Risk Is Uncertainty

Part A:

a) In finance, risk is uncertainty. Comment (1 sentence) on whether or not Nortel stock is risky, giving a bit of evidence (Hint – think about our homework assignment)

b) The bond rating firms are paid by the corporations and governments that wish to issue bonds. What do investors in bonds worry about, regarding this fact?

c) State ONE advantage and ONE disadvantage of long term corporate bonds compared with long term Treasury (federal government) bonds.

d) State ONE difference between a bond and a preferred share

e) If you sell short 1,000 shares of RIM at $100/share, what is your profit or loss if you cover your short position exactly 2 months later, if the shares are then trading at $130/share?

Answer:

a) Nortel stock price has varied dramatically in recent years (as per our homework assignment), so the stock would be considered very risky.

b) Investors worry about the possibility that the bond rating firms will give bonds a higher rating than they deserve, in order to please their clients – the firms and governments wishing to issue bonds.

c) Corporate bonds have slightly higher yields, but are a little bit more risky than Treasury bonds.

d) Dividends on preferred shares are not contractually required as coupon payments are with bonds OR preferred shares are almost always like perpetuities that pay dividends indefinitely, while bonds almost always mature after a fixed number of years.

e) You were making a bet that the shares would fall, but they increased by $30/share. You will lose $30 x 1,000 = $30,000

Part B:

1. A firm is facing the following situation. The firm has debt of $80 million, which will be due in 1 month. It has no assets or activities happening currently. The firm has two projects it is considering:

Project 1: pays off with $100 million in 1 month, for sure.

Project 2: Pays $50 million in 1 month, with probability 1/3

Pays $100 million in 1 month, with probability 1/3

Pays $150 million in 1 month, with probability 1/3

a) What is the expected outcome for debt-holders and shareholders for each project?

b) Faced with this situation repeatedly, which project would the debt-holders prefer the firm choose? What would the shareholders prefer?

Answer:

a) For project 1, debt-holders expect $80 million and shareholders expect $20 million

b) For project 2, debt-holders expect (1/3)(50 + 80 + 80) = $70 million and shareholders expect (1/3)(0+ 20 + 70) = $30 million.

Clearly, the debt-holders will prefer the firm choose project 1 while the shareholders will prefer the firm choose project 2.

2. If the interest rate is 11% annually, how long (in years) would it take for you to triple your money if compounding is:

i) annual

ii) semi-annual

iii) monthly

iv) continuous

Answer:

(1+r/m)mx = the value of 1 in x years, if r is the annual rate with compounding m times/year.

i) Solve (1.11)x = 3 => xln(1.11) = ln(3) => x = 1.0986/.1044 = 10.523 years

ii) Solve (1+.11/2)2x = (1.055)2x = 3 => 2xln(1.055) = ln(3) => 2x = 20.5189 so x = 10.2595 years

iii) Solve (1+.11/12)12x = 3 => 12x = 120.3957 => x = 10.033 years

iv) e.11x = 3 => .11x = ln(3) = 1.0986 => x = 1.0986/.11 = 9.9874 years

3. Over the last 6 months, the price of gold (in US dollars - USD) has risen from $650 to $740 per ounce. In the same period, the Canadian dollar (CAD) has risen from a rate such that $0.90 USD = $1.00 CAD, to equity with the USD. What is the percentage gain (or loss) for a Canadian investor who purchased 100 ounces of gold 6 months ago, and still owns it today?

Answer:

100 x $650 = $65,000 USD = 65,000/.90 = $72,222.22 CAD

Today, the 100 ounces is worth $74,000 USD = $74,000 CAD. The gain is $1777.78. On a percentage basis, the gain is 1777.78/72,222.22 = 2.4615%.

So even though the price of gold increased by 90/650 = 13.85%, because of the negative impact of the rising CAD, our investor has a holding period return of only 2.4615%.

4. Find the present value of a series of 30 consecutive