Carla Vista Energy Company owns several gas stations. Management is looking to open a new station in the western suburbs of Baltimore. One possibility that managers at the company are evaluating is to take over a station located at a site that has been leased from the county. The lease, originally for 99 years, currently has 73 years before expiration. The gas station generated a net cash flow of $87,460 last year, and the current owners expect an annual growth rate of 6.3 percent. If Carla Vista Energy uses a discount rate of 13.8 percent to evaluate such businesses, what is the present value of this growing annuity

The present Value of the growing annuity= $1,158,092.68  

Explanation:

The present value of the growing annuity is going to be computed as follows:

PV = A/(r-g) × (1- (1+g/1+r)^n)

A- annual cash flow- $87,460

g- growth rate - 6.3%

n- number of years =73

r- discount rate - 13.8%

I will break out the formula into two parts to make the workings very clear to follow. So applying this formula, we can work out the present value of the growing annuity  as follows.  

A/(r-g)  = 87,460/(0.138-0.063) =1,166,133.33

(1- (1+g/1+r)^n)  = 1- (1.063/1.138)^73 =0.9931

PV = A/(r-g) × (1- (1+g/1+r)^n)

166,133.33× 0.9931 =  1,158,092.68  

The present Value of the growing annuity= $1,158,092.68  

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