FNCE10002 Lecture Notes - Lecture 2: Cash Flow, Market Price, Investment

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amaranthbadger280

19 Jun 2018

School

University of Melbourne

Department

Finance

Course

FNCE10002

Professor

Howard Chan

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Principles of Finance

Lecture 2: Introduction to Financial Mathematics and Debt

Valuing Perpetuities and Annuities

A perpetuity is an equal, periodic cash flow that goes on forever. Cash flows occur at the end of each

period. The present value of a perpetuity is:

Where C = cash flow and r= rate

A deferred perpetuity is an equal periodic cash flow that starts at some future date and then goes on

forever. The present value of the perpetuity is deferred to the end of time period n+1 is:

Where n= number of periods.

A growth perpetuity is a perpetuity of C dollars today growing at a constant rate of g percent per

period and has the cash flow stream C(1 + g), C(1 + g)2, ... C(1 + g)n, and so on. Note that the first cash

flow is C(1 + g) not C. The present value of a growth perpetuity is:

Where g = growth rate.

Note this C(1+g) is for when t=1, so if given t=0, t=1 must be found first.

Valuing Ordinary Annuities

An ordinary annuity is a series of equal, periodic cash flows occurring at the end of each period and lasting

for n periods with n cash flows. That is the first cash flow is at the end of period 1 and the last cash flow is

at the end of period n. Ordinary annuities can be valued as the difference between two perpetuities:

The present value of an ordinary annuity over n time periods can be obtained as the difference between an

ordinary perpetuity (starting at the end of period 1) and a deferred perpetuity (starting at the end of

period n+1). Given in the equation:

The future value of an ordinary annuity is found by computing the future value of the above present value

at time period n:

Valuing Deferred Ordinary Annuities

A deferred ordinary annuity is a series of equal, periodic cash flows occurring at the end of each

period where the first cash flow occurs at a future date.

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Document Summary

Lecture 2: introduction to financial mathematics and debt. A perpetuity is an equal, periodic cash flow that goes on forever. Cash flows occur at the end of each period. Where c = cash flow and r= rate. A deferred perpetuity is an equal periodic cash flow that starts at some future date and then goes on forever. The present value of the perpetuity is deferred to the end of time period n+1 is: A growth perpetuity is a perpetuity of c dollars today growing at a constant rate of g percent per period and has the cash flow stream c(1 + g), c(1 + g)2, c(1 + g)n, and so on. Note that the first cash flow is c(1 + g) not c. the present value of a growth perpetuity is: Note this c(1+g) is for when t=1, so if given t=0, t=1 must be found first.

Related Questions

Question 1 5 pts

0 multiple_choice_question 22046808

The internal rate of return (IRR) is the interest rate that sets the net present value of the future cash flows equal to ________.

Question 2 5 pts

On a timeline, the space between date 0 and date 1 represents the _______ between dates. Letâs assume it is the first year of the loan. Date 0 is the beginning of the first year, and date 1 is the end of the first year.

Question 3 5 pts

As the interest rate __________, present value decreases.

Question 4 5 pts

The present value (PV) of a stream of cash flows is the _______ the present values of each individual cash flow

Question 5 5 pts

When a constant cash flow will occur at regular intervals for a finite number of periods of time, it is called a(n) __________.

Question 6 5 pts

Edit this Question Delete this Question

0 multiple_choice_question 22047052

There are two basic types of annuities:

Discounted and compounded annuities

Ordinary annuities and annuities due.

Future value and present value annuities

None of the above

Question 7 5 pts

The NPV measures the ______ change in shareholder wealth that arises from undertaking a project.

Question 8 5 pts

The Net Present Value rule implies that we should compare a projectâs net present value (NPV) to ________

Question 9 5 pts

To endow a perpetuity is the same as calculating the present value (PV) of a perpetuity. Say you want to endow an annual graduation party at your alma mater. You want the event to be a memorable one, so you budget $30,000 per year forever for the party. If the university earns 8% per year on its investments, and if the first party is in one yearâs time, how much will you need to donate to endow the party?

The formula for PV of a perpetuity = C\r; = $30,000 \ 0.08; =

Question 10 5 pts

With an Ordinary Annuity, payments are required at the ________ of each period. An example of this is bonds which usually pay coupon payments at the end of every six months until the bond's maturity date.

beginning

middle

end

payments are not required

limemacaw827

12. Which one of these statements related to growing annuities andperpetuities is correct?
A. The cash flow used in the growing annuity formula is the initialcash flow at time zero.
B. Growth rates cannot be applied to perpetuities if you wish tocompute the present value.
C. The future value of an annuity will decrease if the growth rateis increased.
D. An increase in the rate of growth will decrease the presentvalue of an annuity.
E. The present value of a growing perpetuity will decrease if thediscount rate is increased.

raspberrymarten593

4.3	Need help with 4.4 a and b at bottom. 4.3 is required to answerthis. Calculate the following values, assuming a discount rate of8%:
	a.	present value of a perpetuity (also called a perpetual annuity)of $50 received each year at the end of each year
	b.	present value of an annuity of $50 received at the end of eachyear for 5 years
	c.	present value of an annuity of $50 received at the end of eachyear for 10 years, with the first payment to be received at the endof the 6^th year
	d.	present value of a perpetuity of $50, with the first paymentreceived at the end of the 16^th year. *ANSWER:* a. PV of perpetuity = A/i where A is annual payment &i is disc rate SO PV of Perpetuity = 50/8% = $625.00 b. Here it is PV of annuity for n=5 & PMT=$50 SO PVA = PMT(PVIFAi,n) i.e. PVA = $50(PVIFA8%,5). From PV of annuity Table, we get (PVIFA8%,5) = 4.3295 So PVA = 504.3295 = $216.48 c. This has 2 parts. First Find the PV of Annuity at 6 yrs &then find the PV of that amount at T0. Here it is PV of annuity for n=10 & PMT=$50 SO PVA = PMT(PVIFAi,n) i.e. PVA = $50(PVIFA8%,10). From PV of annuity Table, we get (PVIFA8%,5) = 6.7101 So PVA = 506.7101 = $335.51 Now PV = FV/(1+i)^n = $335.51/(1+8%)^6 = $211.43 d. This has 2 parts. First Find the PV of Perpetuity at 16 yrs& then find the PV of that amount at T0. PV of Perpetuity = A/i = 50/8% = $625 Now PV of this amount PV = 625/(1+8%)^16 = $182.43
4.4	a.	Show (with a time line, for example) that the perpetuity in4.3a. is exactly the same as the sum of the annuities andperpetuities in 4.3b. to 4.3d.
	b.	Show that their present values add up to the same amount.

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FNCE10002 Lecture Notes - Lecture 2: Cash Flow, Market Price, Investment

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