problem (1)
(a) You have $1,000 and are given choice of two investments. The first investment returns $1,500 to you 3 in three years time. The second investment returns $3,000 in ten years. Supposing a discount rate of 5% p.a., which investment do you select?
(b) You have choice of two income streams. The first involves receiving $2,000 immediately. The second involves acquiring $1,000 in one year and $1,500 in two years. Supposing a discount rate of 8% p.a., which income stream do you select?
(c) You have the option of two income streams. The first involves acquiring $3,000 in three years and the second involves acquiring $3,500 in four years. At what discount rate are you indifferent between these two income streams? (Hint: find the discount rate that makes the present value of these two income streams equal.)
problem (2)
You buy a house today for $250,000. You give 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.
(b) If you pay off $2,000 per month, how long will it take to repay loan?
problem (3)
Joshua bought a car for $5,000 and sold it two months later for $5,200.
(a) What is the simple yearly interest rate implicit in this transaction?
(b) What is the corresponding effective yearly interest rate?
(c) If inflation is running at 3% pa, what is the real effective annual interest rate?
problem (4)
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 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. (Suppose these are the only dividends paid during this period.) What dividend adjusted yearly rate of return did Wendy receive for the first and for the second year?
problem (5)
Waratahs Ltd have issued a bond with a $1,000 face value and 8%pa coupons paid half yearly (that is, 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 half yearly, but with a maturity of twenty years. Yields are currently at 8% with both bonds selling at par.
(i) What is current value of both these bonds?
(ii) What is value of each of these bonds if yields rise to 10%?
(iii) What is the percentage change in value for each of these bonds if yields rise from 8% to 10%?
(iv) What is value of each of these bonds if yields fall to 6%?
(v) What is percentage change in value for each of these bonds if yields fall from 8% to 6%?
problem (6)
Western Force Ltd has been plagued by various poor seasons and has decided not to pay any dividends for the subsequently seven years while it rebuilds staffing, facilities and players. They have informed investors they will pay a $9 dividend in year seven and raise 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.
(i) How much will the shares be worth in Year six?
(ii) How much are you willing to pay per share today?
problem (7)
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?
(ii) Return on Equity?
(iii) Using the abbreviated Dupont identity, what is their Net Income?