Jay's Jams Inc.was just established with an investment of $3 million.Jay expects his company to generate free cash flow of $800,000 a year for the next 10 years.If Jay's cost of capital is 15%,find the market value and book value of his company.
A) Market value = $8.0 million; book value = $3.0 million
B) Market value = $3.0 million; book value = $4.0 million
C) Market value = $4.0 million; book value = $3.0 million
D) Market value = $8.0 million; book value = $4.0 million

Question

Quizplus · Accepted Answer

To find the market value of the company, we need to calculate the present value of the expected free cash flows discounted at the cost of capital. Using the formula for the present value of an annuity, we get:

PV = C x ((1 - (1 + r)^-n)/r)
Where:

C = annual cash flow = $800,000
r = discount rate = 15%
n = number of years = 10

Plugging in the values, we get:

PV = $800,000 x ((1 - (1 + 0.15)^-10)/0.15)
PV = $4,901,373.11

Therefore, the market value of the company is $4.9 million.

The book value of the company is simply the initial investment of $3 million.

Thus, the best choice is C as it matches the above calculations.