Business Finance - Assignment Example

Business finance (calculation need to show clearly) Question 1 You are now 50 years old and plan to retire at the age of 67. You currently have a share portfolio worth $150,000, a superannuation fund worth $250,000 and a money market account worth $50,000. Your share portfolio is expected to provide you annual returns of 12%, your superannuation will earn you 9.5% annually and the money market account earns 6.25%, compounded monthly. Required: a) If you do not save another cent, what will be the total value of your investments when you retire? The general formula for calculating the future value of the investments is FV= PV(1+i)n Where: FV = future value of the investment PV = Present value of the investment i= Annual interest rate n= Number of periods of compounding the interest Thus: i) The value of share portfolio when I reach the retirement age of 67 years will be given by: FV= PV(1+i)n Where PV = $150,000 i= 12% n = 17 years NB// n = 17 since interest is being compounded annually. Thus FV = $150,000(1+12%)17 = $150,000(1.12)17 = $1,029,906.13 ii) The future value of the superannuation fund at my retirement age of 67 years will be given by: FV= PV(1+i)n Where PV = 250,000 i= 9.5% n = 17 Thus FV = $250,000(1+9.5%)17 =$250,000(1.095)17 =$1,169,445.63 iii) The future value of the money market account at my retirement age of 67 years will be given by: FV= PV(1+i)n Where PV = $50,000 i= 6.5% n = 204 ( Since the interest is compounded monthly) Thus FV = $50,000(1+6.5%/204)204 = $150,511.74 Thus, the total value of my investment at my retirement age of 67 will be given by: Total investment = $1,029,906.13+ $1,169,445.63 +$150,511.74 =$2,349,863.50 b) Assume that your superannuation contribution is $12,000 per year for the next 15 years (starting 1 year from now). How much will your investments be worth when you retire? If I make annual superannuation contributions amounting to $12,000 for the next 15 years, my investments worth when I retire will be calculated as follows: i) The value of share portfolio when I reach the retirement age of 67 years will be given by: FV= PV(1+i)n Where PV = $150,000 i= 12% n = 17 years NB// n = 17 since interest is being compounded annually. Thus FV = $150,000(1+12%)17 = $150,000(1.12)17 = $1,029,906.13 iv) The future value of the money market account at my retirement age of 67 years will be given by: FV= PV(1+i)n Where PV = $50,000 i= 6.5% n = 204 ( Since the interest is compounded monthly) Thus FV = $50,000(1+6.5%/204)204 = $150,511.74 iii) The value of the superrannuation fund will be given by the sum of the future value of lumpsum at my 50th year and the future value of the $12,000 to be contributed for the next 15 years (starting 1 year from now). This is given by; The future value of lumpsum FV= PV(1+i)n Where; PV = $250,000 i= 9.5% n = 16 (bearing in mind that the $12,000 annual contributions start 1 year from now) Thus FV = $250,000(1+9.5%)16 = $250,000(1.095)16 = $ 1,067,986.88 The future value of annuity (the $12,000 annual contribution) will be given by: Where C = annual contributions C = $12,000 i= 9.5% n =15 (15 years with annual compounding) FV = $12,000(1+9.5%)15-1)/9.5%)) FV = $12,000(1.095)15/0.95 FV = $ 366,482.77 Thus at the end of the $12,000 annual payments, the total superannuation fund will be; =$ 1,067,986.88+ $ 366,482.77 =$1,434,469.65 But this amount has to be compounded again for the 67th year. Thus: FV= PV(1+i)n FV = $1,434,469.65(1+9.5%) 1 = $ 1,570,744.27 Thus, my total investment for the period with $12,000 annual contribution is given by Total investment = $ 1,067,986.88 +$ 366,482.77 +$ 1,570,744.27 =$3,005,213.92 c) Assume that you expect to live 23 years after you retire (until age 90). Today, at age 50, you take all of your investments and place them an account that pays 8% annually (use the scenario from part b) in which you continue saving. If you start withdrawing funds starting at age 67, how much can you withdraw every year and leave nothing in your account after the 23rd & final withdrawal? If all the investments are placed in an account paying 8% annually and I continued saving $12,000 annually, then the amount of the portfolio by the time I retire at the age of 67 years is given by the future value of the lump sum at the age of 50 and the future value of the annuity contributions ($12,000 annually) after 15 years. Thus, future value of lump sum is given by; FV= PV(1+i)n But PV = $150,000+$250,000 + $50,000 = $450,000 i= 8% n = 16 years (bearing in mind that $12,000 annual contributions start one year from now) Thus FV = $450,000(1+8%) 16 = $ 1,541,674.19 The value of $12,000 contributions after 15 years will be given by: Where C = annual contributions C = $12,000 i= 8% n =15 FV =$12,000*(1+8%) 15-1))/8% FV = $ 325,825.37 Thus, the total amount of investment after 16 years will be; $ 1,541,674.19+ $ 325,825.37 =$1,867,499.56 But this amount will have to be compounded for the 67th year. Thus at my retirement age of 67 years, the total investment will be; FV= PV(1+i)n FV = $1,867,499.56 (1+8%) 1 FV =$ 2,016,899.52 The amount to be withdrawn for 23 years leaving no balance is given by: Thus, the amount to be paid from the investment per month will be given by: P = 0.08($ 2,016,899.52)/(1-(1+0.08))-23 P = $194,473 Thus, I will be withdrawing $194,473 per year from the investment for the next 23 years leaving no balance. d) At age 67, you want your investments, which are described in the problem statements above, to support a perpetuity that starts a year from now. How much can you withdraw each year without touching your principal (at 8% per year)? In this regard, the amount to be withdrawn each year without touching the principal is given by; Payment = PV of annuity * Interest rate In this case, present value of annuity = $ 2,016,899.52 While interest rate = 8% Thus, the amount to be withdrawn per month is given by; $ 2,016,899.52 × 8% = $161,352 per year. Question 2 Wattyl Group Ltd has 18-year bonds outstanding. These bonds, which pay semi annual coupons, have a coupon rate of 9.375 per cent and a yield to maturity of 7.95 per cent. Required: a) Calculate the bond’s current price. Current price = coupon rate/ Yield to maturity Current price = 93.75/0.0795 =$1,179.25 b) If the bonds can be called after 5 more years at a premium of 13.5% over the par value, what is the investor’s realized yield? Realized yield = Annual interest + (Call price- Market price) years to call) (Call price+ Market price)/2 In this case, Annual interest = 7.95% Market price = $1179 Call price = $1179+ 13.5% Years to call = 13 years Thus, Realized yield = 7.95 %+( 1338-1179)13 (1338+1179)/2 The investor’s realized yield will be =3.69% c) If you bought the bond today & sold it a year later, what is your expected rate of return? =$7.95+3.69 = 11.64% Explain in your own words. I would expect to realize a return that is higher than the one I would realize by having to wait for 18 years since I would have to forego annual interest for 17 years and hence the rate of return for the year should be a premium. Question 3 What would be the effect on the price of bonds of? a) an unexpected rise in interest rates, and The effect on the price of bonds when there is an unexpected rise in interest rates will be that the prices of the bonds will drop or decline. The reason behind this is that bonds have fixed interest and principal payments. This implies that when interest rates increase, the bond becomes less attractive to investors hence bringing their prices down. For instance, suppose a bond has a value of $1000 has a stated interest rate of 9% and has a remaining life of five years .The semi-annual interest on the bond will be $45. When interests increase to 10%, it means that the interest earned semi-annually will be $50. It is obvious that the 9% bond will be rendered unsalable for the same price of $1000 bearing in mind that bond’s interest is fixed. In a bid to make the investors buy the 9% bond in a market offering 10%, the bond’s price would have to be dropped to an amount that would yield a 10% return over the bond’s remaining life. This is why a rise in interest rates causes the price of bonds to drop. An unexpected fall in interest rates? When there is an unexpected fall in interest rates, the prices of bonds would be expected to rise or increase. Based on the example above, when the interest rates decline to 8%, it means that while the expected semi-annual interest on the 9% bond would remain $45, that of the 8% bond would be $40. As such, there would be increased demand on the 9% bond since it has better earnings. This would force the market to adjust its prices upwards such that its overall expected returns are 8% over the bond’s remaining life. b) Would these interest rate changes have a similar effect on the price of shares? I think that these interest rate changes would have a similar effect on the price of shares. In other words, when the interest rates rise, I would expect the prices of shares to drop in the long run. On the other hand, when the interest rates fall, I would expect the prices of shares to rise. Explain in your own words. The reason behind this is the fact that an interest rate rise gives rise to increased cost of borrowing and also of holding money. It means that the disposable incomes of consumers will decline. On the other hand, the companies cost of borrowing would increase and this would also force some companies to withhold some of their development projects that would otherwise lead to increased value of the company to a later date when the interest rates would come down. As such, it means that while investors would have little money left for investing, the companies would also be valued less owing to increased borrowing expenses and postponing some of their development projects. As such, the prices of shares would fall owing to falling values of shares as well as declining demand of the shares from the investors owing to declining disposable incomes. The vice versa would be true when the interest rates fall. References: Jared, B2014, Business finance, London, Rutledge. Robert, W2012, Money and banking, Sydney, Prentice Hall. Johansen, N2015, Contemporary issues in business finance, New York, Taylor & Francis. Read More