Investment and Interest Rate - Assignment Example

Introductory Finance Name University Date Introductory Finance Question 1(a). You have $1,000 and are given the choice of two investments. The first investment returns $1,500 to you n three years time. The second investment returns $3,000 in ten years. Assuming a discount rate of 5% p.a., which investment do you choose? Investment appraisal is effectively achieved using the net present value and internal rates of return approaches. However, the application of the two approaches is limited to certain factors and the type of investment. For instance, the net present value approach is appropriate in evaluating the present value of a possible investment. The internal rate of return gives the rate at which the internal cash flows in an investment. In long term investments the IRR is most appropriate (Geddes 2002). In this case, the investments are evaluated after three and ten years with a fixed discount rate of 5%. The first investment has a $1500 returns in 3years, it follows that the investment has a $5000 return after ten years. On the other hand, the second investment has a overall ten year returns amounting to $3000. Given the fact that the discount rates are constant, the first investment is more viable as opposed to the second investment. Question 1(b) You have the choice of two income streams. The first involves receiving $2,000 immediately. The second involves receiving $1,000 in one year and $1,500 in two years. Assuming a discount rate of 8% p.a., which income stream do you choose? Solution Using the rate of return, the two streams are compared over the two years. The first stream yields $320 in two years and is valued at $2320 at the end of the second year. In the second stream, the amount that is subject to calculation of interest is $1000 because the second part $1,500 is paid after two years and does not attract interest. The total value of the second stream is $1160+$1500 after two years. The value is $2660. Comparing the two figures, the initial amount invested are different, however, in the first stream, the amount invested is less compared to the second investment. The yields over the two years indicate that the first stream is more profitable and more viable. Question 1(c) You have the choice of two income streams. The first involves receiving $3,000 in three years and the second involves receiving $3,500 in four years. At what discount rate are you indifferent between these two income streams? Solution The total accrued at end of the two seasons of the investments determines the difference in interest rate. At the point where the present values of the investments are equal is essential in evaluating the performance of the two investments. 3000+ (3000*R*3)/100=3,500+(3500*R*4)/100 Solving the above equation gives 10%. This is the discount rate where the present of the two investments are equal. Question two You purchase a house today for $250,000. You pay a 10% deposit and borrow the remainder. (a)If repayments for the borrowing are made each month over the next 20 years, what will be the monthly repayment assuming an interest rate of 6% p.a. The cost of the loan is reduced to $225,000. The discount rate 6% and the loan is spread over twenty years. Using the simple interest rate to compute we get I=p*r*n where p is the principal amount payable per month, r is the interest rate and n is the time. Calculating the monthly returns by applying the formula, we get 225,000=p*0.06*20*(12) 225,000/14.4=p P=$15,625per month. Therefore, the monthly repayment is $15,625. (b)If you pay off $2,000 per month, how long will it take to repay the loan? In an event that $2000 is paid off monthly to offset the loan, we assume that the monthly repayment has been increased by $2000. In effect, the new monthly installment is substantially raised to $17,625. The period of repayment of the loan is equally reduced due to the linearity in their relationship. In this case, I=P*r*n Replacing the figures we have, 225,000=17625*0.06*(n) 225,000=(1057.5n) This becomes 225000/1057.5= n Therefore n= 213months this is the number of months. Dividing the figure with 12 gives the number of years needed to complete the repayment. In this case, the period is 18years. Question three Joshua bought a car for $5,000 and sold it two months later for $5,200. (a) What is the simple annual interest rate implicit in this transaction? Calculating the simple interest accrued over the short period is accomplished by employing the interest formulae. The accrued earnings are $5,200 on $5000 initial investment. It follows that: I=p*r*n 5200=5000*i*2 Therefore 5200/10000=r This translates to 0.52%. The implicit interest rate on this transaction is 0.52%. (b)What is the corresponding effective annual interest rate? The above calculation was based on the interest on $5000 over two months. However, this figure is representative of the annual rates calculation. The annual rates of return reveal a different figure. Given the fact that the returns in two months amount to $200, it is important to estimate the returns in twelve months, which constitute a year. In this case, the annual expected returns assuming a two hundred dollar increment translates to $1200. The ratio of the accrued and the principal amount computed against time gives the annual rate. Therefore, ($1200/$5000)*1yr = r R becomes 0.24. The affective annual interest rate is 0.24%. (c)If inflation is running at 3% pa, what is the real effective annual interest rate? Inflation rate affects the initial amount and increases the value of the invested amount. In this case, in one year, the $5000 gains in value thereby shifting the value of the principal fee. The change in the initial $5000 over two months with 3% inflation rate gives a different figure. If calculated over the twelve-month period, the accrued interest is changed. The formulae used in this calculation is (1 + i / n)n – 1 Where i is the stated interest rate and n is the number of periods. In this case, the number of payment periods is six because the interest is quoted after two months. Therefore replacing, and assuming a discount rate of 3%. Effective annual interest rate= (1+3/6)6-1 Effective annual interest rate= (1-0.5)5 (0.5)5= 0.03125 The effective annual interest rate is 0.03125 Question four Wendy bought 1,000 shares in BHP-Billiton on 30th Jan, 2010 at a cost of $29.45 per share. On the 30th Jan, 2011 the shares had a market value of $37.25 and paid a dividend of $1.50 on that date. On 30th Jan, 2012 the shares had a market value of $34.00 and also paid a dividend of $1.50 on that date. (Assume these are the only dividends paid during this period.) What dividend adjusted annual rate of return did Wendy receive for the first and for the second year? The annual rate of return is often adjusted to reflect expense and earnings on dividends on investments over a given period. In Wendys’ case, the return on shares is adjusted to reflect the dividends accrued over two different periods and changing share prices. The annual return on investments is calculated by the following formula. Rate of return = net proceeds + dividends earned / (cost of shares purchased – 1) The cost of shares =$29,450 The shares are valued at 37.25 Dividend earned in the first period=1.50*1000=$1,500 Therefore, the rate of return=37250+1500/(29450-1) This becomes 38750/29449 The dividend adjusted annual rate of return in the first year is 1.366% The share prices slumped in the second year but the dividend offered remained constant. In this case, the cost of investment is the same but net proceeds have changed. The dividend adjusted annual rate of return is (34*1000)+1500/29450-1 34000+1500/29449 35500/29449=1.205 The dividend adjusted rate of return for the second year is 1.205% Question five Waratahs Ltd have issued a bond with a $1,000 face value and 8%pa coupons paid semi-annually ( 4% each 6 months) and three years to maturity. Brumbies Ltd has also issued a bond with $1,000 face value and 8%pa coupons paid semi-annually, but with a maturity of twenty years. Yields are currently at 8% with both bonds selling at par. (i) What is the current value of both these bonds? Calculating the bond value is process that involves a series of steps. For the two bonds, the first step involves determining the coupon rate, which is the bond yield at par value. In the first case, the face value is $1000 and 8% coupon rate. The interest on this rate is (0.08*1000)=$80. Since the face value and coupon rates are equal, the second bond has $80 interest rate. The second step involves determining the annual interest paid. The two bonds pay interest semi annually. Therefore, the annual interest is $40 for each bond. Assuming a 8% expected rate of return, the minimum rate of return needed for each bond is obtained by dividing the payment periods in a year. For the two bonds, k is obtained by : K=8/2=4%. This is followed by establishing the number of interest payment periods. This achieved by multiplying the maturity period with the number of times in one-year interest is paid. For the two bonds, N=3*2 =6 for the first and n=20*2=40 for the second bond. The interest payment periods are Bond 1:n=6 and bond 2: n=40 Using the values obtained, the next step is to determine the present value annuity (PVA) using the formula PVA = I[1-(1+k)^-n]/k For the two bonds, the value becomes For bond one, the PVA=40(1-(1+0.04)-6)/6 This gives a present value annuity (PVA) of 1.33. For the second bond, the PVA=(40(1-(1+0.04)-40)/0.04 The present value (PV) is used to get the bond principal using the face value (FV), For the first bond, PV=FV/(1+K)n This gives; PV=$1000/(1+0.04)6 PV=1000(1.04)6 1000(1.265) The present value on principal is $1265. The current bond value is achieved by adding the present principal to the present value on interest. For bond one, the present price is $1266.30. Using the same procedure for the second bond, the value of the bonds is $1,000.00. What is the value of each of these bonds if yields rise to 10%? The first bonds price value drop to $949.24 while the second bond sells at $828.41. What is the percentage change in value for each of these bonds if yields rise from 8% to 10%? For the first bond, the percentage change in value is 25.03% while the second bond the change is 17.2%. What is the value of each of these bonds if yields fall to 6%? When the yield drops to 6%, the bond value is stated at $1,054.17. For the second bond, the price of the bond is stated at $1,231.15 if yields drop to 6%. What is the percentage change in value for each of these bonds if yields fall from 8% to 6%? For the first bond, the percentage change is 2.76% while the percentage change for the second bond is 26.08%. Question six Western Force Ltd has been plagued by numerous poor seasons and has decided not to pay any dividends for the next seven years while it rebuilds staffing, facilities and players. They have informed investors they will pay a $9 dividend in year seven and increase the dividends by 5%pa and will maintain that dividend growth indefinitely. Given the risks, you require a 13%pa return and are thinking of investing. How much will the shares be worth in Year six? The value of the shares after six years will be $24. How much are you willing to pay per share today? At present, the appropriate share price is $6 Question seven The Rampaging Reds have a debt equity ratio of 0.80 and a Return on Assets of 8.9%. Also, if their Total Equity is valued at $590m then: (i) What is their Equity Multiplier? The equity multiplier of accompany is the ratio of the total assets and equity and is given by the formulae Equity multiplier =Total assets /total equity. Using the debt equity ratio, it is possible to determine the company’s equity multiplier. In this case, 0.8=debt/equity and debt =Assets –equity. It follows that 0.8=(assets –equity)/equity This gives 0.8=(A-E)/E Therefore 0.8E=A-E and A=0.8E+E For this company, the assets are 1.8E*$590m which is $1062M The equity multiplier= 1062/590= 1.8 What is the return on equity using DuPont identity? By restating the DuPont equation the return on equity is determined by ROE=Net income/total equity Therefore the ROE =945.18/590 ROE= 1.602. Using the abbreviated DuPont identity, what is their Net Income? ROA=NET INCOME /TOTAL ASSETS 0.89=N.I/1062 Net income=0.89*1062 The net income is $945.18m References Geddes, R. (2002).Valuation and investment appraisal. Kent: Financial World Pub. Read More