FNCE 4101 Week 3 Present Value Discounting Exercise Example

Discounting Five Years of Halvorsen's Projected Free Cash Flow at 8.5 Percent: A Period-by-Period Table With the Factor Shown, Where the Rate Came From and Why Cash Is Treated as Arriving at Year End

Student Name

Walden University

FNCE 4101: Corporate Finance

Instructor Name

Month Day, Year

Discounting Five Years of Halvorsen's Projected Free Cash Flow at 8.5 Percent: A Period-by-Period Table With the Factor Shown, Where the Rate Came From and Why Cash Is Treated as Arriving at Year End

The Cash Flows

This exercise discounts five projected years of Halvorsen's firm-level free cash flow; Halvorsen is the composite distributor whose fiscal 2025 free cash flow was built in Week 2 at $109.6 million. The projection grows that figure at 4 percent a year, the company's average sales growth over the past five years, on the assumption that margins and investment needs stay in proportion to sales. That is a simplifying assumption. In practice, Halvorsen's free cash flow could grow faster than sales if margins widen as fixed costs are spread over more volume, or more slowly if growth requires heavier investment in inventory and warehouses. A single growth rate keeps the exercise focused on discounting rather than forecasting; Week 10's forecast and Week 11's valuation paper return to the projection in detail. All amounts are in millions of dollars.

The Table

The factor column is shown so that each present value can be checked by hand: multiply the cash flow by the factor. Year 1's $114.0 million is worth $105.1 million today; year 5's $133.3 million is worth only $88.7 million. Over five years, $617.3 million of projected cash has a present value of $483.5 million.

Table 1

Present Value of Projected Free Cash Flow at 8.5 Percent (in millions of dollars)

Discount factor = 1 / (1.085)^t. Composite company; figures constructed for this course. Totals may differ slightly from the sum of rounded rows.

Where the Rate Came From

The rate is Halvorsen's weighted average cost of capital, about 8.5 percent, because free cash flow to the firm belongs to both lenders and shareholders and must be discounted at the blended return they require (Brealey et al., 2020). The cost of equity is 9.8 percent, built from the 10-year Treasury yield, a peer beta and a market risk premium, all set out in Week 5. The beta reflects comparable listed distributors of industrial parts, whose median beta over five years of monthly returns was close to 1.1. The after-tax cost of debt is 4.4 percent, from the 5.8 percent yield on Halvorsen's traded bonds less the 24 percent tax saving on interest. Weighted by market values, about 76 percent equity and 24 percent debt, these give 8.5 percent. The full derivation appears in the Week 5 brief; here the important point is that the rate matches the riskiness of the cash flows. A rate chosen for convenience, such as a round 10 percent, would understate the present value by about $19 million.

The Timing Convention

Each year's cash flow is treated as arriving at the end of the year, which is why year 1 is discounted for one full period. In reality, Halvorsen collects cash throughout the year. A mid-year convention, discounting each year's cash flow by half a period less, would treat it as arriving on average at mid-year. Under that convention each factor would rise by the square root of 1.085, about 4.2 percent, and the total present value would be about $503.6 million, roughly $20 million more. Damodaran (2012) notes that the mid-year convention is more realistic for firms with steady cash inflows, while the year-end convention is simpler and more conservative. This exercise uses year-end timing for clarity and states the difference so a reader can adjust. Either convention is defensible; what matters is stating which one was used, since an unstated choice can move the answer by several percent.

What the Result Means

The $483.5 million is the value today of five years of Halvorsen's cash flow at the return its investors require. The table also shows how distance in time erodes value: year 5's cash flow is about 17 percent larger than year 1's, yet its present value is about 16 percent smaller. The result is not the value of the company, which would also include the cash flows beyond year 5, summarized later in the course by a terminal value. Two sensitivities are worth noting. A rate of 7.5 percent would raise the total to about $496.7 million; a rate of 9.5 percent would lower it to about $470.8 million. The rate matters, and later weeks will test how much (Koller et al., 2020).

References

Brealey, R. A., Myers, S. C., & Allen, F. (2020). Principles of corporate finance (13th ed.). McGraw Hill.

Damodaran, A. (2012). Investment valuation: Tools and techniques for determining the value of any asset (3rd ed.). Wiley.

Koller, T., Goedhart, M., & Wessels, D. (2020). Valuation: Measuring and managing the value of companies (7th ed.). Wiley.