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**Unformatted text preview: **Introduction to Finance Principles Question 1: a) 3 marks Ted Ltd is entitled to receive a cash flow of $8,000 in 2 years’ time and a further cash inflow of $14,000 in 5 years’ time (in year 5). If the interest rate is 8.5% per annum, how much is this stream of cash inflows worth: i. today (1.5 marks) FV = $8,000 n = 2 i = 8.5% ii. in 5 years’ time (1.5 marks) FV = $14,000 n = 5 i = 8.5% b) 4 marks On your 18th birthday your uncle states that he will give you $1,500 each year for 5 years commencing on your 21st birthday. What is the value to you at the time of your 18th birthday of this promised cash flow if the rate of interest is 10%? PMT = $1,500 n = 5 i = 10% FV = $5,686.18 n = 20-18 = 2 i = 10% c) 5 marks What is the present value of a perpetual cash inflow of $1,000 received at the end of each year, the first inflow occurring 2 years from now, if the interest rate is 5% per annum? (3 marks) If the above cash inflows can be produced by investing $15,000 in a business this year (year 0) and $6,000 next year (year 1), what is the present value of the investment? (2 marks) i. ii. d) 3 marks An investment returns nothing to its owner in the first 2 years. In the following 2 years, the returns are $100,000 and $150,000, respectively, and after that the return is $200,000 per year in perpetuity. All cash flows occur at year end. What is the present value of these cash flows if the discount rate is 8% per annum? e) 5 marks Your friend is celebrating her 35th birthday today and wants to start saving for her anticipated retirement at age 65. She wants to be able to withdraw $10,000 from her savings account on each birthday for 10 years following her retirement; the first withdrawal will be on her 66th birthday. Your friend intends to invest her money in the local savings bank, which offers 7% per annum. She wants to make equal, annual payments on each birthday in a new savings account she will establish for her retirement fund. If she starting these deposits on her 36 th birthday and continues to make deposits until she is 65 (the last deposit will be on her 65 th birthday), what amount must she deposit annually to be able to make the desired withdrawals on retirement? PMT = $10,000 n = 10 i = 7% FV = $70,235.82 n = 30 i = 7% Question 2: a) 2 marks Ted deposits $2,000 in a bank fixed deposit for 6 months at an interest rate of 13.25% per annum. How much interest will he earn? PV = $2,000 n = 0.5 (6 months) i = 13.25% b) 5 marks Ted Bank charges 7% per annum compounded daily (365 days in a year), on its personal loans. Pine Bank charges 7.1% per annum compounded semi-annually. As a potential borrower, which do you prefer? c) 8 marks You are considering the purchase of a new home for $700,000. You have a deposit of $100,000. The bank will lend you money at 7% per annum compounded monthly over a period of up to 20 years. If you borrow the required funds over 20 years, what are the monthly repayments? (3 marks) After 2 years, how much do you still owe the bank? (3 marks) What is the interest component of the 25 th repayment? (2 marks) PV = $700,000 - $100,000 = $600,000 n = 20 X 12 = 240 months i = 0.5833% After 24th payment, n = 240 - 24 = 216 months PMT = $4,651.25 n = 216 months i = 0.5833% 25th Payment Interest = $570,419.49 X 0.005833 = $3,327.26 d) 5 marks Mickey is planning to save $20,000 per quarter for 10 years. Savings will earn interest at an (nominal) interest rate of 12% per annum. Calculate the present value for this annuity if interest is compounded semi-annually. NIR = 12% m=4 Question 3: a) You have predicted the following dividends for the next three years on Ted Ltd’s shares: Year 1 2 3 Projected Dividend $0.20 $0.35 $0.40 Beginning in the 3rd year, you project that the dividend will increase at 8% per annum indefinitely. The required return is 12% per annum. i. Calculate the price today for the shares (3 marks) r= 12% g= 8% ii. Calculate the price at year 3 (2 marks) D = 0.432 g = 8% i = 12% b) Ted Ltd is contemplating selling some 10 year bonds to raise funds for a planned expansion. Ted currently has as issue outstanding with an $8 annual coupon, paid semiannually. These bonds currently sell for $93.49, a discount relative to their $100 face value, and they have 10 years remaining to maturity. What coupon rate must the new issue have if it is to sell at par which it is issued? FV = 100 P = $93.49 C = 8/2 = 4 n = 10 X 2 = 20 c) 7 marks Ted Investment Ltd has a portfolio of 3 bonds (A, B and C). Their terms to maturity are 5, 10 and 25 years, respectively. Each of the bonds has a coupon interest rate of 8% per annum and a yield of 6% per annum. All 3 bonds pay annual coupons. i. Calculate the price of each bond (2.5 marks) Bond A: Bond B: Bond C: ii. Re-calculate the price of each bond if the required yield on each bond increases to 7% per annum. (2.5 marks) Bond A: Bond B: Bond C: iii. Comparing your answers to parts (a) and (b), what patterns are evident? Explain. (2 marks) d) 5 marks The required rate of return on the shares in the firms identified in parts (i) to (ii) is 15% per annum. Calculate the current share price in each part. i. The current dividend per share in Firm A is 80 cents. This dividend is expected to grow at 5% per annum. (2 marks) D = 0.08 g = 5% i = 15% ii. Current dividend per share in Firm B is 60 cents. The dividend had been growing at 12% per annum in recent years, a rate expected to be maintained for a further 3 years. It is envisaged that the growth rate will then decline to 5% per annum and remain at that level indefinitely. (3 marks) D = 0.9019 g = 7% i = 15% Question 4: You are evaluating a proposal to buy a new machine. The base price is $108,000, and shipping and installation costs would add another $12,500. The machine is depreciated using straight line method, and it would be sold after 3 years for $60,000. The machine would require a $5,500 increase in net operating working capital. There would be no effect on revenues, but pre-tax labour costs would decline by $44,000 per year. The marginal tax rate is 35%, and the WACC is 12%. i) What are the project’s annual cash flows during years 0, 1, 2 and 3? Year Depreciation tax savings After tax savings Salvage value Tax on sale Cost Net change in WC CFC Year 0 Year 1 $14,058.3 3 $28,600 Year 2 $14,058.3 3 $28,600 Year 3 $14,058.33 $42,658 $42,658 $87,158 $-120,500 $-5,500 $-126,000 $28,600 $60,000 $-20,999 The Net Cost is $126,000 Price Increase in NWC Installation and Shipping Cash Outlay for New Machine $108,000 $5,500 $12,500 ($126,000) Operating Cash Flow: Year 1 Year 2 Year 3 After-tax savings $28,600 $28,600 $28,600 Depreciation tax savings $14,058 $14,058 $14,058 Net Cash Flow $42,658 $42,658 $42,658 Cost Savings After-Tax is $44,000(1-TC) = $44,000 X (1-0.35) = $28,600 For depreciation, the net cost of the machine in Year 0 = $108,000 + $12,500 = $120,500 Depreciation Tax Savings: The terminal year cash flow is $44,501: Tax on Sale Salvage Value Return of NWC ($20,999) $60,000 $5,500 $44,501 Book Value in the Year 4 = $120,500 - $40,166 - $40,166 - $40,166 = $2 Tax on Sale = ($60,000 - $2)(0.35) = $20,999 ii) Calculate NPV. Year 0 Future Cash Flow $-126,000 Present Value $-126,000 Net Present $8,132.33 Value iii) Calculate IRR. Year 1 $42,658.33 $38,087.79 Year 2 $42,658.33 $34,006.96 Year 3 $87,158.33 $62,037.58 iv) Calculate MIRR. Year 0 Year 1 Year 2 Year 3 $ -126000 i) Calculate payback. The payback period is 2.47 years. ii) Calculate discounted payback. Present Value Cumulative Discounted Cash Flow Year 0 $-126,000 $-126,000 Year 1 $38,087.79 $-87,912.21 The discounted payback is 2.87 years. Year 2 $34,006.96 $-53,905.25 Year 3 $62,037.58 $8,132.33 Question 5: a) 4 marks The expected return on the ith asset is given by: i. What is the expected return on ith asset where ? (2 marks) ,, = 0.08 + 1.25(0.06) = 0.08 + 0.075 = 0.155 ii. What is the expected return on market portfolio where? (2 marks) ,, = 0.09 = 0.12 b) 6 marks Calculate the expected return and standard deviation of the following share. State of the economy Probability of state of economy 0.30 0.70 Recession Boom Economy status Recessio n Boom Probability of state of economy, Rate of return if state occurs, 0.30 0.70 14% 20% Expected Return, E() Rate of return if state occurs 14% 20% 1.00 0.042 0.14 0.182 Expected Return, = 0.042 + 0.14 = 0.182 Variance, = 0.0005292 + 0.0002268 = 0.0007560 Standard Deviation, σ = = = 0.027495454169735 ≈ 0.027495 -4.2% 1.8% 0.001764 0.000324 0.0005292 0.0002268 Variance, 0.0007560 c) 10 marks Ted has invested one-third of his funds in Share A and two-thirds of his funds in Share B. His assessment of each investment is as follows: Share A Expected return Standard deviation Correlation between the returns 15% 18% 0.5 Share B 21% 25% i. Calculate the expected return and the standard deviation of return of Ted’s portfolio? (5 marks) ii. Re-calculate the expected return and the standard deviation where the correlation between the returns is 0 and 1, respectively. (3 marks) iii. Is Ted better or worse off as a result of investing in the portfolio rather than in one share? (2 marks) ...

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