Question

please show work, step by step. unsure of what formula to use.

14) An asset pays $1,000 at the end of every year for 10 years, which starts growing at a constant rate of 2% from the 11th year and last forever (so the payment at the end of the 11th year is $1,020, 12th year is $1,020"(1+2%)= $1,040.40. What is the price of the asset given an annual discount rate of 5%? A) $28,594.79 B) $27,571.60 C) $28,185.51 D) $27,211.04

Answer 1

Present value of first 10 year cash flow can be calculated with annuity formula. The present value for remaining cash flows can be calculated with perpetuity, however they also needs to discount back for 10 year as they are started from 11 year.

The price of the asset is calculated below:

(1-(1+i)" Cash flow at 11 year Asset price = Cash flow x 1 + i-9 (1 + i) -10

Asset price = 1,000 x 1-(1 + 0.05) -10 0.05 + 1,020 0.05 -0.02 *(1 +0.05) 10

Asset price = '1,000 x 7.721735 + 34,000 x 0.613913

Asset price = 7,721.74 +20,873.05

Asset price = 28,594.79

Thus, the correct option is A.