Question 1 - Capital Budgeting
PART A - Project Evaluation
Firm ABC decides to invest in a 6-year project with constant annual after tax cash flows. The project has a simple pay-back period of 4 years and a discounted pay-back period of 5 years. All assets required for the implementation of this project are depreciated on a straight-line basis and expected to be fully depreciated by the end of the project so that their salvage value is zero. At the announcement of the project, the stock price of ABC increases by 4$ CAN. Depreciations and amortizations (D&A) are tax deductible; there are no opportunity costs associated with the project and no changes in NWC. Corporate tax rate is 30%. ABC does not operate other projects. Number of shares outstanding is 10 million.
1. What is the NPV of the project?
2. What is the minimum rate of return expected by the investors of firm ABC (i.e., the discount rate used to estimate the project NPV)?
3. What is the annual after tax cash flow of the project (including annual tax savings obtained by depreciating the assets)?
4. What is the initial investment of the project?
5. What is the annual amount of D&A?
6. What is the present value of the tax shield?
7. One year before the end of the project, the Government increases the corporate tax rate to 40%. What is the impact of this announcement on the stock price of ABC?
PART B - Project Ranking
ABC is financially constrained. Total debt financing available for financing new projects is 41,400 CAD. The firm's investment opportunities are as follows:
|
Project
|
|
Initial investment
|
|
Constant After tax cash flows
|
|
Discount rate
|
|
Horizon
|
|
NPV
|
IRR
|
Pay-back
|
|
A
|
|
12,600
|
|
2,520
|
|
10%
|
|
10
|
|
|
15%
|
|
|
B
|
|
8,500
|
|
2,975
|
|
7%
|
|
7
|
|
|
29%
|
|
|
C
|
|
20,250
|
|
3,240
|
|
12%
|
|
35
|
|
|
16%
|
|
|
D
|
|
120
|
|
72
|
|
12%
|
|
15
|
|
|
60%
|
|
|
E
|
|
1,500
|
|
310
|
|
13%
|
|
6
|
|
|
7%
|
|
1) Calculate the NPV and the simple pay-back period of each investment opportunity. When computing the pay-back period, assume that cash flows are evenly distributed during the year.
2) How much value will ABC create if the IRR of the project is used as a selection criterion?
3) How much value will ABC create if the NPV of the project is used as a selection criterion?
4) If ABC had to repay 25,100 CAD of debt financing after 2 years, what would be the cost of this liquidity constraint for its shareholders (for simplicity, assume that funds not used for investment purposes do not earn interests)?
Question 2 - Replacement Decision
Your boss is trying to figure out when to replace an important piece of machinery in your main production facility. The Siemens NR550, costs $5.45 million brand new and generally lasts about 15 years before needing to be replaced (CCA Rate = 15%). The currently installed version was put in place 5 years ago. Since the product being produced will be obsolete in 10 years, management had not planned on replacing the NR550 (though the asset pool would remain open as a number of other projects are underway which involve similar systems). The salvage value on the NR550 today would be $2.5 million, or $1.5 million in year 10.
Last week, Siemens offered an upgrade, the NR600, which will cost $5 million and do the same job as the NR550 for the remaining 10 years of the project after which it can be salvaged for $1.2 million. Although its salvage is less than then NR550, the NR600 is expected to reduce operating costs in the production facility by $1 million, pre-tax, every year. Its CCA rate is 15%, your firm's cost of capital is estimated at 14% and its tax rate is 30%.
1. Should the NR550 be replaced with the NR600?
2. After reviewing the technical specifications of the NR600, one of your engineers feels they may be able to make some basic modifications to the existing NR550 to make it more efficient. This would require some experimentation over the next year at a post-tax cost of $40,000 paid today. If the experiments prove successful (35% chance), a capital expense of $500,000 would improve efficiency for the remaining 9 years of the project producing savings of $150,000 per year (pre-tax). Salvage value would be unaffected. If the experiments fail to yield any benefit (65% chance), there would be no improvements to efficiency. Does this new information affect your decision regarding the NR600 in part a?
Question 3 - Real Options
Three Kings is considering launching a new product but there is some uncertainty about how the product will actually be received. Accordingly, your junior analyst has provided you with three sets of market conditions and estimated the probability of each set of circumstances (we know in year 1 what will happen from that point forward). Starting the project today would incur costs of $12,000,000, the appropriate cost of capital is 11% and the firm's tax rate is 25%. Ignore salvage and depreciation.
- "Good": The product is very well received and operating profits are estimated to start at $1,100,000 in year 1 with a 40% annual growth for the following 2 years and then slowing to 4% growth into the foreseeable future. The probability of this occurring is estimated to be 30%.
- "Average": Year 1 operating profits are $1,100,000 and grow at 5% in perpetuity (55% probability).
- "Poor": Year 1 operating profits are $800,000 but decline by 10% each year (15% probability).
1. What is the NPV of this project?
2. If you wait until year 1 so that there would be no uncertainty about the project's outcome before investing (another firm introduces the product first), what is the project's NPV?
3. How much Three Kings would value the option to postpone the decision to invest?
4. Upon presenting your findings above to your boss, she presents the concern that waiting a year and allowing another firm to enter the market first forfeits potential gains from early branding in the new market. This would be expected to reduce first year of operating profits to 85% of those initially projected (under all cases) AND the probability of a "good" outcome drops to 20% (probability of average becomes 65%, "bad" probability stays at 15%). Should you wait to invest or not?
5. How much Three Kings would value the option to postpone in this new scenario?
Question 4 - Equity Options and Hedging
PART A - Option Portfolios
1. Consider the following options on stock A, that all expire at a future date T:
| Security |
Maturity |
Strike price (X) |
Price (today) |
| Put option |
T |
$30 |
$3 |
| Call option |
T |
$10 |
$21 |
| Call option |
T |
$20 |
$12 |
| Call option |
T |
$30 |
$5 |
Compute the payoff/profit table and draw a payoff/profit diagram (a diagram with the portfolio value on the vertical axis and the stock price at maturity on the horizontal axis) for the following portfolio:
- Long 1 put with X = 30
- Long 3 calls with X = 10
- Short 6 calls with X = 20
- Long 3 calls with X = 30
2. Consider the following options on stock B, that all expire at a future date T:
| Security |
Maturity |
Strike price (X) |
Price (today) |
| Put option |
T |
$30 |
$15 |
| Put option |
T |
$20 |
$11 |
| Put option |
T |
$10 |
$5 |
Compute the payoff/profit table and draw a payoff/profit diagram (a diagram with the portfolio value on the vertical axis and the stock price at maturity on the horizontal axis) for the following portfolio:
- Long 4 puts with X = 30
- Short 6 puts with X = 20
- Long 3 puts with X = 10
PART B - Arbitrage
Consider the following prices:
| Security |
Maturity (years) |
Strike |
Price (today) |
| Apple stock |
- |
- |
$95 |
| Put on Apple stock |
1 |
$90 |
$10 |
| Call on Apple stock |
1 |
$90 |
? |
The continuously compounded annual risk-free interest rate is 2% and there are no transaction costs.
1. What should be the price of the call option?
2. Assume that the call option on Apple with strike price $90 and maturity in one year is currently trading at $17. You immediately tell your broker that you found a different price in part (1), but he replies that you must be wrong: markets should be efficient and the price you computed in point (1) is useless. The formula you used to price the call option probably works in theory, but in practice the market evidently knows something that you don't. For example, it could expect the stock price to increase a lot. Do you agree with him or not? Support your answer with computations.
3. Assume that you need to pay a trading fee of 8 cents per option or per stock you buy/sell. Would your answer to part (2) change?
PART C - Hedging
You have an exclusive contract to supply oranges to Juice&Co. and you are expected to deliver 10,000 oranges in one year from now at the market price in place at that time. You will pay a cost of $2,000 in one year to provide the 10,000 oranges. Today market price for one orange is $0.52. Assume that the continuously compounded risk free interest rate is 6%.
You expect the price to be between $0.50 and $0.55 and you have decided to hedge using one- year European options: buy 10,000 put options with strike price $0.52 for $84 and sell 10,000 call options with strike price $0.54 for $74.
1. Determine the range of possible profits you can get in one year from now. Show your answer.
2. Compute your profit if instead of hedging with options, you agree today to sell 10,000 oranges at a price of $0.53 in one year from now (i.e., you enter a futures contract).
3. Draw the profit diagram for both hedging strategies. Which one is preferable? Discuss.