Question

3. A project with an up-front cost at t=0 of $1500 is being considered by Nationwide PharmaceuticalCorporation (NPC). (All dollars in this problem are in thousands.) The project’s subsequent cash flows arecritically dependent on whether a competitor’s product that is now under development is approved by the Food and Drug Administration. If the FDA rejects the competitive product upon the completion of its development, NPC’s product will have high sales and cash flows, but if the competitive product is approved, that will negatively impact NPC. There is a 75% chance that the competitive product will be rejected, inwhich case NPC’s expected cash flows will be $550 at the end of each of the next seven years (t = 1 to 7). There is a 25% chance that the competitor’s product will be approved, in which case the expected cashflows will be only $20 at the end of each of the next seven years (t = 1 to 7). NPC will know only sometime later whether the competitor’s product is going to be approved.

NPC will proceed with the investment today to take advantage of the untapped market potential and at theend of the project’s life, after finding out about the FDA’s decision about the demand for competitor’sproduct, they will decide whether or not to renew the patent and rerun the project. The project rerun’s up- front cost (at t = 7) will remain at $1,500, and the subsequent cash flows will remain unchanged and will be received for seven additional years (t = 8 ... 14). They will only rerun the project if the rerun of the project adds value.

Assuming that all cash flows are discounted at 10%, use the black-Scholes model to estimate the value of the option. Assume that the variance from the project’s rate of return is 0.2524 and the risk-free rate is 7%. (5 points)

Answer 1

we have to calculate the value option that we will exercise if competitors product is rejected by the FDA.

There is 75% probability that competitors product will rejected.

We are making the investment now for period of 7 years and we have the option ot continue the project for next 7 more years if competitors prducts gets rejected.

Hence we have to value that option after 7 years using black-scholes model.

for blac-scholes model we need two more variables i.e. spot price which is equal to present value of cash flows for the period from 8th year to 14th year, and strike price is equal to $1,500.

Strike price = $1,500

Spot price = $1,374.05

Year	Cash flow	Discouting factor @ 10%	Present value
8	$     550.00	0.467	$            256.58
9	$     550.00	0.424	$            233.25
10	$     550.00	0.386	$            212.05
11	$     550.00	0.350	$            192.77
12	$     550.00	0.319	$            175.25
13	$     550.00	0.290	$            159.32
14	$     550.00	0.263	$            144.83
Present value	$        1,374.05

Interest rate = 7%

Time to maturity = 7 Years

Standar Deviation (SD) = (0.2524)^0.5 = 0.5024

Black-scholes formula

Call option price = S*N(d1) - K*e^-rt*N(d2)

where,

d1 = [ Ln(S/K) + (r + (SD)^2/2)*t ] / SD*t^0.5

d2 = d1 - SD*t^0.5

where,

S = spot price

K = strike price

r = interest rate

t = time to maturity

N = Normal distribution

by substituting inputs

d1 = 1.1252

d2 = -0.2039

N(d1) = 0.8697

N(d2) = 0.4192

Call option value = $882.85

But therese only 75% chances that competitors product will rejected and we will continue after 7 years.

Hence Call price = $882.85*75% = $662.14

Answer is $662.14.