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Homework answers / question archive / 1)What would be the annualized investment rate if a Treasury bill was purchased for $9,360 maturing in 270 days for $10,000? You must show your calculation, otherwise, your mark will be deducted
1)What would be the annualized investment rate if a Treasury bill was purchased for $9,360 maturing in 270 days for $10,000? You must show your calculation, otherwise, your mark will be deducted.
2)You and your friend, Polly Horn are thinking of going on a year trip around the world in exactly
3 years’ from today. Unfortunately, you will need a lot of money to ensure you can afford all
the fun activities you have planned! You have determined that you will each need $30,000 to
fund this trip. Polly Horn has been lucky enough to win the lottery recently and can afford to
put a single lump sum into the bank account today. Unfortunately, you are unable to do the
same, and have to place fortnightly payments into the bank account for the next three years,
starting in a fortnight from today. Given this, and the fact that the interest rate available to
both Polly Horn and yourself is 9% p.a. compounded monthly, calculate:
a) The lump sum Polly Horn puts into the bank today; and,
b) The fortnightly payment you have to place into the bank account to have exactly
$30,000 in three years’ time.
3)
You are considering investing in JouJou Ltd, a public company that manufactures bottle
openers and other kitchen tools. In considering purchasing shares in JouJou Ltd, you are
utilising your valuation skills to see if the market price is fair. Using the information below, find
the theoretical value of one share of JouJou Ltd and compare it to the current market price of
$42.53:
? A dividend was paid out yesterday of $0.50;
? The next dividend of $0.50 is expected to occur in two years’ time, and this
dividend will be constantly paid every six months for 6 consecutive dividend
payments (this includes the dividend at year 2);
? Thereafter, dividends will grow at 6% p.a. compounded semi?annually in
perpetuity; and,
? The required rate of return on equity is 8% p.a. compounded quarterly and
all dividends are paid out semi?annually.
Would you purchase JouJou Ltd? In providing your decision, you may need to state some
assumptions that allow you to compare the market value with the calculated share price.
1)
Face value of T-bill =10000
Value or purchase price = 9360
Maturity days = 270
Annualized rate of investment = ((face value/purchase price)-1)*365/Maturity days
=((10000/9360)-1)*365/270
=0.09243431466 or 9.24%
So annualized rate of investment is 9.24%
2)FV (future value) = 30,000; APR = 9%; n (frequency of compounding p.a.) = 12; N (number of compoundings during the investment period) = 3*12 = 36
Amount to be invested today = FV/(1 + APR/n)^N
= 30,000*(1+9%/12)^36 = 22,924.47
b). Here, the frequency of deposit (m = 52/2 = 26) is different from the frequency of compounding (n = 12), so
effective fornightly rate = [(1 + APR/n)^(n/m)] -1
= [(1+9%/12)^(12/26)] -1 = 0.3455%
Amount to be invested every fortnight: FV = 30,000; PV = 0; N (number of deposits) = 3*26 = 78; rate = 0.3455%; Type = End (or 0), solve for PMT.
Deposit per fortnight = 335.78
Note: This can also be solved using FV of ordinary annuity formula.)
3)
Let us calculate the price of the stock 4.5 years from now
Price of Stock = Dividend (1 + growth rate) / (Required rate of return on equity - growth rate)
Price of Stock = $0.5 (1 + (6% / 2)) / ((8% / 2) - (6% / 2))
Price of Stock 4.5 years from now = $51.5
Price of the stock today
Price of Stock = 
Dividend / (1 + Required rate of return on equity / Compounding frequency )period * Compounding frequency + Price of Stock 4.5 years from now / (1 + Required rate of return on equity / Compounding frequency)period * Compounding frequency
Price of Stock = $0.5 / (1 + (8% / 2))2 * 2 + $0.5 / (1 + (8% / 2))2.5 * 2 + $0.5 / (1 + (8% / 2))3 * 2 + $0.5 / (1 + (8% / 2))3.5 * 2 + $0.5 / (1 + (8% / 2))4 * 2 + $0.5 / (1 + (8% / 2))4.5 * 2 + $51.5 / (1 + (8% / 2))4.5 * 2
Price of Stock = $0.43 + $0.41 + $0.40 + $0.38 + $0.37 + $0.35 + $36.18
Price of Stock = $38.51
The theoretical calculated share price $38.51 is lower than the current market price of $42.53. I would not purchase this share.
