Questlion
2

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Einomial Model
This question combines concepts from FIN
4
1
3
and FIN
2
0
1
/
3
0
1
.
Long Ule Drugs Incorporabed
(
LUDi
)
has been developing a drug cal

Question

Questlion
2
 
-
 ﻿Einomial Model
This question combines concepts from FIN 
4
1
3
 ﻿and FIN 
2
0
1
/
3
0
1
.
Long Ule Drugs Incorporabed 
(
LUDi
)
 ﻿has been developing a drug called Centurion which they claim will eliminate al diseases and enable people to live for 
2
0
0
 ﻿years. Fou are attempting to value this frm
.
 ﻿Yow are aware that comparies in the biobedhnologr industry can often have signilicant waluations even though they do not yet have any reverve stream. The value comes from the future cash flow opportumities If the drag is successful.
LLD
'
s 
é
rug is about to undergo two years of clinical triah. These will take two years at a cost of SEM per year, with a probability of succens of 
3
0
%
 ﻿at the end of the two pears 
(
although nobody really lonows yet if any of the participants will live to 
2
0
0
)
.
 ﻿If these clinical trials are declared a success, the drug can proceed to market. In this stage, there would be a $
1
0
M
 ﻿cost of marketing rach year, and the sales could run for a total of sky years. A succenful drug would eurn a net operating problit 
(
not counting the advertising
)
 ﻿of $
1
5
M in its fri

VIPSolutions · Accepted Answer

# Solution: Binomial Model Valuation for Long Life Drugs Incorporated (LLDI)

## **Summary of the Problem**

LLDI is developing a potentially revolutionary drug. The project requires:
- **2 years of clinical trials**: **Cost: $6M/year**, **Probability of success: 30%**.
- If successful, **6 years of market**: **Annual marketing cost: $10M**.
- **Net operating profit (NOP)**: $15M in Year 3, **grows at 20%/year** (with high volatility, but we’ll use expected values for binomial model).
- **Required return:** 20% per year.

A standard DCF gives a negative NPV (about **-$4.7M**).  
**Goal:** Build a binomial tree incorporating the option to abandon (real options approach) and estimate the value of the project under this more realistic framework.

---

## **Step 1: Reconstruct the Cash Flow Table**

| Year | Phase   | Cost ($M) | Exp. Income ($M) | Net CF ($M) | Prob. |
|------|---------|-----------|------------------|-------------|-------|
| 1    | Trials  | -6        |                 | -6          | 100%  |
| 2    | Trials  | -6        |                 | -6          | 100%  |
| 3    | Market  | -10       | 15               | 5           | 30%   |
| 4    | Market  | -10       | 18               | 8           | 30%   |
| 5    | Market  | -10       | 21.6             | 11.6        | 30%   |
| 6    | Market  | -10       | 25.92            | 15.92       | 30%   |
| 7    | Market  | -10       | 31.10            | 21.10       | 30%   |
| 8    | Market  | -10       | 37.32            | 27.32       | 30%   |

Discount factor per year: $ \frac{1}{1.20} $

---

## **Step 2: Binomial Model Setup**

### **Key Parameters**
- **Time period per step:** 1 year.
- **Up move (u):** $ 1 + .20 = 1.2 $
- **Down move (d):** $ 1 - .80 = .2 $ (since standard deviation is 100%, but for basic model use d = .8, i.e., 20% drop; or could use d = .83 for 20% down if using lognormal, but here keep it simple).
- **Risk-neutral probability (p):**
  $$
  p = \frac{e^{r\Delta t} - d}{u - d}
  $$
  Where $ r = 20\% $ and $ \Delta t = 1 $.

$$
  p = \frac{1.2 - .8}{1.2 - .8} = \frac{.4}{.4} = 1.
  $$
  This suggests the risk-neutral probability is 1. if using these up/down moves, but that's not realistic for a binomial tree with large volatility. For practical purposes, let's use:
  - $ u = 1.2 $
  - $ d = .8 $
  - $ r = 1.2 $
  - $$
    p = \frac{1.2 - .8}{1.2 - .8} = 1.
    $$
  This shows a problem; normally, for option pricing, u and d are set based on volatility. Let's instead use standard binomial tree logic, but focus on the abandonment option.

### **Clinical Trial Phase**
- **Year 1 & 2:** Always -$6M each year, no abandonment option (must be paid to try).
- **At end of Year 2:** If trial fails (70% chance), project ends, payoff is zero. If trial succeeds (30% chance), we proceed to market phase.

### **Market Phase (Real Option)**
At each year during the market phase, you can choose to:
- **Continue** (pay $10M, receive growing NOP), or
- **Abandon** (receive $, avoid future losses).

### **Tree Structure**
- **Node:** Value at each year = max(continue, abandon).
- **Backwards induction:** Start from Year 8 (end), move backwards, at each node choose to continue or abandon.

---

## **Step 3: Build the Binomial Tree with Abandonment Option**

### **Step 3.1: Calculate Expected Cash Flows for Market Years**

Let’s use expected cash flows (as in the DCF model), but at each year, allow for the abandonment if NPV of continuing is negative.

#### **Year 8 (last year):**
- Cash Flow = $27.32M - $10M = $17.32M (if reached, just take this, no more future).

#### **Year 7:**
- Cash Flow = $31.10M - $10M = $21.10M
- Value = $21.10M discounted one year at 20%, plus expected value from Year 8 (discounted)
- But if negative, can choose to abandon and get $.

So, **at each market year $ t $**:
- **Continue:** $ CF_t + \frac{E[\text{Value}_{t+1}]}{1.2} $
- **Abandon:** $

### **Step 3.2: Backward Induction Example**

#### **Year 8:**
- Value = $17.32M

#### **Year 7:**
- Value = max[$21.10M + ($17.32M / 1.2), $$]
- = max[$21.10M + $14.43M, $$]
- = $35.53M

#### **Year 6:**
- Value = max[$15.92M + ($35.53M / 1.2), $$]
- = max[$15.92M + $29.61M, $$]
- = $45.53M

#### **Year 5:**
- Value = max[$11.60M + ($45.53M / 1.2), $$]
- = max[$11.60M + $37.94M, $$]
- = $49.54M

#### **Year 4:**
- Value = max[$8.00M + ($49.54M / 1.2), $$]
- = max[$8.00M + $41.28M, $$]
- = $49.28M

#### **Year 3:**
- Value = max[$5.00M + ($49.28M / 1.2), $$]
- = max[$5.00M + $41.07M, $$]
- = $46.07M

#### **Year 2 (after trials):**
- Probability of reaching market = 30%.
- Value = .3 × $46.07M = $13.82M

#### **Year 1 and Year 2 (trials):**
- Year 2: Pay $6M now, expected value in Year 3 is $13.82M, discounted one year:
  - Value = -$6M + ($13.82M / 1.2) = -$6M + $11.52M = $5.52M
- Year 1: Pay $6M now, expected value in Year 2 is $5.52M, discounted one year:
  - Value = -$6M + ($5.52M / 1.2) = -$6M + $4.60M = **-$1.40M**

---

## **Step 4: Interpretation**

- *

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