Question

You purchased a rental property that generates $50,000 during the first year. The property will produce an additional 49 cash flows growing at a rate of 4 percent per year. If the interest rate is 8 percent compounded yearly and rental payments are made at the beginning of each year, what should the value of this property be?

Answer 1

ANSWER:

I = 8%

N = 50

first payment = 50,000

second payment = first payment + increase in growth rate * first payment = 50,000 + 4% * 50,000 = 50,000 + 2,000 = 52,000

pw = first payment + second payment / (r - g) ( 1 - ( (1 + g) / (1 + r) ^ n) )

pw = 50,000 + 52,000 / (8% - 4%) (1 - ( ( 1 + 4%) / (1 + 8%) ^ 49) )

pw = 50,000 + 52,000 / 4% ( 1 - ( ( 1.04 / 1.08) ^ 49) )

pw = 50,000 + 1,300,000 ( 1 - ( (0.9629) ^ 49) )

pw = 50,000 + 1,300,000 (1 - 0.1573)

pw = 50,000 + 1,300,000 * 0.8426

pw = 50,000 + 1,095,443.653

pw = 1,145,443.653

so the present worth is $1,145,443.653