To calculate the equity return, we need to determine the purchase price for the company and the sale price for the company in three years.
The purchase price for the company is calculated by multiplying the EBITDA by the multiple:
$1,400 x 7 = $9,800
The equity investment is $4,000, so the remaining amount is financed through debt:
$9,800 - $4,000 = $5,800
After three years, the EBITDA is $1,600, and the multiple is still 7, so the sale price for the company is:
$1,600 x 7 = $11,200
If the debt is paid down to $5,000, then the equity value is:
$11,200 - $5,000 = $6,200
The equity return is the final equity value minus the initial equity investment, divided by the initial equity investment:
($6,200 - $4,000) / $4,000 = 0.55 or 55%
So the equity return is 55%.