Question

Let PV be the present value of a growing perpetuity (the ‘time 1 perpetuity’) with an initial payment of C beginning one period from now and a growth rate of g. If we move all the cash flows back in time one period, the present value becomes PV*(1+r) Note that this is the present value of a growing perpetuity with an initial payment of C beginning today (‘time 0 perpetuity’).

Question: How do the cash flows of the time 1 perpetuity compare to those of the time 0 perpetuity from time 1 on?

Answer #1

The general PV formula for perpetual growing periodic cash flows
of say **C** beginning one period from now is given
by

**PV =C / r-g where r is the discount rate and g is the
periodic growth rate of cash flows**

**If the cash flows start immediately (i.e each cash flow
is preponed by one period) it essentially means that each cash flow
C is being discounted for one period less than what it was being
done previously.**

**This implies that Equation (A) becomes PV x (1+r) = [Cx
(1+r) / r-g]**

**The cash flows of time 1 perpetuity will be similar to
those of time 0 perpetuity in terms of their individual magnitude.
However, each cash flow C of time 0 perpetuity will be discounted
for one time period less as compared to time 1
perpetuity.**

w6 11/12 (Related to Checkpoint 6.5) (Present value of a
growing perpetuity) What is the present value of a perpetual
stream of cash flows that pays $2 comma 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 13%? What if the
appropriate discount rate is 11%?

A growing monthly perpetuity will start 6 months from today. If
the discount rate is 6% APR compounded monthly, what is the value
of the perpetuity today (at time t=0) if the growth rate is 1.2%
APR compounded monthly and the first payment is $100? *Round to the
nearest $

1)
What is a limitation for the formula for the present value of a
growing perpetuity, PV = C/(r-g)?
A) There no Limitations
b) g > r
c) g only takes into account the growth in revenue
D) r > g
2) In your will, you bequeath $6000000 into an account that
earns 11% annually. The account will fund an annual award in
perpetuity that will be given to a world leader who has excellent
intentions to promote peace. If...

11. Part A) (Present value of a growing?
perpetuity) What is the present value of a perpetual
stream of cash flows that pays ?$7,000 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 11?%? What if the appropriate
discount rate is 9?%? (Round to the nearest? cent.)
Part B) (Loan amortization) On December? 31,
Beth Klemkosky bought a yacht for ?$50,000. She paid...

What is the present value (PV) today of a stable perpetuity that
pays $15,000 every 4 years, starting 2 years from today? The
appropriate annual discount rate is 19% p.a. Round
your answer to the nearest dollar.

Find the present value of the following perpetuity.
Perpetuity Payment
Made
At:
Payment Period
Interest Rate
Conversion Period
$370
beginning
3 months
6.2%
monthly
The present value is $__.
(Round the final answer to the nearest cent as needed. Round
all intermediate values to six decimal places as needed.)

f we use the "growing perpetuity value" approach to calculate
the terminal value, we
A.
All of these answers are correct.
B.
must assume that the terminal growth rate of free cash flows is
less than the asset cost of capiptal.
C.
must use the formula TV = FCFn/RA .
D.
typically assume a relativley high terminal growth for free cash
flows.

What is the present value of a growing perpetuity, where the
first payment of $28 occurs 6 months from now, after which payments
will grow at the constant rate of 1.2% per annum, and where the
interest rate is 11% p.a., compounded semi-annually?

a. Calculate the present value (PV?) of a cash inflow of $500 in
one year, and a cash inflow of $1,000 in 5 years, assuming a
discount rate of 15%.
b. Calculate the present value (PV?) of an annuity stream of 5
annual cash flows of $1,200, with the first cash flow received in
one year, assuming a discount rate of 10%.
c.What is the present value of a perpetual stream of annual cash
flows of $100, with the first...

1. Which of the following statements is incorrect?
a. The time value of money implies that a dollar received today
is worth more than a dollar received tomorrow.
b. The time value of money implies that the further in the
future you receive a dollar, the more it is worth today.
c. All the answers are correct except one.
d. A dollar today is worth more than a dollar received in the
future.
e. The earnings from compounding drive much...

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