An investment opportunity has just paid a cash flow of $4,920.The cash flow from this...

An investment opportunity has just paid a cash flow of $4,920. The cash flow from this investment is expected to grow at a constant growth rate of 6% for its expected life of 35 years. What is the fair value of this opportunity today if its required rate of return is 9%?

Expert Solution

Value of opportunity = Cash flow₁ * (1+g) / (1+r) + Cash flow₂ * (1+g)² / (1+r)² + ......+ Cash flow₃₅ * (1+g)³⁵ / (1+r)³⁵

= 4920 * 1.06 / 109 + 4920 * 1.06² / 109² + ...... + 4920 * 1.06³⁵ / 109³⁵

= 4920 * [ 1.06 / 1.09 + 1.06² / 109² + ...... + 4920 * 1.06³⁵ ]

It is geometric progression with first term, a = 1.06/1.09 and common ratio, r = 1.06/1.09

Sum of GP = a * ( 1 - rⁿ ) / ( 1 - r )

= 4920 * [ 1.06/1.09 * ( 1 - (1.06/1.09)³⁵ ) / ( 1 - 1.06/1.09) ]

= 4920 * [ 0.9725 * ( 1 - 0.9725³⁵ ) / ( 1 - 0.9725 ) ]

= 4920 * [ 0.9725 * 0.6235 ] / 0.0275

= 4920 * 22.0492

= $ 108,482.20

The value of an opportunity is $ 104,482.20.

jeff jeffy answered 2 years ago

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