Revised Shockley, Chapter 8 Problems:
Problem 1:
If UNDi > K then given technical success, the outcome is [UNDi – K] – ptech* [UNDi – K]
Problem 2:
Today:
Pre-Clinical:
IND and Phase I:
Phase II:
Dec–03
Jun-04
Dec–04
Jun-05
Jun-06
Dec-06
Jun-07
Dec-07
Jun-08
7.50
16.63
36.86
108.05
273.73
857.47
1264.43
1845.08
2673.13
103.30
367.77
567.03
851.90
1258.72
131.89
223.17
362.20
561.32
120.75
217.46
20.92
47.92
Phase III
NDA
Dec–08
Jun-09
Dec–09
Jun-10
Dec–10
Jun-11
Dec–11
5934.07
8461.26
12060.53
17186.59
24487.00
69783.23
99397.13
2912.65
4158.39
5932.73
8459.88
12059.12
34385.68
48986.80
1422.88
2036.78
2911.31
4157.01
5931.32
16932.25
24131.04
688.32
990.68
1421.54
2035.40
2909.90
8326.51
11875.45
326.13
474.88
686.98
989.30
1420.13
4083.29
5832.60
147.59
220.56
324.79
473.50
685.57
1991.10
2853.06
60.31
95.23
146.21
219.18
323.38
959.50
1383.94
20.02
34.77
58.29
93.78
144.80
450.85
659.57
17.31
32.21
56.74
200.05
302.40
13.81
76.39
126.29
17.23
39.46
Problem 3:
Today:
Pre-Clinical:
IND and Phase I:
Phase II:
Dec–03
Dec–04
Jun-05
Jun-06
Dec-06
Jun-07
Dec-07
Jun-08
24.05
49.83
137.30
347.71
910.49
1340.19
1953.25
2827.44
1.86
4.25
39.92
131.54
393.58
604.05
904.89
1334.45
Phase III
NDA
Dec–08
Jun-09
Dec–09
Jun-10
Dec–10
Jun-11
Dec–11
6264.12
8931.71
12730.96
18141.81
25847.80
73660.07
104919.19
3074.84
4389.80
6262.72
8930.28
12729.49
36295.99
51708.29
1502.30
2150.32
3073.44
4388.36
6261.26
17872.93
25471.66
1046.10
1500.91
2148.89
3071.98
8789.10
12535.20
1044.67
1499.44
4310.14
6156.63
2101.71
3011.56
1012.80
1460.83
Problem 4:
Today:
Pre-Clinical:
IND and Phase I:
Phase II:
Dec–03
Jun-04
Dec–04
Jun-05
Jun-06
Dec-06
Jun-07
Dec-07
Jun-08
11.44
22.89
44.85
116.80
292.26
910.49
1340.19
1953.25
2827.44
2.69
6.15
34.92
112.12
393.58
604.05
904.89
1334.45
0.00
28.82
143.69
241.08
387.98
598.31
36.95
71.37
133.11
235.34
10.75
24.61
56.39
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
Phase III
NDA
Dec–08
Jun-09
Dec–09
Jun-10
Dec–10
Jun-11
Dec–11
6264.12
8931.71
12730.96
18141.81
25847.80
73660.07
104919.19
3074.84
4389.80
6262.72
8930.28
12729.49
36295.99
51708.29
1502.30
2150.32
3073.44
4388.36
6261.26
17872.93
25471.66
1046.10
1500.91
2148.89
3071.98
8789.10
12535.20
1044.67
1499.44
4310.14
6156.63
0.00
13.79
31.58
143.69
241.08
387.98
598.31
36.95
71.37
133.11
235.34
10.75
56.39
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
156.17
233.19
343.23
500.22
724.07
2101.71
3011.56
64.00
100.91
154.73
231.76
341.76
1012.80
1460.83
Problem 5:
Notice, the risk-free is useless information in this context.
Problem 6:
Tree of Underlying Values:
Today:
Phase I
Phase II
0 months
6 months
12 months
18 months
24 months
30 months
36 months
30.05
39.87
52.91
70.20
93.15
123.60
164.01
17.07
22.65
30.05
39.87
52.91
12.86
17.07
Option Pricing Tree:
Today:
Phase I
Phase II
0 months
6 months
12 months
18 months
24 months
30 months
36 months
20.44
30.07
42.91
70.20
93.15
123.60
164.01
12.84
20.05
39.87
52.91
70.20
93.15
22.65
30.05
39.87
52.91
12.86
17.07
22.65
30.05
21.36
37.03
61.93
99.40
153.26
475.90
696.21
18.55
34.41
60.31
211.17
319.20
15.00
80.63
133.31
18.18
41.65
NPV of developing the project: $20.44 million – $5 million = $15.44 million.
Problem 7:
Today:
Phase I
Phase II
0 months
6 months
12 months
18 months
24 months
30 months
36 months
8.18
12.03
17.16
70.20
93.15
123.60
164.01
5.14
8.02
39.87
52.91
70.20
93.15
2.83
30.05
39.87
52.91
12.86
17.07
22.65
30.05
9.69
12.86
17.07
7.31
9.69
5.51
NPV of developing the project: $8.18 million – $5 million = $3.18 million.
Problem 8:
Today:
Phase I
Phase II
0 months
6 months
12 months
18 months
24 months
30 months
36 months
5.77
8.84
12.93
56.16
74.52
98.88
131.21
3.33
5.62
31.90
42.33
56.16
74.52
1.46
18.12
24.04
31.90
42.33
10.29
13.65
18.12
24.04
7.76
10.29
13.65
5.84
7.76
4.40
An iterative solution (such as Goal Seek in Excel) is best to find the strike price that sets
the NPV to zero. A strike price of $2.72 million will work.
Problem 9:
Tree of Underlying Values:
9.69
12.86
17.07
7.31
9.69
5.51
Today:
Phase I
Phase II
Phase III
0 months
6 months
12 months
18 months
24 months
30 months
36 months
38.44
58.75
89.80
137.26
209.80
320.67
490.14
Option Pricing Tree:
Today:
Phase I
Phase II
Phase III
0 months
6 months
12 months
18 months
24 months
30 months
36 months
15.05
30.77
60.59
117.66
189.80
320.67
490.14
4.26
10.38
39.15
69.80
137.26
209.80
0.00
7.57
18.44
58.75
89.80
0.00
0.00
25.15
38.44
0.00
10.77
16.45
4.61
7.04
3.01
Problem 10:
Tree with 10% failure rates:
Today:
Phase I
Phase II
Phase III
0 months
6 months
12 months
18 months
24 months
30 months
36 months
9.14
19.53
40.90
93.54
151.94
288.60
441.12
1.98
4.82
29.95
54.74
123.54
188.82
0.00
5.39
13.14
52.88
80.82
0.00
0.00
22.63
34.60
0.00
9.69
14.81
4.15
6.34
2.71
Tree with a final failure rate of 30%:
Today:
Phase I
Phase II
Phase III
0 months
6 months
12 months
18 months
24 months
30 months
36 months
5.87
14.06
33.65
76.48
126.86
224.47
343.10
0.18
0.45
21.52
42.86
96.08
146.86
0.00
2.83
6.91
41.13
62.86
25.15
38.44
58.75
89.80
137.26
209.80
16.45
25.15
38.44
58.75
89.80
10.77
16.45
25.15
38.44
7.04
10.77
16.45
4.61
7.04
3.01
Tree with 30% failure rate after Phase I:
Today:
Phase I
Phase II
Phase III
0 months
6 months
12 months
18 months
24 months
30 months
36 months
10.54
21.54
42.41
117.66
189.80
320.67
490.14
39.15
69.80
137.26
209.80
18.44
58.75
89.80
25.15
38.44
10.77
16.45
17.60
26.91
11.52