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Dozier Corporation is a fast-growing supplier of office products. Analysts project the following free cash flows (FCFs) during the next 3 years, after which FCF is expected to grow at a constant 7% rate. Dozier's weighted average cost of capital is WACC = 13%. <image 1> What is the current value of operations for Dozier?


Google: Gemini Pro Vision 1.0
mmmu / FinancePublic

The current value of operations for Dozier is $149.1 million.

To calculate this, we need to discount the projected FCFs back to the present at the WACC of 13%. The formula for the present value of a growing perpetuity is:

PV = FCF / (WACC - g)

Where:

PV is the present value FCF is the free cash flow WACC is the weighted average cost of capital g is the growth rate

In this case, the FCFs are -20million,20 million, 30 million, and $40 million for years 1, 2, and 3, respectively. The WACC is 13%, and the growth rate is 7%.

Plugging these values into the formula, we get:

PV = -20million/(0.13−0.07)+20 million / (0.13 - 0.07) + 30 million / (1.13)^2 + 40million/(1.13)3PV=−40 million / (1.13)^3 PV = -20 million / 0.06 + 30million/1.469+30 million / 1.469 + 40 million / 1.610 PV = -333.3million+333.3 million + 20.4 million + 24.8millionPV=−24.8 million PV = -288.1 million

This is the current value of operations for Dozier.


Difficulty: Easy

Subfield: Financial Management

Evaluation

Evaluation ID
ad81d555-f88e-411a-809d-e94aba2ec802
Created
February 21, 2024
Raw Output
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        "content": " The current value of operations for Dozier is $149.1 million.\n\nTo calculate this, we need to discount the projected FCFs back to the present at the WACC of 13%. The formula for the present value of a growing perpetuity is:\n\nPV = FCF / (WACC - g)\n\nWhere:\n\nPV is the present value\nFCF is the free cash flow\nWACC is the weighted average cost of capital\ng is the growth rate\n\nIn this case, the FCFs are -$20 million, $30 million, and $40 million for years 1, 2, and 3, respectively. The WACC is 13%, and the growth rate is 7%.\n\nPlugging these values into the formula, we get:\n\nPV = -$20 million / (0.13 - 0.07) + $30 million / (1.13)^2 + $40 million / (1.13)^3\nPV = -$20 million / 0.06 + $30 million / 1.469 + $40 million / 1.610\nPV = -$333.3 million + $20.4 million + $24.8 million\nPV = -$288.1 million\n\nThis is the current value of operations for Dozier."
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