Build A Model Solution Chapter 26 Problem 9 ✓ Solved

Build A Model Solution 7 16 15 Chapter 26 Problem 9

Build A Model Solution 7/16/15 Chapter: 26 Problem: 9

Bradford Services Inc. (BSI) is considering a project that has a cost of $10 million and an expected life of 3 years. There is a 30 percent probability of good conditions, in which case the project will provide a cash flow of $9 million at the end of each year for 3 years. There is a 40 percent probability of medium conditions, in which case the annual cash flows will be $4 million, and there is a 30 percent probability of bad conditions and a cash flow of -$1 million per year. BSI uses a 12 percent cost of capital to evaluate projects like this. a. Find the project's expected cash flows and NPV.

WACC= 12% Condition Probability CF CF x Prob. Good 30% $9 Medium 40% $4 Bad 30% -$1 Expected CF= Time line of Expected CF -$10 NPV= Without any real options, reject the project. It has a negative NPV and is quite risky. b. Now suppose the BSI can abandon the project at the end of the first year by selling it for $6 million. BSI will still receive the Year 1 cash flows, but will receive no cash flows in subsequent years.

Assume the salvage value is risky and should be discounted at the WACC. WACC= 12% Salvage Value = $6 Risk-free rate = 6% Decision Tree Analysis Cost Future Cash Flows NPV this Probability 0 Probability Scenario x NPV 30% -$% 30% Expected NPV of Future CFs = When abandonment is factored in, the very large negative NPV under bad conditions is reduced, and the expected NPV becomes positive. Note that even though the NPV of medium is still negative, it is higher than it would be if the project was abandoned at year 1 if conditions are medium. c. Now assume that the project cannot be shut down. However, expertise gained by taking it on will lead to an opportunity at the end of Year 3 to undertake a venture that would have the same cost as the original project, and the new project's cash flows would follow whichever branch resulted for the original project.

In other words, there would be a second $10 million cost at the end of Year 3, and then cash flows of either $9 million, $4 million, or -$1million for the following 3 years. Use decision tree analysis to estimate the value of the project, including the opportunity to implement the new project in Year 3. Assume the $10 million cost at Year 3 is known with certainty and should be discounted at the risk-free rate of 6 percent. Hint: do one decision tree for the operating cash flows and one for the cost of the project, then sum their NPVs. WACC= 12% Risk-free rate = 6% Decision Tree Analysis Cost Future Operating Cash Flows (Discount at WACC) NPV this Probability 0 Probability Scenario x NPV 30% -$% 30% Expected NPV of Future Operating CFs = Future Cost of Implementing Additional Project (Discount at Risk-free rate) NPV this Michael C. Ehrhardt: Discount at risk-free rate since cost is known with certainty.

Don't include orginal cost, since it is already included in the decision tree above. Prob. 0 Probability Scenario x PV 30% 40% 30% Expected NPV of Future Operating CFs = Total NPV (NPV of Future Operating CF plus NPV of Future Year 3 cost of implementing additional project) = Here the project has a positive expected NPV, so by this criterion it can be accepted. d. Now suppose the original (no abandonment and no additional growth) project could be delayed a year. All the cash flows would remain unchanged, but information obtained during that year would tell the company exactly which set of demand conditions existed..

Use decision tree analysis to estimate the value of the project if it is delayed by 1 year. Hint: Discount the $10 million cost at the risk-free rate since it is known with certainty. Show two time lines, one for operating cash flows and one for the cost, then sum their NPVs. WACC= 12% Risk-free rate = 6% Decision Tree Analysis: Optg. CFs Future Operating Cash Flows (Discount at WACC) NPV this Probability 0 Probability Scenario x NPV 30% 40% 30% Expected PV of Future CFs = Decision Tree Analysis: Costs Future Cost of Implementation (Discount at Risk-Free Rate) Cost NPV this Michael C. Ehrhardt: Discount at risk-free rate since the cost is known with certainty. Probability 0 Probability Scenario x NPV 30% 40% 30% Expected PV of Future CFs = Total NPV (NPV of Future Operating CF plus NPV of Future Year 1 cost of implementing additional project) = Since the NPV from waiting is positive and the NPV from immediate implementation is negative, it makes sense to delay the decision for a year. e. Go back to part c. Instead of using decision tree analysis, use the Black-Scholes model to estimate the value of the growth option.

The risk-free rate is 6 percent, and the variance of the project's rate of return is 22 percent. Risk-free rate= 6% Variance of project's rate of return= 22% Financial Option Real Option rRF = Risk-free interest rate = Risk-free interest rate t = Time until the option expires = Time until the option expires X = Strike price = Cost to implement the project P = Current price of the underlying stock = Current value of the additional project s2 = Variance of the stock's rate of return = Variance of the project's rate of return Find current value of the additional project's cash flows. This includes all cash flows except cost of implementation.

Cost Future Operating Cash Flows of Additional Project (Discount at WACC) NPV this Michael C. Ehrhardt: Discount at WACC since these are risky cash flows. This should include all cash flows, just like the price of a stock includes all cash flows, even those that occur if you don't exercise a stock option. Also, since a stock's price isn't affected by an option's exercise price, the current value of the project is not affected by the "exercise" cost of the real option. Michael C. Ehrhardt: Sum of -$1 operating CF and salvage value of $6. Prob. 0 Probability Scenario x NPV 30% 40% 30% Expected NPV of Future Operating CFs = rRF = t = X = P = s2 = d1 = { ln (P/X) + [rRF + s2 /2) ] t } / (s t1/2 ) = d2 = d1 - s (t 1 / 2) = N(d1)= N(d2)= V = P[ N (d1) ] - Xe-rRF t [ N (d2) ] = Value of original project= DII Labs: NPV from part a. Michael C. Ehrhardt: Discount at risk-free rate since cost is known with certainty.

Don't include orginal cost, since it is already included in the decision tree above. Michael C. Ehrhardt: Discount at risk-free rate since the cost is known with certainty. Michael C. Ehrhardt: Use the NORMSDIST function. Michael C. Ehrhardt: Use the NORMSDIST function. Value of growth option= Total Value= Even though the original project has a negative NPV, the value of the growth option is large enough so that the combination of the original project and the growth option is greater than zero. Therefore, the project should be accepted.

Paper For Above Instructions

1. Introduction

Bradford Services Inc. (BSI) is evaluating a new project that presents an interesting set of financial challenges due to differing cash flow scenarios based on market conditions. This report will analyze the expected cash flows, net present value (NPV), and the implications of potential decisions such as abandonment, future project opportunities, and decision delays. The analysis will use a risk-adjusted discount rate (WACC) of 12% and examine probabilities of cash flow under good, medium, and bad conditions.

2. Project Evaluation under Different Conditions

The project's expected cash flows need to be calculated based on the given probabilities:

  • Good conditions (30% probability): $9 million annually for 3 years
  • Medium conditions (40% probability): $4 million annually for 3 years
  • Bad conditions (30% probability): -$1 million annually for 3 years

2.1) Expected Cash Flow Calculation

Using the probabilities with respective cash flows, we can calculate the expected cash flow (ECF):

ECF = (0.3 9) + (0.4 4) + (0.3 * -1) = 2.7 + 1.6 - 0.3 = 4 million annually.

2.2) NPV Calculation

The project's NPV can be calculated using the formula:

NPV = Σ (Cash Flows / (1 + r)^t) - Initial Investment

NPV = (4/(1+0.12)^1 + 4/(1+0.12)^2 + 4/(1+0.12)^3) - 10 million

Calculating the above will yield a negative NPV indicating the project should be rejected based on financial metrics alone.

3. Abandonment Option

If BSI implements an option to abandon the project after Year 1 for a salvage value of $6 million, the future cash flows need to be reconsidered. The expected NPV under abandonment can be computed similarly, with cash flows for Year 1 and the option to exit. The cash flows would provide more favorable conditions than previously explored.

NPV (abandon = 6 million) = (4 million / (1 + 0.12)^1) + (0.7 * 6 million / (1 + 0.12)^1) - 10 million.

This analysis shows that the grossly negative outcomes in bad conditions can be capped with the abandonment option, potentially leading to an overall positive expected NPV.

4. Growth Opportunity Post-Project

If BSI proceeds without abandoning the project, they could acquire expertise leading to a new project after three years. The costs and expected cash flows of this subsequent project need to be accounted for as expected cash flows would depend on the results found during the first project, along with potential implementations at Year 3. Creditably, the analysis will consider future costs, potential termination fees, and net cash flow returns overlaid by the decision tree analysis.

4.1) Decision Tree Analysis

This method involves estimating probabilities and respective valuations to display cash flow analysis thoroughly for both the operational aspect as well as the cost aspect. The weighted expected values of operational cash flows from the first project, combined with subsequent projects represent an active growth value and not the annual costs of the initial investment.

5. Delay in Project Start

Delaying the project's start could enable BSI to gather more market data and choose the most advantageous conditions. By applying similar decision tree analyses as previous sections, BSI can gauge the present value of waiting versus immediate action. Probabilities and cash flows would remain unchanged, yet allow BSI to have more calculated insights.

6. Black-Scholes Model Approach

To quantify the growth option potential quantitatively, the Black-Scholes model can be applied. Utilizing the risk-free rate of 6% and the variance of 22% offers the potential financial metrics intended for the project evaluation, accessing probabilities, costs, and cash flow values tied to risk-adjusted valuations to judge total returns gained through this unique option.

In no case should the original cost be double-counted as project estimates are refined and adjusted through all stages.

References

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  • Koller, T., Goedhart, M., & Wessels, D. (2010). Valuation: Measuring and Managing the Value of Companies. Wiley.
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