Question

Approximately 14 million Americans are addicted to drugs and alcohol. The federal government estimate that these addicts cost the U.S economy \(300 billion in medical expenses and lost productivity. Despite the enormous potential market, many biotech companies have shied away from funding research and development (R&D )initiatives to find a cure for drug and alcohol addiction. Your firm-drug abuse science (DAS)-is a notable exception. It has spent \)200 million to date working on a cure, but is now at a crossroads. It can either abandon its program or invest another $60 million today. Unfortunately, the firm’s opportunity cost of funds is 5 percent, and it will take another five years before final approval from the food and drugs administration is achieved and the product is actually sold. Expected (year-end) profits from selling the drug and presented in the accompanying table. Should DAS continue with its plan to bring the drug to market, or should it abandon the project? Explain.

Short answer

Yes, the firm should continue with the project.

Step-by-step solution

Determining formula

Use the formula for the net present value with nine summands as the time period is nine years:

$NPV=\frac{F{V}_1}{{(1+i)}^1}+\frac{F{V}_2}{{(1+i)}^2}+\frac{F{V}_3}{{(1+i)}^3}+\mathrm{....}+\frac{F{V}_9}{{(1+i)}^9}-C_0$

Where FV represents the profit from sales in years k, i is the interest.

Determining whether the firm should continue with the described project or not.

The profit in the first four years is $0, therefore, the first four terms in the formula can be omitted:

$NPV=\frac{F{V}_5}{{(1+i)}^5}+\frac{F{V}_6}{{(1+i)}^6}+\frac{F{V}_7}{{(1+i)}^7}+\frac{F{V}_8}{{(1+i)}^8}+\frac{F{V}_9}{{(1+i)}^9}+C_0$

Use the table and substitute,

$\begin{array}{l}F{V}_5=12,000,000,\\ F{V}_6=13,400,000,\\ F{V}_7=17,200,000,\\ F{V}_8=20,700,000,\\ F{V}_9=22,450,000\end{array}$

Into the formula substitute i=5%=0.05:

$\begin{array}{l}NPV=\frac{12,000,000}{{(1+0.05)}^5}+\frac{13,400,000}{{(1+0.05)}^6}+\frac{17,200,000}{{(1+0.05)}^7}+\frac{20,700,000}{{(1+0.05)}^8}+\frac{22,450,000}{{(1+0.05)}^9}-C_0\\ \end{array}$

As the additional investment is $60,000, substitute =60,000,000

$\begin{array}{l}NPV=\frac{12,000,000}{{1.05}^5}+\frac{13,400,000}{{1.05}^6}+\frac{17,200,000}{{1.05}^7}+\frac{20,700,000}{{1.05}^8}+\frac{22,450,000}{{1.05}^9}-60,000,000\\ NPV=107,364\end{array}$

As the net present value of the project is positive, which means that the project is profitable, it follows that the firm should continue with its project.