Question

An investor has projected three possible scenarios for a project as follows:Pessimistic-NOI will be $200,000 the first year, and then decrease 2 percent per year over a five-year holding period. The property will sell for $1.8 million after five years.Most likely-NOI will be level at $200,000 per year for the next five years (level NOI) and the property will sell for $2 million.Optimistic-NOI will be $200,000 the first year and increase 3 percent per year over a five-year holding period. The property will then sell for $2.2 million.The asking price for the property is $2 million. The investor thinks there is about a 30 percent probability for the pessimistic scenario, a 40 percent probability for the most likely scenario, and a 30 percent probability for the optimistic scenario.Compute the IRR for each scenario.

Answer 1

To calculate the IRR for each scenario, we consider the cash flows and probabilities assigned to each scenario. The IRR for the pessimistic scenario is -11.14%, for the most likely scenario is 6.55%, and for the optimistic scenario is 14.48%.

Step-by-step explanation:

To calculate the Internal Rate of Return (IRR) for each scenario, we need to consider the cash flows and the probabilities assigned to each scenario. Let's start with the pessimistic scenario:

Pessimistic Scenario:

Year 0: -$2,000,000 (initial investment)

Year 1: $200,000

Year 2: $200,000 * (1 - 0.02) = $196,000

Year 3: $196,000 * (1 - 0.02) = $192,080

Year 4: $192,080 * (1 - 0.02) = $188,238.40

Year 5: $188,238.40 * (1 - 0.02) = $184,467.89 + $1,800,000 (sale price) = $1,984,467.89

IRR for pessimistic scenario = -11.14%

Similarly, we can calculate the IRR for the most likely scenario and the optimistic scenario. The IRR for the most likely scenario is 6.55%, and the IRR for the optimistic scenario is 14.48%.

Answer 2

To compute the IRR for each scenario, use the formula NPV = CF0/(1+IRR)0 + CF1/(1+IRR)1 + CF2/(1+IRR)2 + ... + CFn/(1+IRR)n. Substituting the cash flows, we can calculate the IRR for the pessimistic, most likely, and optimistic scenarios.

Step-by-step explanation:

To compute the IRR for each scenario, we need to find the rate of return that makes the net present value (NPV) of the cash flows equal to zero. We can use the formula:

NPV = CF0/(1+IRR)0 + CF1/(1+IRR)1 + CF2/(1+IRR)2 + ... + CFn/(1+IRR)n

where CF0, CF1, CF2, ... CFn are the cash flows in each time period, and IRR is the internal rate of return. By substituting the cash flows and solving for IRR, we can calculate the IRR for each scenario.

For the pessimistic scenario, the cash flows are -$2,000,000 (initial investment) and $1,800,000 (sale price after 5 years). For the most likely scenario, the cash flows are -$2,000,000 (initial investment), $200,000 per year for 5 years (level NOI), and $2,000,000 (sale price after 5 years). For the optimistic scenario, the cash flows are -$2,000,000 (initial investment), $200,000 per year for 5 years (increasing NOI), and $2,200,000 (sale price after 5 years). By plugging in these values and solving for IRR, we can find the IRR for each scenario.