A two year Government bond has a face value of $100, a yield of 2.5% pa and a fixed coupon rate of 0.5% pa, paid semi-annually. What is its price?
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}###Question 345 capital budgeting, break even, NPV
| Project Data | ||
| Project life | 10 yrs | |
| Initial investment in factory | $10m | |
| Depreciation of factory per year | $1m | |
| Expected scrap value of factory at end of project | $0 | |
| Sale price per unit | $10 | |
| Variable cost per unit | $6 | |
| Fixed costs per year, paid at the end of each year | $2m | |
| Interest expense per year | 0 | |
| Tax rate | 30% | |
| Cost of capital per annum | 10% | |
Notes
- The firm's current liabilities are forecast to stay at $0.5m. The firm's current assets (mostly inventory) is currently $1m, but is forecast to grow by $0.1m at the end of each year due to the project.
At the end of the project, the current assets accumulated due to the project can be sold for the same price that they were bought. - A marketing survey was used to forecast sales. It cost $1.4m which was just paid. The cost has been capitalised by the accountants and is tax-deductible over the life of the project, regardless of whether the project goes ahead or not. This amortisation expense is not included in the depreciation expense listed in the table above.
Assumptions
- All cash flows occur at the start or end of the year as appropriate, not in the middle or throughout the year.
- All rates and cash flows are real. The inflation rate is 3% pa.
- All rates are given as effective annual rates.
Find the break even unit production (Q) per year to achieve a zero Net Income (NI) and Net Present Value (NPV), respectively. The answers below are listed in the same order.
Question 513 stock split, reverse stock split, stock dividend, bonus issue, rights issue
Which of the following statements is NOT correct?
Estimate the French bank Societe Generale's share price using a backward-looking price earnings (PE) multiples approach with the following assumptions and figures only. Note that EUR is the euro, the European monetary union's currency.
- The 4 major European banks Credit Agricole (ACA), Deutsche Bank AG (DBK), UniCredit (UCG) and Banco Santander (SAN) are comparable companies to Societe Generale (GLE);
- Societe Generale's (GLE's) historical earnings per share (EPS) is EUR 2.92;
- ACA's backward-looking PE ratio is 16.29 and historical EPS is EUR 0.84;
- DBK's backward-looking PE ratio is 25.01 and historical EPS is EUR 1.26;
- SAN's backward-looking PE ratio is 14.71 and historical EPS is EUR 0.47;
- UCG's backward-looking PE ratio is 15.78 and historical EPS is EUR 0.40;
Note: Figures sourced from Google Finance on 27 March 2015.
Below is a graph of the USD against the JPY and EUR from 1980 to 2015, compiled by the RBA. Select the correct statement about what occurred between 1980 and 2015. Note that in 1980 the euro was around 1.3 USD per EUR and the Yen was around 250 JPY per USD.
A trader just bought a European style put option on CBA stock. The current option premium is $2, the exercise price is $75, the option matures in one year and the spot CBA stock price is $74.
Which of the following statements is NOT correct?
Question 708 continuously compounding rate, continuously compounding rate conversion
Convert a 10% continuously compounded annual rate ##(r_\text{cc annual})## into an effective annual rate ##(r_\text{eff annual})##. The equivalent effective annual rate is:
Question 881 Nixon Shock, Bretton Woods, foreign exchange rate, foreign exchange system history, no explanation
In the ‘Nixon Shock’ on August 15, 1971, the United States government:
Question 935 real estate, NPV, perpetuity with growth, multi stage growth model, DDM
You're thinking of buying an investment property that costs $1,000,000. The property's rent revenue over the next year is expected to be $50,000 pa and rent expenses are $20,000 pa, so net rent cash flow is $30,000. Assume that net rent is paid annually in arrears, so this next expected net rent cash flow of $30,000 is paid one year from now.
The year after, net rent is expected to fall by 2% pa. So net rent at year 2 is expected to be $29,400 (=30,000*(1-0.02)^1).
The year after that, net rent is expected to rise by 1% pa. So net rent at year 3 is expected to be $29,694 (=30,000*(1-0.02)^1*(1+0.01)^1).
From year 3 onwards, net rent is expected to rise at 2.5% pa forever. So net rent at year 4 is expected to be $30,436.35 (=30,000*(1-0.02)^1*(1+0.01)^1*(1+0.025)^1).
Assume that the total required return on your investment property is 6% pa. Ignore taxes. All returns are given as effective annual rates.
What is the net present value (NPV) of buying the investment property?