Question

A financial instrument just paid the investor $318 last year. The cash flow is expected to last forever and increase at a rate of 2.5 percent annually. If you use a 5.1 percent discount rate for investments like this, what should be the price you are willing to pay for this financial instrument? (Round to the nearest dollar.)

Answer 1

The price you should be willing to pay for a financial instrument that paid $318 last year, with cash flows growing at 2.5% annually and using a 5.1% discount rate, is approximately $12,231 when rounded to the nearest dollar.

Step-by-step explanation:

To determine the price, you should be willing to pay for a financial instrument that pays a perpetual cash flow which grows at a constant rate, we use the Gordon Growth Model (also known as the Dividend Discount Model for dividends that grow at a steady rate). In this case, the cash flow paid last year was $318 and is expected to grow at a rate of 2.5% annually. The formula to calculate the present value of such an instrument using a discount rate is:

Price = D / (r - g)

Where D is the cash flow paid last year ($318), r is the discount rate (5.1%), and g is the growth rate (2.5%). We substitute the values into the formula:

Price = $318 / (0.051 - 0.025) = $318 / 0.026 = $12,230.77

When rounded to the nearest dollar, the price you should be willing to pay for this financial instrument is $12,231.