Question 65 annuity with growth, needs refinement
Which of the below formulas gives the present value of an annuity with growth?
Hint: The equation of a perpetuity without growth is: ###V_\text{0, perp without growth} = \frac{C_\text{1}}{r}###
The formula for the present value of an annuity without growth is derived from the formula for a perpetuity without growth.
The idea is than an annuity with T payments from t=1 to T inclusive is equivalent to a perpetuity starting at t=1 with fixed positive cash flows, plus a perpetuity starting T periods later (t=T+1) with fixed negative cash flows. The positive and negative cash flows after time period T cancel each other out, leaving the positive cash flows between t=1 to T, which is the annuity.
###\begin{aligned} V_\text{0, annuity} &= V_\text{0, perp without growth from t=1} - V_\text{0, perp without growth from t=T+1} \\ &= \dfrac{C_\text{1}}{r} - \dfrac{ \left( \dfrac{C_\text{T+1}}{r} \right) }{(1+r)^T} \\ &= \dfrac{C_\text{1}}{r} - \dfrac{ \left( \dfrac{C_\text{1}}{r} \right) }{(1+r)^T} \\ &= \dfrac{C_\text{1}}{r}\left(1 - \dfrac{1}{(1+r)^T}\right) \\ \end{aligned}###
The equation of a perpetuity with growth is:
###V_\text{0, perp with growth} = \dfrac{C_\text{1}}{r-g}###You just signed up for a 30 year fully amortising mortgage loan with monthly payments of $1,500 per month. The interest rate is 9% pa which is not expected to change.
To your surprise, you can actually afford to pay $2,000 per month and your mortgage allows early repayments without fees. If you maintain these higher monthly payments, how long will it take to pay off your mortgage?
Find Piano Bar's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.
Piano Bar | ||
Income Statement for | ||
year ending 30th June 2013 | ||
$m | ||
Sales | 310 | |
COGS | 185 | |
Operating expense | 20 | |
Depreciation | 15 | |
Interest expense | 10 | |
Income before tax | 80 | |
Tax at 30% | 24 | |
Net income | 56 | |
Piano Bar | ||
Balance Sheet | ||
as at 30th June | 2013 | 2012 |
$m | $m | |
Assets | ||
Current assets | 240 | 230 |
PPE | ||
Cost | 420 | 400 |
Accumul. depr. | 50 | 35 |
Carrying amount | 370 | 365 |
Total assets | 610 | 595 |
Liabilities | ||
Current liabilities | 180 | 190 |
Non-current liabilities | 290 | 265 |
Owners' equity | ||
Retained earnings | 90 | 90 |
Contributed equity | 50 | 50 |
Total L and OE | 610 | 595 |
Note: all figures are given in millions of dollars ($m).
Question 322 foreign exchange rate, monetary policy, American and European terms
The market expects the Reserve Bank of Australia (RBA) to decrease the policy rate by 25 basis points at their next meeting.
Then unexpectedly, the RBA announce that they will decrease the policy rate by 50 basis points due to fears of a recession and deflation.
What do you expect to happen to Australia's exchange rate? The Australian dollar will:
The Australian cash rate is expected to be 6% pa while the US federal funds rate is expected to be 4% pa over the next 3 years, both given as effective annual rates. The current exchange rate is 0.80 AUD per USD.
What is the implied 3 year forward foreign exchange rate?
Private equity firms are known to buy medium sized private companies operating in the same industry, merge them together into a larger company, and then sell it off in a public float (initial public offering, IPO).
If medium-sized private companies trade at PE ratios of 5 and larger listed companies trade at PE ratios of 15, what return can be achieved from this strategy?
Assume that:
- The medium-sized companies can be bought, merged and sold in an IPO instantaneously.
- There are no costs of finding, valuing, merging and restructuring the medium sized companies. Also, there is no competition to buy the medium-sized companies from other private equity firms.
- The large merged firm's earnings are the sum of the medium firms' earnings.
- The only reason for the difference in medium and large firm's PE ratios is due to the illiquidity of the medium firms' shares.
- Return is defined as: ##r_{0→1} = (p_1-p_0+c_1)/p_0## , where time zero is just before the merger and time one is just after.
Find the cash flow from assets (CFFA) of the following project.
One Year Mining Project Data | ||
Project life | 1 year | |
Initial investment in building mine and equipment | $9m | |
Depreciation of mine and equipment over the year | $8m | |
Kilograms of gold mined at end of year | 1,000 | |
Sale price per kilogram | $0.05m | |
Variable cost per kilogram | $0.03m | |
Before-tax cost of closing mine at end of year | $4m | |
Tax rate | 30% | |
Note 1: Due to the project, the firm also anticipates finding some rare diamonds which will give before-tax revenues of $1m at the end of the year.
Note 2: The land that will be mined actually has thermal springs and a family of koalas that could be sold to an eco-tourist resort for an after-tax amount of $3m right now. However, if the mine goes ahead then this natural beauty will be destroyed.
Note 3: The mining equipment will have a book value of $1m at the end of the year for tax purposes. However, the equipment is expected to fetch $2.5m when it is sold.
Find the project's CFFA at time zero and one. Answers are given in millions of dollars ($m), with the first cash flow at time zero, and the second at time one.
A credit card company advertises an interest rate of 18% pa, payable monthly. Which of the following statements about the interest rate is NOT correct? All rates are given to four decimal places.
A non-dividend paying stock has a current price of $20.
The risk free rate is 5% pa given as a continuously compounded rate.
Options on the stock are currently priced at $5 for calls and $5.55 for puts where both options have a 2 year maturity and an exercise price of $24.
You suspect that the call option contract is mis-priced and would like to conduct a risk-free arbitrage that requires zero capital. Which of the following steps about arbitraging the situation is NOT correct?
Question 964 monetary policy, impossible trinity, foreign exchange rate
It’s often thought that the ideal currency or exchange rate regime would:
1. Be fixed against the USD;
2. Be convertible to and from USD for traders and investors so there are open goods, services and capital markets, and;
3. Allow independent monetary policy set by the country’s central bank, independent of the US central bank. So the country can set its own interest rate independent of the US Federal Reserve’s USD interest rate.
However, not all of these characteristics can be achieved. One must be sacrificed. This is the 'impossible trinity'.
Which of the following exchange rate regimes sacrifices independent monetary policy?