Question

The Gizmo Company is planning to develop new household gadgets. Table 13.4 shows the company’s demand for financial capital for research and development of these gadgets, based on expected rates of return from sales. Now, say that every investment would have an additional 5% social benefit—that is, an investment that pays at least a 6% return to the Gizmo Company will pay at least an 11% return for society as a whole; an investment that pays at least 7% for the Gizmo Company will pay at least 12% for society as a whole, and so on. Answer the questions that follow based on this information.

Estimated rate of return	Private profits of the firm from an R&D project (in \( millions)
10%	\)100
9%	\(102
8%	\)108
7%	\(118
6%	\)133
5%	\(153
4%	\)183
3%	$223

a. If the going interest rate is 9%, how much will Gizmo invest in R&D if it receives only the private benefits of this investment?

b. Assume that the interest rate is still 9%. How much will the firm invest if it also receives the social benefits of its investment? (Add an additional 5% return on all levels of investment.)

Short answer

a. The investment amount will be $102 million.

b. The investment will be $183 million.

Step-by-step solution

Given Information

Based on predicted rates of return from sales, Table 13.4 depicts the company's requirement for financial resources for research and development of these products.

Content Introduction

Private rate of returns refers to the projected rate of return on an investment that goes only to an individual or a company. When the rate of return benefits the entire society, it is referred to as a social rate of return.

Explanation (part a)

Gizmo will invest $102 million in R&D if the investment delivers purely private benefits if the current interest rate is 9%.

Explanation (part b)

Each investment would give an extra 5% societal benefit—for example, an investment that yields at least 6% to the Gizmo Company will deliver at least 11% to society overall, and so on.

Though the interest rate is 9% and the corporation expects to obtain 5% social benefits from the investment, the company will invest $183 million as if the effective rate of return is 9% - 5% = 4%