Question

What is the present value of a perpetual stream of cash flows that pays $3,500 at the end of year one and the annual cash flows grow at a rate of 4​% per year​ indefinitely, if the appropriate discount rate is 8​%? What if the appropriate discount rate is 6​%?

Q). a. If the appropriate discount rate is 8​%, the present value of the growing perpetuity is __ (Round to the nearest cent)

​ Please show your work.

Answer 1

a. If the appropriate discount rate is 8​%, the present value of the growing perpetuity is

$     87,500.00

Working:

As per discounted cash flow method,

Present value of cash flow

=

D1/(Ke-g)

Where,

=

3500/(8%-4%)

D1

Cash flow at the end of year 1

$       3,500

=

$     87,500.00

Ke

Discount rate

8%

g

Growth rate

4%

b. If the appropriate discount rate is 6​%, the present value of the growing perpetuity is

$ 1,75,000.00

Working:

As per discounted cash flow method,

Present value of cash flow

=

D1/(Ke-g)

Where,

=

3500/(6%-4%)

D1

Cash flow at the end of year 1

$       3,500

=

$ 1,75,000.00

Ke

Discount rate

6%

g

Growth rate

4%