Capital Budgeting with Real Options

Expected cash flow = 0.6 × $120M + 0.4 × $0 = $72M. NPV = -$50M + $72M / 1.10 = -$50M + $65.45M = $15.45M.

Abandonment option: If Phase II results are poor (which we assume is known at year 1), the company can abandon and save $20M. The probability of poor results is not given, but we can infer from the 60% approval probability. However, the abandonment decision is based on Phase II results, which are not perfectly correlated with final approval. For simplicity, assume Phase II failure probability is 40% (complement of approval). Then expected savings = 0.4 × $20M = $8M at year 1. PV of savings = $8M / 1.10 = $7.27M. But this is a simplification; a more detailed decision tree would be needed. Alternatively, the abandonment option can be valued using a decision tree: At year 1, if Phase II fails (prob 0.4), abandon and save $20M. If Phase II succeeds (prob 0.6), continue and invest remaining $30M (since total investment $50M, $20M saved if abandon, so remaining $30M). At year 2, if approved (prob 0.6? Actually conditional probabilities need to be specified). Given the complexity, we'll use the provided probabilities: approval probability 0.6. Assume Phase II success probability is also 0.6 (independent). Then at year 1: if Phase II fails (0.4), abandon, cash flow = $20M (savings). If Phase II succeeds (0.6), continue, invest $30M at year 1. At year 2, approval (0.6) gives $120M, failure (0.4) gives $0. Expected value at year 1 if continue = (0.6×$120M + 0.4×$0)/1.10 - $30M = $65.45M - $30M = $35.45M. So at year 1, value = 0.4×$20M + 0.6×$35.45M = $8M + $21.27M = $29.27M. PV at year 0 = $29.27M / 1.10 = $26.61M. NPV with abandonment = -$50M + $26.61M = -$23.39M. This seems lower than without abandonment, which is incorrect. The error is that the initial investment of $50M is at year 0, but if abandoned, we save $20M at year 1, so the net investment is $30M at year 0 and $20M at year 1? Actually, the $50M is total investment; if abandoned after Phase II, we avoid $20M of Phase III costs. So the cash flow at year 1 if abandon is +$20M (savings). But we already spent $50M? No, the $50M is the total investment, presumably spent over time. To simplify, assume $50M is spent at year 0. Then abandonment saves $20M at year 1, so we get $20M back. Then NPV with abandonment = -$50M + PV of expected cash flows including abandonment. Let's do a proper decision tree: At year 0: invest $50M. At year 1: Phase II results. If fail (prob 0.4), abandon, get $20M (savings). If success (prob 0.6), invest $30M (remaining) and proceed. At year 2: approval (prob 0.6) gives $120M, failure (0.4) gives $0. Expected value at year 1 if success = (0.6×$120M + 0.4×$0)/1.10 - $30M = $65.45M - $30M = $35.45M. So at year 1, total value = 0.4×$20M + 0.6×$35.45M = $8M + $21.27M = $29.27M. PV at year 0 = $29.27M / 1.10 = $26.61M. NPV = -$50M + $26.61M = -$23.39M. This is worse than the original NPV of $15.45M, which is impossible because the option to abandon should add value. The mistake is that in the original NPV, we assumed $50M invested at year 0 and $120M received at year 2? Actually, original NPV: expected cash flow at year 2? The $120M is present value, so it's already discounted. The original NPV calculation was -$50M + 0.6×$120M = $22M? No, I did -$50M + $72M/1.10 = $15.45M. That assumes the $120M is received at year 2. But if we abandon, we save $20M at year 1, so the investment is not $50M at year 0; it's $50M at year 0, but we get back $20M at year 1. So the net investment is $30M at year 0 and $20M at year 1? That doesn't make sense. The correct approach is to model cash flows: Year 0: -$50M. Year 1: if abandon, +$20M; if continue, -$30M (additional investment). Year 2: if approved, +$120M; else $0. Then expected NPV = -$50M + [0.4×$20M + 0.6×(-$30M + (0.6×$120M)/1.10)]/1.10. Compute: (0.6×$120M)/1.10 = $65.45M. So inside: -$30M + $65.45M = $35.45M. Then 0.4×$20M = $8M; 0.6×$35.45M = $21.27M; sum = $29.27M; PV = $29.27M/1.10 = $26.61M. NPV = -$50M + $26.61M = -$23.39M. But original NPV without option was -$50M + (0.6×$120M)/1.10 = -$50M + $65.45M = $15.45M. The difference is that in the original, we assumed $50M invested at year 0 and $120M received at year 2, but we didn't account for the timing of the $50M? Actually, the original NPV is correct if the $50M is at year 0 and the $120M is at year 2. But with the option, we are changing the investment timing: we invest $50M at year 0, but if we abandon, we get $20M back at year 1, so the net investment is $30M at year 0 and $20M at year 1? That's not right because the $50M is spent at year 0. The $20M savings is a cash inflow at year 1. So the NPV with abandonment should be: -$50M + [0.4×$20M + 0.6×(-$30M + $65.45M)]/1.10 = -$50M + $26.61M = -$23.39M. This is lower than $15.45M, which is impossible because having the option to abandon cannot reduce value. The error is that in the original NPV, we assumed that if the project fails, we get $0, but we still spent $50M. In the abandonment scenario, if Phase II fails, we get $20M back, so the loss is only $30M. So the original NPV should have been -$50M + 0.6×$120M/1.10 + 0.4×$0 = $15.45M. But with abandonment, the expected cash flow at year 1 is 0.4×$20M + 0.6×(-$30M) = $8M - $18M = -$10M, and at year 2, 0.6×0.6×$120M = $43.2M. So NPV = -$50M - $10M/1.10 + $43.2M/1.10^2 = -$50M - $9.09M + $35.70M = -$23.39M. Still negative. The problem is that the original NPV of $15.45M was calculated as -$50M + $72M/1.10 = $15.45M, which assumes the $72M is received at year 1? No, it's at year 2? Actually, $72M/1.10 = $65.45M, so that's discounting one year. So the original NPV assumes the expected cash flow of $72M occurs at year 1. But if the project generates $120M at year 2, then the expected cash flow at year 2 is $72M, and PV = $72M/1.10^2 = $59.50M, NPV = $9.50M. So the original calculation was inconsistent. To avoid confusion, let's assume the $120M is received at the end of year 2, and the $50M is invested at year 0. Then original NPV = -$50M + 0.6×$120M/1.10^2 = -$50M + $72M/1.21 = -$50M + $59.50M = $9.50M. Now with abandonment: Year 0: -$50M. Year 1: if fail (0.4), +$20M; if success (0.6), -$30M. Year 2: if approved (0.6), +$120M; else $0. Expected NPV = -$50M + [0.4×$20M + 0.6×(-$30M + 0.6×$120M/1.10)]/1.10. Compute: 0.6×$120M/1.10 = $65.45M. -$30M + $65.45M = $35.45M. 0.4×$20M = $8M; 0.6×$35.45M = $21.27M; sum = $29.27M; PV = $29.27M/1.10 = $26.61M. NPV = -$50M + $26.61M = -$23.39M. Still lower than $9.50M. Something is wrong: the option to abandon should increase NPV. The issue is that in the original NPV, we assumed that if the project fails, we lose the entire $50M, but with abandonment, we get back $20M, so the loss is smaller. So the original NPV should be lower than with abandonment. Let's recalc original NPV properly: If no abandonment, we invest $50M at year 0, and at year 1 we invest another $30M? No, the total investment is $50M. If we don't have abandonment, we spend $50M at year 0 and then if Phase II fails, we still spend the remaining $20M? That doesn't make sense. The $50M is the total cost of the project. If we abandon, we save $20M of that cost. So the investment is $50M minus $20M if abandoned. So the cash flows are: Year 0: -$30M (initial investment, since $20M is contingent). Year 1: if fail, -$0 (no further investment); if success, -$20M (remaining investment). Year 2: if approved, +$120M; else $0. Then original NPV without abandonment (i.e., always invest full $50M) would be: Year 0: -$50M; Year 1: $0; Year 2: +$120M with prob 0.6. NPV = -$50M + 0.6×$120M/1.10^2 = -$50M + $59.50M = $9.50M. With abandonment: Year 0: -$30M; Year 1: if fail (0.4), $0; if success (0.6), -$20M; Year 2: if approved (0.6), +$120M. Expected NPV = -$30M + [0.4×$0 + 0.6×(-$20M + 0.6×$120M/1.10)]/1.10. Compute: 0.6×$120M/1.10 = $65.45M. -$20M + $65.45M = $45.45M. 0.6×$45.45M = $27.27M. PV = $27.27M/1.10 = $24.79M. NPV = -$30M + $24.79M = -$5.21M. Still lower than $9.50M. This is confusing. The error is that in the original NPV, we assumed $50M invested at year 0, but with abandonment, we only invest $30M at year 0 and $20M at year 1 if successful. So the original NPV should be compared to a scenario where we invest $50M at year 0. But if we have the option to abandon, we can defer some investment. So the value of the option is the difference between the NPV with flexibility and without. Without flexibility, we commit to full investment: NPV = -$50M + 0.6×$120M/1.10^2 = $9.50M. With flexibility, we invest $30M at year 0, and then $20M at year 1 only if Phase II succeeds. So the expected NPV = -$30M + 0.6×(-$20M + 0.6×$120M/1.10)/1.10 = -$30M + 0.6×(-$20M + $65.45M)/1.10 = -$30M + 0.6×$45.45M/1.10 = -$30M + $27.27M/1.10 = -$30M + $24.79M = -$5.21M. This is lower than $9.50M, which is impossible because having the option to abandon cannot reduce value. The mistake is that in the flexible scenario, we are assuming that if Phase II fails, we don't invest the remaining $20M, but in the inflexible scenario, we invest the full $50M at year 0 regardless. But if Phase II fails, the project is worthless, so investing the remaining $20M is a waste. So the inflexible scenario should have a lower NPV. Let's recalc inflexible: invest $50M at year 0. If Phase II fails (0.4), we still spend the remaining $20M? No, the $50M is all spent at year 0. So cash flow at year 0 is -$50M. Then at year 2, we get $120M with prob 0.6. NPV = -$50M + 0.6×$120M/1.10^2 = $9.50M. In the flexible scenario, we invest $30M at year 0, and then if Phase II succeeds (0.6), we invest $20M at year 1. If Phase II fails, we invest nothing more. So cash flows: Year 0: -$30M. Year 1: -$20M with prob 0.6. Year 2: +$120M with prob 0.6×0.6=0.36? Wait, approval probability given Phase II success is not necessarily 0.6. We need conditional probabilities. The problem states: 60% chance of successful FDA approval. That is the overall probability. It doesn't specify Phase II success probability. To simplify, assume Phase II success probability is also 0.6, and approval given Phase II success is 1.0? That would make overall approval 0.6. But then if Phase II fails, approval is impossible. So let's assume Phase II success probability = 0.6, and if Phase II succeeds, approval is certain. Then overall approval = 0.6. Then in flexible scenario: Year 0: -$30M. Year 1: if Phase II fails (0.4), $0; if succeeds (0.6), -$20M. Year 2: if Phase II succeeded, +$120M. So expected NPV = -$30M + [0.4×$0 + 0.6×(-$20M + $120M/1.10)]/1.10 = -$30M + 0.6×(-$20M + $109.09M)/1.10 = -$30M + 0.6×$89.09M/1.10 = -$30M + $53.45M/1.10 = -$30M + $48.59M = $18.59M. This is higher than $9.50M, so the abandonment option adds $9.09M. That makes sense. So the value of the abandonment option is $18.59M - $9.50M = $9.09M. Now expansion option: If approved and demand is high (prob 0.5 given approval), invest $30M at year 2 and get additional $60M PV at year 2? The problem says "generate an additional $60 million in present value". That likely means at the time of expansion (year 2), the additional cash flows have a PV of $60M. So at year 2, if high demand, invest $30M and receive $60M, net +$30M. The probability of high demand given approval is 0.5. So expected additional cash flow at year 2 = 0.6 (approval) × 0.5 (high demand) × $30M = $9M. PV at year 0 = $9M / 1.10^2 = $7.44M. So total adjusted NPV = NPV with abandonment + value of expansion option = $18.59M + $7.44M = $26.03M. Alternatively, if the $60M is already PV at year 0, then the expansion option value is 0.6×0.5×($60M - $30M) = $9M, but that $9M is at year 2? The problem says "generate an additional $60 million in present value" – present value typically means at the time of the decision, so at year 2. So we discount the net $30M from year 2 to year 0. So $9M/1.21 = $7.44M. So adjusted NPV = $18.59M + $7.44M = $26.03M. Note: The original NPV without options was $9.50M. The abandonment option adds $9.09M, and the expansion option adds $7.44M, for a total of $26.03M. This is the answer.