A stock is expected to pay the following dividends:
| Cash Flows of a Stock | ||||||
| Time (yrs) | 0 | 1 | 2 | 3 | 4 | ... |
| Dividend ($) | 0.00 | 1.15 | 1.10 | 1.05 | 1.00 | ... |
After year 4, the annual dividend will grow in perpetuity at -5% pa. Note that this is a negative growth rate, so the dividend will actually shrink. So,
- the dividend at t=5 will be ##$1(1-0.05) = $0.95##,
- the dividend at t=6 will be ##$1(1-0.05)^2 = $0.9025##, and so on.
The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.
What is the current price of the stock?
The required return of a project is 10%, given as an effective annual rate. Assume that the cash flows shown in the table are paid all at once at the given point in time.
What is the Net Present Value (NPV) of the project?
| Project Cash Flows | |
| Time (yrs) | Cash flow ($) |
| 0 | -100 |
| 1 | 11 |
| 2 | 121 |
A project has the following cash flows. Normally cash flows are assumed to happen at the given time. But here, assume that the cash flows are received smoothly over the year. So the $250 at time 2 is actually earned smoothly from t=1 to t=2:
| Project Cash Flows | |
| Time (yrs) | Cash flow ($) |
| 0 | -400 |
| 1 | 200 |
| 2 | 250 |
What is the payback period of the project in years?
Three years ago Frederika bought a house for $400,000.
Now it's worth $600,000, based on recent similar sales in the area.
Frederika's residential property has an expected total return of 7% pa.
She rents her house out for $2,500 per month, paid in advance. Every 12 months she plans to increase the rental payments.
The present value of 12 months of rental payments is $29,089.48.
The future value of 12 months of rental payments one year ahead is $31,125.74.
What is the expected annual capital yield of the property?
Question 397 financial distress, leverage, capital structure, NPV
A levered firm has a market value of assets of $10m. Its debt is all comprised of zero-coupon bonds which mature in one year and have a combined face value of $9.9m.
Investors are risk-neutral and therefore all debt and equity holders demand the same required return of 10% pa.
Therefore the current market capitalisation of debt ##(D_0)## is $9m and equity ##(E_0)## is $1m.
A new project presents itself which requires an investment of $2m and will provide a:
- $6.6m cash flow with probability 0.5 in the good state of the world, and a
- -$4.4m (notice the negative sign) cash flow with probability 0.5 in the bad state of the world.
The project can be funded using the company's excess cash, no debt or equity raisings are required.
What would be the new market capitalisation of equity ##(E_\text{0, with project})## if shareholders vote to proceed with the project, and therefore should shareholders proceed with the project?
Question 419 capital budgeting, NPV, interest tax shield, WACC, CFFA, CAPM, no explanation
| Project Data | ||
| Project life | 1 year | |
| Initial investment in equipment | $6m | |
| Depreciation of equipment per year | $6m | |
| Expected sale price of equipment at end of project | 0 | |
| Unit sales per year | 9m | |
| Sale price per unit | $8 | |
| Variable cost per unit | $6 | |
| Fixed costs per year, paid at the end of each year | $1m | |
| Interest expense in first year (at t=1) | $0.53m | |
| Tax rate | 30% | |
| Government treasury bond yield | 5% | |
| Bank loan debt yield | 6% | |
| Market portfolio return | 10% | |
| Covariance of levered equity returns with market | 0.08 | |
| Variance of market portfolio returns | 0.16 | |
| Firm's and project's debt-to-assets ratio | 50% | |
Notes
- Due to the project, current assets will increase by $5m now (t=0) and fall by $5m at the end (t=1). Current liabilities will not be affected.
Assumptions
- The debt-to-assets ratio will be kept constant throughout the life of the project. The amount of interest expense at the end of each period has been correctly calculated to maintain this constant debt-to-equity ratio.
- Millions are represented by 'm'.
- 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 2% pa.
- All rates are given as effective annual rates.
- The 50% capital gains tax discount is not available since the project is undertaken by a firm, not an individual.
What is the net present value (NPV) of the project?
Acquirer firm plans to launch a takeover of Target firm. The deal is expected to create a present value of synergies totaling $2 million. A scrip offer will be made that pays the fair price for the target's shares plus 70% of the total synergy value.
| Firms Involved in the Takeover | ||
| Acquirer | Target | |
| Assets ($m) | 60 | 10 |
| Debt ($m) | 20 | 2 |
| Share price ($) | 10 | 8 |
| Number of shares (m) | 4 | 1 |
Ignore transaction costs and fees. Assume that the firms' debt and equity are fairly priced, and that each firms' debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money.
Calculate the merged firm's share price and total number of shares after the takeover has been completed.
Below is the Australian central bank’s cash rate.
From 2011 to 2017 the Australian central bank has implemented:
Question 869 economic order quantity
A Queensland farmer grows strawberries in greenhouses and supplies Australian supermarkets all year round. The farmer must decide how often he should contract the truck driver to deliver his strawberries and how many boxes to send on each delivery. The farmer:
- Sells 100,000 boxes of strawberries per year;
- Incurs holding costs (refrigeration and spoilage) of $16 per box per year; and
- Must pay the truck driver delivery fees at $0.20 per box plus a $500 fixed fee per delivery.
Which of the following statements about the Economic Order Quantity is NOT correct?