## Time Value of Money

Question 1: Time Value of Money a)4 marks Ted Ltd is entitled to receive a cash inflow of $80,000 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 (2 marks) ii.in 5 years’ time (2 marks) b)4 marks On your 18th birthday your uncle states that he will give you $1,000 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%? c)6 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 $10,000 in a business this year (year 0) and $6,000 next year (year 1), what is the present value of the investment? (3 marks) d) 6 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 36th birthday and continues to make deposits until she is 65 (the last deposit will be on her 65th birthday), what amount must she deposit annually to be able to make the desired withdrawals on retirement? Question 2: Interest Rates a) 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? b) 9 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 25th repayment? (3 marks) c) 6 marks Mickey is planning to save $50,000 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. Question 3: Bonds and Stock Valuation a) 3 marks Ted Ltd shares currently sell for $3 per share. The last dividend was $0.2 per share. The dividend is expected to grow at 5%. i. What is the required return on Ted Ltd? (2 marks) ii. The dividend yield? (1 mark) b) 4 marks Ted Ltd is contemplating selling some 10 year bonds to raise funds for a planned expansion. Ted currently has an issue outstanding with an $8 annual coupon, paid semi-annually. 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 when it is issued? c) 8 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 bond has a coupon interest rate of 8% per annum and a yield of 6% per annum. All 3 bonds pay annual coupons. a) Calculate the price of each bond (3 marks) b) Re-calculate the price of each bond if the required yield on each bond increases to 7% per annum. (3 marks) c) Comparing your answers to parts (a) and (b), what patterns are evident? Explain. (2 marks) d) 5 marks You have predicted the following dividends for the next three years on Ted Ltd’s shares: Beginning in the 3rd year, you project that the dividend will increase at 8% per annum indefinitely. The required return is 15% per annum. i. Calculate the price today for the shares (3 marks) ii. Calculate the price at year 3 (2 marks) Question 4: Investment Decision Rules A firm with a 14% WACC is evaluating 2 projects for this year’s budget. After-tax cash flows are as follows: i. Calculate NPV for each project. (4 marks) ii. Calculate IRR for each project. (4 marks) iii. Calculate MIRR for each project. (4 marks) iv. Calculate payback for each project. (4 marks) v. Calculate discounted payback for each project. (4 marks) Question 5: Risk and Return a) 4 marks What are the portfolio weights for a portfolio that has 200 shares that sell for $10 per share and 100 shares that sell for $4 per share? b) 6 marks Calculate the expected return and standard deviation of the following share. 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 AShare B Expected return 15% 21% Standard deviation 18% 25% Correlation between the returns0.5 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)