1. A payment schedule requires 20 payments of $10,000, the first payment to be made 15 years from today. Assuming a discount rate of 10%, what is the present value of this series of payments? (2 marks) 2. Assume the payment schedule in problem 1 changes as follows: . the payment 17 years from today is waived, and . a payment of $20,000 is made 18 years from today. Assuming a discount rate of 10%, what is the present value of this series of payments? (2 marks) 3. Your friend is celebrating his 35th birthday today and wants to start saving for his anticipated retirement at age 65. He wants to be able to withdraw $10,000 from his savings account on each birthday for 10 years following his retirement; the first withdrawal will be on his 66th birthday. Your friend intends to invest his money in the local savings bank, which offers 8 per cent interest per year. He wants to make equal, annual payments on each birthday in a new savings account he will establish for his retirement fund. If he starts making these deposits on his 36th birthday and continues to make deposits until he is 65 (the last deposit will be on his 65th birthday), what amount must he deposit annually to be able to make the desired withdrawals on retirement? (3 marks) 4. Calculate an equivalent annual income for 20 years on the following income stream received over 30 years if the interest rate is 10% per annum compounded annually: Years 1-15 $15,000pa Years 16-20 $20,000pa Years 21-30 $30,000pa (3 marks) 5. Pagoda Industries Ltd expects its new product will give it a significant first mover advantage in the market and that is expected to provide growth in earnings per share of 400% within the coming year, and 75% growth in each of the subsequent 3 years. After that time, it is expected competitors will have developed and brought to market similar products with the result that Pagoda would expect earnings growth to drop back to its normal level of 3% per year forever. Pagoda’s cash dividend was 10 cents per share last year and is expected to remain at that amount for each of the next 5 years as the company builds it retained earnings to finance research and development. In the sixth year, it is expected shareholders will be rewarded with payout ratio will be 80% of the earnings per share, and the payout ratio is expected to remain at that level forever. The required rate of return on Pagoda’s ordinary shares is 20% per year and the latest earnings per share was 25 cents.
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