Question

Chipotle expects to earn a free cash flow of $500 in one year; further, these cash flows are expected to grow at a rate of 3% forever. The firm’s unlevered cost of capital is 15%. Chipotle also has debt outstanding with a face value of $1000 and a maturity of 1 year, with an annual interest rate of 10%. The discount rate for its debt (i.e. yield-to-maturity) is also 10%. After the debt matures in 1 year, Chipotle will not issue more debt. What is the value of Chipotle if its tax rate is 40%?

Answer 1

Answer:

The value of Chipotle is 3,746.206 $.

Explanation:

We must first calculate company's terminal value under given assumption of steady rise of cash flow forever by using the following formula:

(FCF* (1+g))/(d-g), where g is expected growth rate of future cash flow and d is discount rate or in this case unlevered cost of capital. Based on our numbers we get:

500*1,03/0.12 or 4,291.66

Company's cost of debt before taxes is 1000/(1 + 0,1) or 909.09 dollars. However, since the tax rate is 40 %, after taxes the cost of debt is 909.09 - 363.636 or 545.454. Company's value is therefore 4,291.66 - 545.454 or 3,746.206 dollars.  

Answer 2

Following are the calculation to the Chipotle value:

Chipotle value$=\frac{ \text{1- year cash flow}}{ \text{(Cost of capital - growth rate)}}$

So, the un-levered value:

$=\frac{ \ 500}{(0.15 - 0.03)}\\\\= \ 4,166.67$

Calculating the tax shield for PV:

$= 1000 \times 10\% \times \frac{40\%}{1.1} = 36.36$

So, the levered value:

$\text{= un-levered value + tax shield for PV}\\\\= 4,166.67 + 36.36\\\\= 4203.03$

OR

$=\frac{500}{(15\%-3\%)}+1000\times 10\% \times \frac{40\%}{1.1}\\\\=\frac{500}{(12\%)}+1000\times 0.10 \times \frac{0.40}{1.1}\\\\=\frac{500}{(0.12)}+100 \times0.3636\\\\=4166.66+36.36\\\\=4203.02$

Therefore, the final answer is "4203.02"

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