INSTRUCTIONS: Answer any four (4) questions. Write your answers on the answer sheets provided. Question 1 Smith is considering two investments. He can either purchase shares in NGL or bonds from NPP. NGL shares cost $95 each and paid $8 in dividends per share at the end of the last year. NGL is expected to keep dividend payments at $8 per year for the foreseeable future. NPP bonds also cost $95 but they have a face value of $100, a coupon rate of 10% and a time to maturity of 5 years. a) What would be Smith s annual rate of return if he invests in NPP bonds? (10 marks) b) What would be Smith s annual rate of return if he invests in NGL shares for 5 years, selling each share for $140 at the end of the fifth year? (Hint: the rate of return is greater than the rate calculated in part a) (10 marks) c) Briefly discuss two differences between stocks and bonds. (5 marks) Question 1 ANSWER a) Using a Financial Calculator Face Value = $100 Price = $95 Coupon Payments = $10 (10% of Face Value) Time to maturity = 5 years Therefore, Smith s rate of return = 11.37% Using Financial Tables PVIFA PVIF ( 11,5 $100) $95 ( 11,5 $10)+ (3.696 $ 10)+(0.593 $ 100)
36.96+59.3=$ 96.26 Therefore,Smit h ' s rate of return 11 10 marks b) Using a Financial Calculator FV = $140 Price = $95 PMT = $8 N = 5 years Therefore, Smith s rate of return = 15.39% Using Financial Tables PVIFA PVIF ( 15,5 $ 140) $ 95 ( 15, 5 $ 8)+ (3.352 $ 8)+(0.497 $140) 26.82+69.58=$ 96.4 Therefore,Smit h ' s rate of return 15 10 marks c) 1. Holders of stock have ownership rights, holders of bonds do not 2. Cash payments to stockholders (dividends) can fluctuate over time based on the performance of the company while coupon payments to bondholders are fixed by the contractual agreement
5 marks (2.5 per point) Question 2 Mike is searching for a stock to include in his current portfolio. He is interested in Apple Inc.; he has been impressed with the company s computer products and believes Apple is an innovative market player. However, Mike realizes that any time you consider a so-called high-tech stock, risk is a major concern. The rule he follows is to include only securities with a coefficient of variation of returns below 0.9. Mike has obtained the following information for the period 2006 through 2009. Apple stock, being growth oriented, did not pay any dividends during these four years. Stock Price Year Beginning End 2006 $14.36 $21.55 2007 $21.55 $64.78 2008 $64.78 $72.38 2009 $72.38 $91.80 a) Calculate the rate of return for each year, 2006 through 2009 for Apple stock. (4 marks) b) Assume that each year s return is equally probable and calculate the average return over this time period. (4 marks) c) Calculate the standard deviation of returns, over the four year period. (10 marks) d) Based on b and c determine the coefficient of variation of returns for the security. (2 marks) e) Briefly discuss the difference between diversifiable and non-diversifiable risk. (5 marks) Question 2 ANSWER a) Year Calculations Rate of Return 2006 21.55 14.36 50.07% 100 14.36 2007 64.78 21.55 100 21.55 2008 72.38 64.78 100 64.78 200.6% 11.73%
2009 91.80 72.38 100 72.38 26.83% 4 marks b) Average return = 50.07+ 200.6+11.73+26.83 =72.31 4 4 marks c) σ r = n (r t r p ) 2 t=1 n 1 = σ [ (50.07 72.31 )2 +(200.6 72.31 ) 2 +(11.73 72.31 ) 2 + (26.83 72.31 ) 2 ] r 4 1 = σ [ ( 22.24 )2 + (128.29 ) 2 +( 60.58 ) 2 +( 45.48 ) 2 ] r 3 σ r= [494.6176+16,458.3241+3,669.9364+2,068.4304 ] 3 = σ 22,691.3085 r 3 σ r = 7,563.7695 standard deviation of returns=86.97
10 marks d) Coefficient of Variation= standarddeviation average return = 86.97 72.31 =1.2 2 marks e) Diversifiable risk represents variations in an asset s rate of return brought on by factors unique to a particular industry or the particular asset in question. Investors can protect themselves from diversifiable risk by investing in a portfolio or collection of assets whose expected rates of return are inversely correlated. Non-diversifiable risk on the other hand represents variations in an asset s rate of return caused by broad-based factors which affect the rates of returns of all other assets in the same way (for example a nationwide earthquake). The impacts of non-diversifiable risk cannot be reduced by diversification. 5 marks Question 3 Jamie Peters invested $300,000 to set up the following portfolio one year ago: Asset Cost Beta at purchase Yearly income Value today A $60,000 0.80 $5,600 $60,000 B $105,000 0.95 $3,400 $150,000 C $100,000 2.50 - $90,500 D $35,000 1.25 $975 $40,500 a. Calculate the portfolio beta on the basis of the original cost figures. (5 marks) b. Calculate the percentage return of the portfolio on the basis of original cost, using income and capital gains during the year. (5 marks) c. At the time Jamie made his investments, investors were estimating that the market return for the coming year would be 10%. The estimate of the risk-free rate of return averaged 4% for the coming year. Calculate an expected rate of return for each stock on the basis of its beta and the expectations of market and risk-free returns. (10 marks) d. Briefly discuss the significance of Beta values. (5 marks)
Question 3 ANSWER a) Total cost of portfolio = $60,000 + $105,000 + $100,000 + $35,000 = $300,000 Asset Beta at purchase Weight in portfolio Weight multiplied by beta A 0.80 60,000 0.8 0.2=0.16 =0.20 300,000 B 0.95 105,000 0.95 0.35=0 =0.35 300,000 C 2.50 100,000 2.5 0.33=0.8 =0.33 300,000 D 1.25 35,000 1.25 0.117= =0.11 300,000 5 marks Portfolio Beta 1.47 b) Asset Weight in portfolio Cost Yearly income Value today Rate of Return A 0.2 $60,000 $5,600 $60,000 (60,000 60,000 )+5,600 = 60,000 0.093 B 0.35 $105,000 $3,400 $150,000 150,000 105,000 +3,400 105,000 =0.461 C 0.33 $100,000 - $90,500 90,500 100,000 = 0.095 100,000 D 0.117 $35,000 $975 $40,500 (40,500 35,000)+ 975 =0.18 35,000 Percentage return of portfolio = (0.093 0.2)+(0.461 0.35 )+( 0.095 0.33 )+ (0.185 0.117 )=0.0186+0.16135 0.03135+0.021645=0.17024
OR (341,000 300,000 )+9,975 300,000 50,975 300,000 =0.1699 16.99 5 marks c) Asset CAPM Calculations Expected return A r j =4 +[0.8 (10 4 )] 8.8% B r j =4 +[0.95 (10 4 )] 9.7% C r j =4 +[2.5 (10 4 )] 19% D r j =4 +[1.25 (10 4 )] 11.5% 10 marks d) Beta values measure the responsiveness of the return of an asset to changes in the market rate of return. Beta values are therefore measures of non-diversifiable risk. A beta value of 1 indicates that an asset s return moves in tandem with the average market rate. Consequently, a 3% increase in the market rate leads to a 2% increase in the assets return. An asset with a beta value of two will experience a 2% increase or decrease in its return of the market rate increases or decreases by 1%. Therefore, the higher the beta value of an asset, the greater it s responsiveness to changes in the average market rate and the greater its degree of non-diversifiable risk. The greater the risk of an asset the higher its rate of return. 5 marks Question 4 Colnet Ltd, an online marketing firm, has invited you to invest in their company by purchasing shares of common or preferred stock.
a) Briefly describe two advantages and two disadvantages of investing in common stock as opposed to preferred stock. (8 marks) b) If the company paid dividends per common share of $25 at the end of the last year and dividend payments are forecasted to increase at a rate of 5% per year, what is the maximum amount you would be willing to pay for a share of common stock if you would like to earn an annual rate of return of no less than 15%? (10 marks) c) If the company s preferred shares have a par value of $120 each and pays dividends at a rate of 10%, what is the maximum amount you would be willing to pay for a share of preferred stock in order to at least earn an annual rate of return of 15%? (7 marks) Question 4 ANSWER a) Advantages Common stockholders have voting rights while preferred stockholders usually do not Common stockholders can benefit substantially as residual claimants through large dividend payments (or via the distribution of the assets of a liquidated company) if a substantial amount of net cash flow (or assets) remains after the firm pays its creditors and preferred stockholders. Disadvantages Firms may choose to reinvest significant amounts of profits, forgoing dividend payments to common stockholders in the short term. This may persuade a common stockholder looking for a positive short term return to sell his stock even if he may want to remain a part owner of the company. Common stockholders as residual claimants may not receive dividend payments or assets at the liquidation of a firm if insufficient assets remain after creditors and preferred stockholders are given their share first. 8 marks (2 marks each) b) P 0 = 0 (1+g) r s g
P 0 = 25 (1+0.05) 0.15 0.05 P 0 = 26.25 0.1 0 P 0 =$262.50 10 marks c) P 0 = r $ 120 10 P 0 = 0.15 P 0 = 12 0.15 P 0 =$80 7 marks Question 5 Hook industries is considering the replacement of one of its old drill presses. Three alternative replacement presses are under consideration. The relevant cash flows associated with each are shown in the following table. The firm s cost of capital is 15%. Press A Press B Press C Initial investment $85,000 $60,000 $130,000 Year Net cash inflows 1 $18,000 $12,000 $50,000 2 $18,000 $14,000 $30,000 3 $18,000 $16,000 $20,000 4 $18,000 $18,000 $20,000 5 $18,000 $20,000 $20,000 6 $18,000 $25,000 $30,000
7 $18,000 - $40,000 8 $18,000 - $50,000 a) Calculate the Net Present Value (NPV) of each press. (9 marks) b) Evaluate the acceptability of each press using NPV. (9 marks) c) Briefly explain what is meant by the term Internal Rate of Return. (7 marks) Question 5 ANSWER a) Press A PV =CF PVIFA 15, 8 PV =$ 18,000 4.487 PV =$ 80,766 NPV =$ 80,766 $ 85,000 NPV = $ 4,234 (-$4,228.21 using a financial calculator) Press B Year Cash Flow PVIF 15, 6 PV 1 $12,000 0.870 $10,440 2 $14,000 0.756 $10,584 3 $16,000 0.658 $10,528 4 $18,000 0.572 $10,296 5 $20,000 0.497 $9,940 6 $25,000 0.432 $10,800 Total $62,588 NPV =$62,588 $60,000
NPV =$ 2,588 ($2,584.34 using a financial calculator) Press C Year Cash Flow PVIF 15, 6 PV 1 $50,000 0.870 $43,500 2 $30,000 0.756 $22,680 3 $20,000 0.658 $13,160 4 $20,000 0.572 $11,440 5 $20,000 0.497 $9,940 6 $30,000 0.432 $12,960 7 $40,000 0.376 $15,040 8 $50,000 0.327 $16,350 Total $145,070 NPV =$ 145, 070 $ 13 0,000 NPV =$15,070 ($15,043.89 using a financial calculator) 12 marks (4 marks each) b) Press A should be rejected since it has a negative NPV. Both Press B and C have positive NPVs and should be considered Press C is preferred to Press B since it has a larger NPV indicating that it will earn the firm a greater amount of net cash flow than Press B. 6 marks (2 marks each) c) The internal rate of return is the forecasted annual rate of return of a project. It is calculated by equating the present value of all future net cash flows of a project with the initial price of the investment and solving for the interest or discount rate. 7 marks Question 6
Sauce Doubles Inc. is selling bonds to raise capital to expand its operations to Latin America. Each bond has a face value of $10,000, a coupon rate of 12% and a time to maturity of 5 years. a) What is the maximum amount you would be willing to pay for a bond if your next best investment opportunity earns you an annual rate of return of 7%? (7 marks) b) If you deposit your earnings from the bonds as they are received (at the end of each year) into an account paying annually compounded interest of 5%, how much money would you have in your bank account at the end of the five years assuming you purchased one hundred bonds? (7 marks) c) Assuming that the bonds were sold at face value, what would be your rate of return if you purchased one hundred bonds and then sold them for $12,000 each after one year? (5 marks) d) Briefly explain why the price of a bond may differ from its face value. (6 marks) Question 6 ANSWER a) PVIFA ( 7,5 years 1,200)+(PVIF 7,5 years 10,000) PV = PV =(4.1 1,200 )+(0.713 10,000) PV =4,920+7,130 PV =$ 12,050 7 marks b) FV =[ (FVIFA 5,5 years 1,200 )+10,000 ] 100 FV =[ (5.526 1,200 )+10,000 ] 100 FV =(6,631.2+10,000) 100 FV =16,631.2 100
FV =$ 1,663,120 7 marks c) r= C+P t+1 P t P t (12,000+1,200 ) 10,000 r= 10,000 r=32 5 marks d) Changes in market interest rates would cause the price of a bond to change also. For example, if market interest rates rise from 10% to 12%, then a coupon bond with a coupon rate of 10% would have to sell for a price that is lower than its face value to increase its yield and attract buyers. If the price of the coupon bond remains at face value, investors would invest elsewhere since the bond s yield would be 10% while investors can earn 12% elsewhere. The decrease in the price of the bonds will aligned its yield with the market yield thus increasing its attractiveness to investors. 6 marks Basic Time Value Calculations One off cash flows 1. FV =PV (1+i) n END OF EXAMINATION Formula Sheet
2. PV = FV (1+i ) n FV PV i n = the future value of cash flow = the present value of cash flow = the rate of interest / the rate of required return = the time period in years of the investment (the time (in years) to maturity of a debt instrument) (1+i) n = the Future Value Interest Factor (FVIF i,n ) 1 (1+i) n = the Present Value Interest Factor (PVIF i,n ) Annuities 3. FV n =CF FVIFA i, n 4. PV n =CF PVIFA i, n FV n = the future value of an annuity PV n = the present value of an annuity i = the rate of interest / the rate of required return n = the time period in years of the investment (the time (in years) to maturity of a debt instrument) FVIFA i,n = the future value interest factor for annuities given i and n PVIFA i,n = the present value interest factor for annuities given i and CF n = the annuity s annual cash flow
Perpetuities PV = CF i PV CF i = the present value of a perpetuity = the perpetuity s annual cash flow = the rate of interest / the rate of required return Bonds 5. PV = CP 1+i + CP CP + + 2 (1+i) (1+i) + FV n (1+i) n FV PV CP i = the face value of the bond = the present value of the bond = the bond s annual coupon payment = the market rate of interest or the rate of required return / the bond s yield to maturity n = the bond s time to maturity 6. Annual Interest Payments Current Yield= Initial Investment(the price of the bond) 100 Stocks 7. P o = 1 (1+r s ) + 2 (1+r s ) + + 2 (1+r s )
8. P 0 = 0 (1+g) = 1 r s g r s g P 0 =toda y ' s value of the stock (its price ) t =dividend payments year' t ' r s =therequired returnontheinvestment g = the annual growth rate of dividends Risk and return 9. r= C+P t+1 P t P t r=returnon holding a fin ancial asset time t t+1 P t =price of the asset at time t P t +1 = price of asset at timet +1 C=Interest payments madeby the asset 10. n j=1 r j P j r j =the returnof the jth outcome P j =the probability of the jth outcome n=the number of possible outcomes scenarios 11. σ r = n (r j r ) 2 Pr j j=1
σ r =the standard deviationof returns for a particular investment r =the expected rate of returnof the investment Pr j =the probability associated withthe rate of returnfor outcome j 12. CV = σ r CV =the coefficient of variation of an investment σ =the standard deviationof aninvestment ' sreturns r =the expected returnof aninvestment = 13. σ r p t =1 n (r t r p ) 2 n 1 σ r p =the standard deviationof the portfolio r t =the expected returnonthe portfolio time t r p =the portfoli o ' s expected annual rate of return n=thenumber of yearsof the investment 14. r j =R F +[b j (r m R F )] r j =the required returnonasset j R F =the risk free rate returnusuallymeasured by the returnongovernment bonds
b j =asset j ' s betacoefficient r m =themarket rate of return Capital Budgeting 15. NPV =( NCF 1 1+x + NCF 2 (1+x ) + + NCF n 2 (1+ x) ) IV n 0 16. IRR 1+ ( n ) NCF 1 1+IRR + NCF 2 (1+IRR ) + + NCF n 2 IV 0 = Where : NPV =Net Present Value NCF n =Net Cash Flow year n n=thelenght years of the project x=the fir m ' s cost of capital IV 0 =theinitial cost of the investment IRR=the internal rate of return