Free cash flow next year is $100m, grows 8% a year for five years, then 3% forever. The cost of capital is 10%. Use the mid-year convention for the five explicit years and discount the terminal value at the full five years. What is the enterprise value?

Free cash flow next year is $100m, grows 8% a year for five years, then 3% forever. The cost of capital is 10%. Use the mid-year convention for the five explicit years and discount the terminal value at the full five years. What is the enterprise value?

Approach: Discount each explicit year at an exponent half a year earlier than the year end, then build the terminal value off the year six cash flow and discount it at the full five years.

1703. The enterprise value is $1,703m. The five explicit flows are 100, 108, 116.64, 125.97 and 136.05. Discounting them at 1.1^0.5, 1.1^1.5, 1.1^2.5, 1.1^3.5 and 1.1^4.5 gives 95.35 + 93.61 + 91.92 + 90.24 + 88.60, which is 459.7. Year six free cash flow is 136.05 * 1.03, or 140.13, so the terminal value is 140.13/(0.10 - 0.03), which is 2,001.9, and dividing by 1.1^5 of 1.6105 gives 1,243.0. The enterprise value is 459.7 + 1,243.0, which is 1,702.7. The mid-year convention adds 4.9% to the explicit period because cash is assumed to arrive evenly through each year rather than on the final day. The terminal value is 73% of the total, so the 3% perpetual growth assumption carries most of this discounted cash flow.

Follow-up: How does the value change if the terminal value is discounted at 4.5 years for consistency with the mid-year convention?

Key concepts: mid-year convention, terminal value, discounted cash flow, perpetual growth.