Question

What is the present value of the following series of cash payments: $1,200 per year for four consecutive years starting one year from today, followed by annual cash payments that increase by 3% per year in perpetuity (i.e. cash payment in year 5 is $1,200*1.03, cash payment in year 6 is $1,200*1.032, etc.)? Assume the appropriate discount rate is 9%/year.

Answer 1

Answer:

$21,964

Explanation:

Present Value = 1200 × cumulative pv factor for year 1 to 4 (9%, 4y) + $\frac{1200(1\ +\ .03)}{(.09\ -\ .03)}$

Present value = 1200 × 3.2397 + 1236/.06

Present Value =  3887.64 + 20,600 = $21,964 approx.

For the first four years, cash flows can be computed by multiplying $1200 by cumulative present value factor at 9% rate for 4 years.

Fifth year onwards, the cash flows are expected to increase by 3% whereas discounting factor is 9%. So the value 5th year onwards till perpetuity would be increased cash flow for year 5 discounted by excess of present value factor over growth rate (9% - 3 %)