Question

Wildhorse 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 $95,710 last year, and the current owners expect an annual growth rate of 6.3 percent. If Wildhorse Energy uses a discount rate of 14.6 percent to evaluate such businesses, what is the present value of this growing annuity? (Round factor values to 6 decimal places, e.g. 1.521253 and final answer to 2 decimal places, e.g. 15.21.)

Answer 1

The present value of the growing annuity is calculated by using the following formula

The Present value of growing annuity = [CF1 / (r – g)] x [1 – {(1+g) / (1 + r)}ⁿ]

Where, Expected Cash flow in next year (CF1) = $1,01,739.73 [$95,710 x 1.063]

Annual Growth Rate (g) = 6.30%

Required Rate of Return (r) = 14.60%

Number of years (n) = 73 Years

Therefore, the Present value of growing annuity = [CF1 / (r – g)] x [1 – {(1+g) / (1 + r)}ⁿ]

= [$1,01,739.73 / (0.1460 – 0.063)] x [1 – {(1 + 0.063) / (1+ 0.1460)}⁷³]

= [$1,01,739.73 / 0.0830] x [1 – (0.927574)⁷³]

= $12,25,779.88 x [1 – 0.004134]

= $12,25,779.88 x 0.99586

= $12,20,711.56

“Therefore, the present value of this growing annuity would be $12,20,711.56”