company pays no dividend.  The current market price of the bond is £110, and at the end of three years it is expected to trade at £120, and at the end of four years at £130.
Required:
If an investor expects to earn a return of 12% per year, are the convertible bonds an attractive investment over a three or four year horizon? Explain your answer in full.

Bank finance versus lease finance
(1) Brand Corporation has decided to purchase a new machine that costs $5m. The machine will be worthless after four years. A bank has offered Brand Corporation a loan of $5m for four years. The interest rate on the loan is 10% per annum. The corporation tax rate is 40%. The tax authorities will allow straight line depreciation for this type of machine. A leasing company offers to lease the same machine to Brand Corporation for a period of four years for an annual lease rental of $1.6 million to be paid at the end of the year. 
Required:
(a) Should Brand Corporation lease the machine or buy it with bank financing?
(c) What is the annual lease payment that will make Brand Corporation indifferent to whether it leases the machine or purchases it?

(2) Bedford Ltd  is evaluating a new investment of  £4.0 million in plant and machinery. The  plant and machinery has a  life of five years.   Its scrap value will be zero.  
The  investment  will generate incremental cash flows of  £ 2.0 million per annum before  taxation.  Capital allowances of  20% pa on a straight line basis are available for the  investment.   The taxation rate is  40%. It is considered that a discount rate of 20% would reflect the risk of the project's  operating  cash flows. 

The plant and machinery can be acquired through  a  lease  which involves five annual payments of   £1.15 m per annum, the first payable at the beginning of the first year (and subsequent payments at the beginning of each year) or through  loan finance at  the rate of 15% per annum. 

Required:
Advise the company 
(a)  whether  the project should be undertaken 
 (b) which method of financing is lower in cost. 

6. Dividend Policy
(1) The earnings and dividends of  Bamtex plc in the last five years are as below:
                    Earnings  after tax       Number of ordinary  shares        Dividends
                   	(£’000)			(million)			(£’000)
2001		12,025			10				3,400
2002		11,218			10				3,400
2003		13,230			10				3,400
2004		16,225			10				3,400
2005		17,945			10				3,400
Discuss the merits and drawbacks of the dividend policy of the above company 
with reference to the various theories on dividend policy.

(2) The shares of Panafrica Limited are currently selling at $10 per share. Next year’s earnings are expected to be $2 per share. The company has announced a policy of paying out 50% of its earnings each year as dividends, and ploughing back the remainder inside the company. Funds invested in internal projects earn a return of  25%. The company has an endless supply of such projects into the future. Assume the share is currently priced correctly.  
Calculate the following:
(a) what is the rate of return that Panafrica shareholders require?
(b) If  instead of  paying out 50% of its earnings each year, the company changed its policy to paying out 75% of earnings, what do you expect will happen to the share price?
(c) If  instead of reinvesting any amount, all the earnings were paid as dividends, what do you expect will happen to the share price?

 (3) Lintner developed a simple model as follows:
	Div =  Dt-D(t-1) = γ ( λ  E (t) - Div(t-1) ) 
	ie  the change in dividend  (Div)  is expressed in terms of:
a target dividend payout  λ  E (t), of current earnings  and  
	-   a  speed of adjustment coefficient ` γ’  
Assume a company paid £1m dividends last year. This year the earnings are expected to be £4m and  earnings are expected to remain at this level for the foreseeable future.
Forecast the dividends that this company will pay for the next 5 years, if its management has a target payout ratio of 50% of earnings and the speed of adjustment coefficient is 30%.  

7. Capital Structure

Cost of Capital
(1) Vartex Limited’s capital is made up of equity and loans as under:
300,000 equity shares  
5000 Irredeemable Bonds with a face value of  $100, and a 5% coupon. 
The Company has been paying a regular dividend of  $1/share.
The market price of  the  share is $6, and the market price of the Bond 
is  $92.00. 
(i) (a) What is the cost of equity capital of the company? 
(b) What is the cost of debt capital of the company?
(b) What is the WACC of the company? 
(ii)  Recalculate the WACC assuming the debt was redeemable in five years at par.
  
MM no tax	 
Geared Limited and Ungeared Limited are companies with the same business risk. The operating profit of both companies is £90 million per year and no change is
expected. The geared company has irredeemable debt of  £300m at 10% pa interest. Geared stock sells for £90 per share and there are 5.0 million outstanding shares. Ungeared has 10 million shares trading at £70 each.  An investor with a 1% share in 
Ungeared  is examining his returns at similar levels of risk. Assume there are no taxes.
(a) Compare the return on investments in Geared and Ungeared at similar risk levels and advise the investor  which company shares are the better buy. 
(b)What do you expect will happen in due course?
(c) Compare the WACC, and Values of the companies, and cost of equity capital iof the geared company at equilibrium. 

(2) Helms plc, a  company  in the Foods industry is financed by  
-100,000  6%  irredeemable debentures with a face value of  £100 each;  now   quoted at  £ 101-70 each. 
-5 million ordinary shares of  nominal value 25p, now quoted at £ 7 each
cum dividend. The company has been paying a regular dividend of £1 per share for several years.
It  is considering  an investment  of  £ 4m for expanding in the same business. Additional finance required by the project will be raised as equity.
Taxation is to be ignored 
(a)  What  is the existing WACC of   Helms  plc?
(b) At what  rate of  return  should the new  project  cashflows be  discounted at?
(c)  If  as a result of the expansion cashflows will increase by £ 0.5 million per year from the end of the first year to perpetuity,  should the project be undertaken?	

(2) Fruitex Limited is an all-equity financed company. The company has 1,800,000 shares outstanding. The market value of the shares now are £10 each.  It has been regularly paying a dividend of £2.00 per share for many years. Assume there is no taxation.
(a) The company plans to issue £3,000,000 debt @10%pa interest to repurchase stock. 
(i) What is the company’s current cost of  equity capital?
(ii) What will be the cost of equity capital after the stock repurchase?
(b) Rework the above based on the company issuing £5m debt to buy back shares. 

MM with tax
Marden Limited is an all equity financed company which generates an operating profit before tax of £8.0m.  The company’s tax rate is 34%. Its cost of
Equity capital is 15%, the cost of debt is 10%.
(a) (i) What is the current value of  the company?  
(b) If its capital structure is now to include £ 8m of irredeemable debt
(i) what is the value of the company  (ii) what is the cost of equity capital?
(c) Suppose the debt in (b) is £15m, rework (i) and (ii).

8. MM-CAPM synthesis
A company which manufactures food products is considering entering the field of
mobile phones manufacture. The company’s equity Beta is 1.2 and it is financed by 1,000,000 equity shares quoted at £ 10/share and  irredeemable 10,000 debentures quoted at par and with an interest rate of 8%.  The risk free rate is 7% and the return on the market portfolio is 15%.  To finance the mobile phones project, the company decides to raise another 10,000 debentures at par. A competing mobile phones  manufacturer with a  debt/equity ratio of 0.3 has an equity beta of 1.8 and a debt beta of 0.2.  Ignore taxes.   
(a) What is the company’s existing WACC?
(b) What is the rate of return at which the company should evaluate the mobile phone project?

9. Adjusted Present Value 
A company is considering an investment of £4 million. The return on the market portfolio is 14%; the risk free rate is 6%. The beta of  the project’s assets are estimated at 1.25.  The project is expected to deliver an annual cash flow of £850,000 to perpetuity. The Corporation tax rate is 30%. 
Discuss the acceptability of the project
(i) If it is all equity financed.
(ii) It is financed by £1m 10 year debt which carries an interest rate of 8% pa and the remaining by equity. 
(iii) As in (ii) but this time the debt is irredeemable.

10. Mergers and Acquisitions
(1) Matrix Limited intends to acquire Inven Limited.  Financial data on the two companies are as under:
				Matrix 		Inven
Number of shares (m)		15.0		2.0
Earnings (£’000)		3000		700
Share Price (pence)		500		420					
(a) Calculate the existing eps, P/E ratio and market value of the two enterprises.
(b) Assuming Matrix will be the continuing enterprise and there are no economic gains, calculate the exchange ratio, P/E ratio, eps and market values of the combined enterprise assuming exchange takes place on the basis of  (i) market value (ii) earnings.
(c) Discuss what is meant by the bootstrap effect.

(2) Regex plc is considering the acquisition of  all the shares of   Newtech plc. 
The following information relates to the two companies:
					Regex		Newtech
	Earnings per share	 	45p		50p
	Dividend per share 	 	30p		50p
	Issued shares.		10,000,000	1,000,000
	Current price per share	£ 1.35		£ 3.00
The management of  Regex plc feel they can increase the profits of Newtech plc 
by 100% after the takeover, without any additional investment.   
(a) If   Regex  plc’s estimates are right then what is the total value of  Newtech plc  after the takeover?   Hint: first calculate the cost of equity capital of Newtech, the return expected by shareholders consistent with its risk.				
(b) If the management of  Regex plc decide the total gain from the takeover is  to be 
shared 50% by the shareholders of each company, then 
(i) what is the maximum price which  Regex  plc can offer for the shares of   Newtech plc ?
(ii) how many shares of  Regex plc can be offered for each share of  Newtech plc?		

11. Interest rate and currency risk Management

(1) It is now late March. The Finance Manager of a company needs to borrow  £10m for a three 
month period beginning June. Interest rates are now 9% pa. 3 month interest rate futures for 10%pa 
are trading at 90.00, and 3 month put options with a strike price of 90.00 cost £500 per contract.   
The contract size for both is £500,000.   Examine the implications of  hedging using futures or 
options and compare with a 'Do Nothing' strategy.

(2) Company A requires a fixed rate of loan of £100 M for a period of 5 years. 
It can borrow this amount at a fixed rate of 10% or a floating rate of LIBOR+.5%
Company B requires a floating rate  loan of £100 M. It can borrow this amount 
for a rate of  LIBOR + .25% or it could borrow it at a fixed rate of 9.25%.
Required:
 Suggest a scheme whereby there could be benefits to both companies 
for  entering into an interest rate swap.
Assuming the same arrangement was made through an intermediary,  who 
charges 0.25% pa in total, examine a possible scheme and advise if  there would 
be any benefit to the companies.
What is the benefit to a company of arranging a swap through a financial 
intermediary?

(3) A UK company sold a machine to an American Customer for  US $ 1.40 million on 1 Jan to be paid for on 30 Jun. The current spot rate is  1.39 $/ £.  
The UK exporter has the possibility of covering his currency exposure through futures or options.
June Futures are quoted  at  1.40$/£, contract size  £62,500.
June Options are quoted as below:
Contract Size:  £ 25,000; premium in cents per £.
Strike Price
$/£			Calls				Puts
1.35			3.0c				2.0c
1.40			2.0c				3.0c
1.45			1.0c				4.0c
(i)	a `Do Nothing' strategy
(ii)	hedging through currency futures versus hedging with currency options, if  the  actual exchange rate on 30 Jun is
(a)  1.30 $/£    (b) 1.50$/£     

Formulas for  Corporate Finance

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 w1w212 12 )

     (iii) Covariance =  12 12 
      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

D.	Cost of Capital Relationships (with taxation), asset and equity beta 

(i)  Cost of Equity Capital:        Keg  = Ku + ( Ku-Kd) (l - T) (B/VS)
(ii)  Value of Geared Firm :       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

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%	
1	0.990	0.980	0.971	0.962	0.952	0.943	0.935	0.926	0.917	0.909	
2	0.980	0.961	0.943	0.925	0.907	0.890	0.873	0.857	0.842	0.826	
3	0.971	0.942	0.915	0.889	0.864	0.840	0.816	0.794	0.772	0.751	
4	0.961	0.924	0.888	0.855	0.823	0.792	0.763	0.735	0.708	0.683	
5	0.951	0.906	0.863	0.822	0.784	0.747	0.713	0.681	0.650	0.621	
6	0.942	0.888	0.837	0.790	0.746	0.705	0.666	0.630	0.596	0.564	
7	0.933	0.871	0.813	0.760	0.711	0.665	0.623	0.583	0.547	0.513	
8	0.923	0.853	0.789	0.731	0.677	0.627	0.582	0.540	0.502	0.467	
9	0.914	0.837	0.766	0.703	0.645	0.592	0.544	0.500	0.460	0.424	
10	0.905	0.820	0.744	0.676	0.614	0.558	0.508	0.463	0.422	0.386	
11	0.896	0.804	0.722	0.650	0.585	0.527	0.475	0.429	0.388	0.350	
12	0.887	0.788	0.701	0.625	0.557	0.497	0.444	0.397	0.356	0.319	
13	0.879	0.773	0.681	0.601	0.530	0.469	0.415	0.368	0.326	0.290	
14	0.870	0.758	0.661	0.577	0.505	0.442	0.388	0.340	0.299	0.263	
15	0.861	0.743	0.642	0.555	0.481	0.417	0.362	0.315	0.275	0.239	
16	0.853	0.728	0.623	0.534	0.458	0.394	0.339	0.292	0.252	0.218	
17	0.844	0.714	0.605	0.513	0.436	0.371	0.317	0.270	0.231	0.198	
18	0.836	0.700	0.587	0.494	0.416	0.350	0.296	0.250	0.212	0.180	
19	0.828	0.686	0.570	0.475	0.396	0.331	0.277	0.232	0.194	0.164	
20	0.820	0.673	0.554	0.456	0.377	0.312	0.258	0.215	0.178	0.149	
											
YEAR/r	11%	12%	13%	14%	15%	16%	17%	18%	19%	20%	
1	0.901	0.893	0.885	0.877	0.870	0.862	0.855	0.847	0.840	0.833	
2	0.812	0.797	0.783	0.769	0.756	0.743	0.731	0.718	0.706	0.694	
3	0.731	0.712	0.693	0.675	0.658	0.641	0.624	0.609	0.593	0.579	
4	0.659	0.636	0.613	0.592	0.572	0.552	0.534	0.516	0.499	0.482	
5	0.593	0.567	0.543	0.519	0.497	0.476	0.456	0.437	0.419	0.402	
6	0.535	0.507	0.480	0.456	0.432	0.410	0.390	0.370	0.352	0.335	
7	0.482	0.452	0.425	0.400	0.376	0.354	0.333	0.314	0.296	0.279	
8	0.434	0.404	0.376	0.351	0.327	0.305	0.285	0.266	0.249	0.233	
9	0.391	0.361	0.333	0.308	0.284	0.263	0.243	0.225	0.209	0.194	
10	0.352	0.322	0.295	0.270	0.247	0.227	0.208	0.191	0.176	0.162	
11	0.317	0.287	0.261	0.237	0.215	0.195	0.178	0.162	0.148	0.135	
12	0.286	0.257	0.231	0.208	0.187	0.168	0.152	0.137	0.124	0.112	
13	0.258	0.229	0.204	0.182	0.163	0.145	0.130	0.116	0.104	0.093	
14	0.232	0.205	0.181	0.160	0.141	0.125	0.111	0.099	0.088	0.078	
15	0.209	0.183	0.160	0.140	0.123	0.108	0.095	0.084	0.074	0.065	
16	0.188	0.163	0.141	0.123	0.107	0.093	0.081	0.071	0.062	0.054	
17	0.170	0.146	0.125	0.108	0.093	0.080	0.069	0.060	0.052	0.045	
18	0.153	0.130	0.111	0.095	0.081	0.069	0.059	0.051	0.044	0.038	
19	0.138	0.116	0.098	0.083	0.070	0.060	0.051	0.043	0.037	0.031	
20	0.124	0.104	0.087	0.073	0.061	0.051	0.043	0.037	0.031	0.026	

											

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%	
1	0.990	0.980	0.971	0.962	0.952	0.943	0.935	0.926	0.917	0.909	
2	1.970	1.942	1.913	1.886	1.859	1.833	1.808	1.783	1.759	1.736	
3	2.941	2.884	2.829	2.775	2.723	2.673	2.624	2.577	2.531	2.487	
4	3.902	3.808	3.717	3.630	3.546	3.465	3.387	3.312	3.240	3.170	
5	4.853	4.713	4.580	4.452	4.329	4.212	4.100	3.993	3.890	3.791	
6	5.795	5.601	5.417	5.242	5.076	4.917	4.767	4.623	4.486	4.355	
7	6.728	6.472	6.230	6.002	5.786	5.582	5.389	5.206	5.033	4.868	
8	7.652	7.325	7.020	6.733	6.463	6.210	5.971	5.747	5.535	5.335	
9	8.566	8.162	7.786	7.435	7.108	6.802	6.515	6.247	5.995	5.759	
10	9.471	8.983	8.530	8.111	7.722	7.360	7.024	6.710	6.418	6.145	
11	10.368	9.787	9.253	8.760	8.306	7.887	7.499	7.139	6.805	6.495	
12	11.255	10.575	9.954	9.385	8.863	8.384	7.943	7.536	7.161	6.814	
13	12.134	11.348	10.635	9.986	9.394	8.853	8.358	7.904	7.487	7.103	
14	13.004	12.106	11.296	10.563	9.899	9.295	8.745	8.244	7.786	7.367	
15	13.865	12.849	11.938	11.118	10.380	9.712	9.108	8.559	8.061	7.606	
16	14.718	13.578	12.561	11.652	10.838	10.106	9.447	8.851	8.313	7.824	
17	15.562	14.292	13.166	12.166	11.274	10.477	9.763	9.122	8.544	8.022	
18	16.398	14.992	13.754	12.659	11.690	10.828	10.059	9.372	8.756	8.201	
19	17.226	15.678	14.324	13.134	12.085	11.158	10.336	9.604	8.950	8.365	
20	18.046	16.351	14.877	13.590	12.462	11.470	10.594	9.818	9.129	8.514	
											
YEAR/r	11%	12%	13%	14%	15%	16%	17%	18%	19%	20%	
1	0.901	0.893	0.885	0.877	0.870	0.862	0.855	0.847	0.840	0.833	
2	1.713	1.690	1.668	1.647	1.626	1.605	1.585	1.566	1.547	1.528	
3	2.444	2.402	2.361	2.322	2.283	2.246	2.210	2.174	2.140	2.106	
4	3.102	3.037	2.974	2.914	2.855	2.798	2.743	2.690	2.639	2.589	
5	3.696	3.605	3.517	3.433	3.352	3.274	3.199	3.127	3.058	2.991	
6	4.231	4.111	3.998	3.889	3.784	3.685	3.589	3.498	3.410	3.326	
7	4.712	4.564	4.423	4.288	4.160	4.039	3.922	3.812	3.706	3.605	
8	5.146	4.968	4.799	4.639	4.487	4.344	4.207	4.078	3.954	3.837	
9	5.537	5.328	5.132	4.946	4.772	4.607	4.451	4.303	4.163	4.031	
10	5.889	5.650	5.426	5.216	5.019	4.833	4.659	4.494	4.339	4.192	
11	6.207	5.938	5.687	5.453	5.234	5.029	4.836	4.656	4.486	4.327	
12	6.492	6.194	5.918	5.660	5.421	5.197	4.988	4.793	4.611	4.439	
13	6.750	6.424	6.122	5.842	5.583	5.342	5.118	4.910	4.715	4.533	
14	6.982	6.628	6.302	6.002	5.724	5.468	5.229	5.008	4.802	4.611	
15	7.191	6.811	6.462	6.142	5.847	5.575	5.324	5.092	4.876	4.675	
16	7.379	6.974	6.604	6.265	5.954	5.668	5.405	5.162	4.938	4.730	
17	7.549	7.120	6.729	6.373	6.047	5.749	5.475	5.222	4.990	4.775	
18	7.702	7.250	6.840	6.467	6.128	5.818	5.534	5.273	5.033	4.812	
19	7.839	7.366	6.938	6.550	6.198	5.877	5.584	5.316	5.070	4.843	
20	7.963	7.469	7.025	6.623	6.259	5.929	5.628	5.353	5.101	4.870