Jadin Davis

Chapter $26.$ Ch $26-9$ Build a Model

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 $30\%$ $$9$ $$2\mathrm{.}70$

Medium $40\%$ $$4$ $$1\mathrm{.}60$

Bad $30\%-$$$1-$$$0\mathrm{.}30$

Expected CF$=$ $$4\mathrm{.}00$

Time line of Expected CF

$0123$

$-$$$10$ $$4\mathrm{.}00$ $$4\mathrm{.}00$ $$4\mathrm{.}00$

NPV$=-$$$0\mathrm{.}39$

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 $=6\%$ Discounted$=$ $$5\mathrm{.}357$

Decision Tree Analysis

Cost Future Cash Flows NPV this Probability

$0$ Probability $123$ Scenario x NPV

$$9$ $$0$ $$0$

$30\%$

$-$$$1040\%$ $$4\mathrm{.}00$ $$0$ $$0$

$30\%$

$-$$$1$ $$0$ $$0$

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.

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 $1234$ Scenario x NPV

$-$$$10$

$30\%$

$40\%-$$$10$

$30\%$

$-$$$10$

Expected PV of Future CFs $=$

Decision Tree Analysis: Costs "Future Cost of Implementation

$($Discount at Risk$-$Free Rate$)"$

Cost NPV this Probability

$0$ Probability $1234$ 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 implenting 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.