A firm has a project cash flow of $1,000 today. This cash flow is expected to grow at a rate of 30% for the next five years and then taper off to a growth rate of 5% indefinitely. What is the
Terminal value of this project at the end of the fifth year if the cost of capital is 10%? Round
Your answer to the nearest dollar.

Question

Quizplus · Accepted Answer

To calculate the terminal value, we need to first calculate the cash flow in year 5. Using the formula for the present value of a growing perpetuity with a finite period, we get:

CF5 = 1000 * (1 + 0.3) ^5 = $3,061.43

Then, using the formula for the present value of a growing perpetuity with an infinite period, we get:

TV = CF5 * (1 + g) / (r - g) = $3,061.43 * (1 + 0.05) / (0.10 - 0.05) = $77,972.04

Rounding to the nearest dollar gives us the final answer of $77,972, which is choice C. To find the terminal value, we can use the formula: 
Terminal Value = (Final Cash Flow x (1+ Terminal Growth Rate)) / (Cost of Capital - Terminal Growth Rate)
First, we need to find the final cash flow:
Year 1: $1,000
Year 2: $1,300 (30% growth)
Year 3: $1,690 (30% growth)
Year 4: $2,197 (30% growth)
Year 5: $2,856 (30% growth)
To calculate terminal value, we need to find the cash flow in year 6 and beyond:
Year 6: $2,999.80 ($2,856 x 1.05)
Using the formula, we get:
Terminal Value = ($2,999.80 x (1+0.05)) / (0.10-0.05) = $77,972. Therefore, the best choice is C.

A Firm Has a Project Cash Flow of $1,000 Today