Joyce's Juice (CEMBA)

This case is a simple business valuation that should reinforce your understanding of the following topics:

- Business cash flows
- The effects of leverage
- Cost of capital calculations
- Adjusted present value methods of valuation

Introduction

Joyce Smith is thinking of opening a juice stand. Her business plan suggests that the initial capital investment (in plant, property, and equipment) will be $250,000. She anticipates that no further capital expenditures will be required over the life of her business. (We're trying to keep things simple here.) Her juice will initially sell for $1 per bottle and will cost $0.30 on average to produce. She anticipates fixed operating costs (excluding depreciation) of $30,000 in the first year. Joyce expects that prices and costs (variable and fixed) will grow at the estimated 3% rate of inflation in perpetuity. She also expects to sell 150,000 bottles each year in perpetuity.

Juice stands typically require net working capital in the amount of 30% of revenues and Joyce expects this will to apply to her business. (To be clear, net working capital balances at the beginning of any given year are 30% of the anticipated revenues for the rest of that year.)

For tax purposes, Joyce's capital assets are subject to a 5-year straight- line depreciation schedule, with a projected zero salvage value. For simplicity, however, we will continue to assume that the assets can actually be used out into the indefinite future (i.e., their actual useful life is effectively infinite). I'll say more about this in class.

Finally, Joyce faces a 40% combined federal and state corporate income tax rate.

Cash Flows (No Leverage)

(This uses the same techniques as the in-class capital budgeting exercise from our first class.)

1. Construct six-year pro forma income statements for Joyce's unlevered business. (Spreadsheet answer.)

2. Calculate six-year projections for Joyce's unlevered cash flows (aka "free cash flow"). Remember to include cash flows from the income statement, changes in net working capital, and capital expenditures or dispositions. (Spreadsheet answer.)

Leverage

Now assume that Joyce partially funds her initial investment by borrowing $200,000 from a bank at an annual interest rate of 7%. Assume that Joyce will roll over the debt when it matures, so that the $200,000 of debt is outstanding in perpetuity, and that she will not increase total debt outstanding any further.

1. Construct six-year pro forma income statements for Joyce's levered business. (Spreadsheet answer.)

2. Calculate the projected interest coverage ratio (aka "times interest earned") in each of the six years. The interest coverage ratio is defined as (EBIT + depreciation and amortization expense)/(interest expense). (Spreadsheet answer.)

3. Calculate the interest tax shields (ITS) for each of the six years in your projection. (Spreadsheet answer.)

Cost of Capital Calculations

To estimate her cost of capital, Joyce has found three firms engaged in very similar business. Each faces a 40% tax rate and has the following parameter values.

1. Calculate unlevered asset betas for each of the comparable firms. Assume each of these firms will keep its leverage ratio constant over time. Note that Leverage = (Debt)/(Debt + Equity). (Spreadsheet answer.)

2. Assume that the long-term risk-free rate (based on Treasury yields) is currently 3.7% and the market risk premium is 7.2%. Using the average of all three comparable firms' unlevered betas as an estimate of Joyce's unlevered beta, what is the estimated cost of capital for Joyce's unlevered business? (Spreadsheet answer.)

Remember that this is an APV case. Do not calculate Joyce's WACC-discounting at WACC is an alternative to APV analysis!

Business Valuation

1. Using your cash flow and cost of capital estimates, calculate the net present value of Joyce's unlevered business. Remember to net out any initial cash outflows. (Spreadsheet answer.)

2. What is the present value of the interest tax shield (ITS) associated with the $200,000 of debt? (Spreadsheet answer accompanied by a

short essay to explain how you arrived at the discount rate for the ITS cash flows.)

We went over this in Section 4 of the notes, so let me briefly review the key points:

a. The rate rITS should be between the debt return rD and the unlevered required return rU.
b. If you think the ITS are roughly as risky as the debt payments themselves, pick a rate closer to rD; if you think they depend heavily on the risk of the firm's unlevered business, pick a rate closer to rU; if you think their risk is in between, pick a rate more in the middle.
c. This is a judgment call, so I am more interested in your thinking here than in getting the "right" answer; in fact, there is no one right answer here!

3. Given your answers to 1 and 2, what is the net APV of Joyce's Juice?