Week 2 - Inflation, Real options

Question 1

Inflation formula

Answer 1

1 + ireal = (1+ nominal rate r )/(1 + inflation rate π)

Question 2

Profitability index

Answer 2

PI = NPV/Investment
Decision rule: select combination of projects w/ HIGHEST WEIGHTED-AVERAGE PI (ie. sum of projects w/ highest NPV)

1. Useful when funds for investment are limited (‘capital rationing’, constrained)
2. To maximise available funds

Question 3

Equivalent Annual Cash Flow (EAC) of a project

Answer 3

EAC = PV(cash flows) / annuity factor
= cash flow per period (annuity) with the same present value as the ACTUAL cash flows of the project

1. Useful for comparing projects w/ different LIVES
2. However, Implicit assumption that the machines will be replaced on exactly the same terms. May not be accurate assumption as may be cheaper/more expensive to buy in the future. If then, EAC is not an appropriate comparison.

Question 4

Real options

Answer 4

The right but not the obligation to modify a project in the future
= expected value of the incremental benefits the option brings

• An option has a NON-NEGATIVE value (>=0)

Question 5

Is it worthwhile to wait to start a project?
What to consider when exercising an American call option early?

Answer 5

1. Exercising an American call option on a NON-DIVIDEND-PAYING underlying is NEVER optimal, ie. always better to wait
2. Early exercise may be optimal for a dividend-paying stock (foregone dividend = cost of waiting)

Question 6

2 benefits & 1 con of waiting to start a project

Answer 6

Pros
1. More information about the market type
2. DEFER COST of project. In terms of time value of money, project costs less

Con
1. Foregone 1st year’s dividends, lost cash flow

Question 7

3 types of Real options

Answer 7

1. Option to abandon (abandonment option)
   - The project may no longer be profitable going forward
   - Value comes from reducing/AVOIDING future LOSSES
   *also PERMANENT abandonment
2. Option to grow/expand (growth option)
   - Investment may turn out to be more profitable than expected
   - Value comes from being able to capitalise on ADDITIONAL EARNING opportunities
3. Option to wait (timing option)
   - You have a +NPV project but if implemented in the future, the NPV may be even higher
   - Value comes from the ability to DELAY investment and LEARN more about MARKET CONDITIONS.

Question 8

2 reasons why we discount using the risk-free rate when calculating NPV for options

Answer 8

1. All risk-neutral probabilities
2. Beta of project is 0

Question 9

2 methods to calculate the Value of the Option to Expand
- 1 is easier, 1 is quicker

Side note: STAGED implementation is usually better

Answer 9

Method 1 (easier)
= NPV with option - NPV w/o option

Method 2 (quicker)
1. Calculate the INCREMENTAL cash flow (difference between getting and not getting 2nd plane), eg. if demand is high
2. Calculate the incremental cash flow, eg. if demand is low
3. Calculate NPV of this incremental investment {incorporating the probabilities}
^might have to do for t=1 first then discount further back to t=0

Question 10

Option to wait formulas
1. Option value
2. Intrinsic value
3. How to decide if it’s better to wait or exercise American call option now?

Answer 10

1. Option value = intrinsic value + time premium (=NET BENEFIT of WAITING)
2. Intrinsic value = NPV if exercise now
3. If TP>0, benefits of waiting > cost of waiting -> better off waiting than exercising now
   - If TP<0, cost of waiting > benefits of waiting -> exercise American call option now