Question

A drug manufacturer is considering how many of four new drugs to develop. Suppose it takes one year and \(10\) million to develop a new drug, with the entire cost being paid up front (immediately). The yearly profits from the new drugs will begin in the second year (with profits, as always, assumed to come at the end of the year. \(),\) and are given in the table below: $$\begin{array}{cl}\hline \text { Drug } & \text { Annual Profit } \\\\\hline \mathrm{A} & \$ 7 \text { million } \\\\\mathrm{B} & \$ 5.5 \text { million } \\\\\mathrm{C} & \$ 5 \text { million } \\\\\mathrm{D} & \$ 4 \text { million }\end{array}$$ These profits, which are certain, accrue only while the drug is protected by a patent; once the patent runs out, profit is zero. a. If the annual interest rate is 10 percent and patents are granted for just two years, which drugs should be developed? b. If the annual interest rate is 10 percent and patents are granted for three years, which drugs should be developed? c. Answer (a) and (b) again, this time assuming the discount rate is 5 percent. d. Based on your answers above, what is the relationship between new drug development and (1) the discount rate; (2) the duration of patent protection? e. Would the relationships in d. still hold in the more realistic case where profits from new drugs are uncertain? f. Is there any downside to a change in patent duration designed to speed the development of new drugs? Explain briefly.

Short answer

The drugs that should be developed would be those for which the profit, discounted over the period of patent protection, exceeds the initial investment cost ($10 million). The exact drugs would depend on the interest rate and duration of patent protection. The relationships found would not necessarily hold if profits were uncertain. There could be downsides to changing patent durations if this resulted in rushing drug development and compromising on quality or safety.

Step-by-step solution

Define the formula for present value

The present value of a future cash flow can be calculated using the formula: PV = CF / (1 + i)^n, where CF is the cash flow, i is the interest rate and n is the number of years.

Calculate present value for each drug

For each drug, calculate the present value of profits over the duration of the patent, subtract the development cost ($10 million), and determine if the investment yields a positive net present value (NPV).

Perform calculations for each scenario

Perform the steps above for each scenario - patents granted for two years and three years, and two different interest rates (10% and 5%).

Analyse the effect of patent duration and discount rate

Use the results of your calculations to explain the relationship between new drug development, the discount rate and the duration of patent protection.

Apply results to context with uncertain profits

Discuss how the findings might vary if the profits from new drugs were uncertain.

Discuss potential downsides to changing patent durations

Finally, provide a brief explanation of potential negative consequences of changing the duration of patents with the intent of accelerating new drug development.

Key concepts

Present Value

Understanding the concept of Present Value (PV) is essential when evaluating the worth of future cash flows today. Present Value helps you determine how much a future sum of money is worth in today's terms. This is crucial because money now has more purchasing power than the same amount in the future due to its earning potential.
To calculate PV, we use the formula:
\[ PV = \frac{CF}{(1 + i)^n} \] Here:

• \( CF \) represents the future cash flow you expect to receive.
• \( i \) is the interest or discount rate, reflecting the opportunity cost of capital.
• \( n \) denotes the number of years until the cash flow is received.

This formula helps in making informed investment decisions. You can gauge whether an investment today will yield sufficient returns in the future, pushing you to choose the best options based on their present value.

Net Present Value (NPV)

Net Present Value (NPV) is a financial metric that considers both the present value of cash inflows and outflows over time. It allows businesses to determine the value or profitability of an investment. In simple terms, NPV measures the difference between what you will make from the investment and what you have to spend to get there, using today's values.
To calculate NPV, subtract the initial investment cost from the total PV of future cash inflows:
\[ NPV = \sum \frac{CF_t}{(1 + i)^t} - C_0 \] Where:

• \( CF_t \) is the cash flow at time \( t \).
• \( i \) is the discount rate.
• \( t \) is the year number.
• \( C_0 \) represents the initial investment, or upfront development cost.

A positive NPV indicates that the expected earnings (adjusted for time and risk) exceed the costs, which suggests a worthwhile investment. Conversely, a negative NPV implies that the net gains from the investment underperform relative to the costs involved.

Patent Protection

Patent protection is a legal right granted to inventors, providing exclusive commercial rights to develop, use, and sell their invention for a limited period of time. In the context of pharmaceuticals, patents play a critical role in ensuring that drug manufacturers can recoup their investment.
When a drug manufacturer holds a patent, competitors cannot produce or sell generic versions of the drug. This exclusivity allows the original developer to charge premium prices, leading to substantial profits during the patent period. As such, patent duration directly influences the projected cash flows and, consequently, the attractiveness of an investment.
A longer patent duration offers more years of guaranteed profits, which enhances the calculated net present values of potential drugs. Shorter patent spans, however, reduce the window of profitability, impacting investment decisions. Changes in patent acts can incentivize or disincentivize drug development, affecting the market and innovation pace.