Question

Crane 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 $89,260 last year, and the current owners expect an annual growth rate of 6.3 percent. If Crane Energy uses a discount rate of 13.1 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.)

Please help to answer togather with the detailed workings. Thanks.

Answer 1

PV of annuity for growing annuity
P = (PMT/(r-g)) x (1-((1+g)/(1 + r)) ^n)
Where:
P = the present value of an annuity stream
PMT = the dollar amount of each annuity payment	89,260
r = the effective interest rate (also known as the discount rate)	13.10%
n = the number of periods in which payments will be made	73
g= Growth rate	6.30%
PV of this annuity	=(PMT/(r-g)) x (1-((1+g)/(1 + r)) ^n)
PV of this annuity	=(89260/(13.10%-6.3%)) * (1-((1+6.30%)/(1 + 13.10%)) ^73)
PV of this annuity	1,298,446.48