1. Corporate finance Lecture 3
Dr. Solt Eszter
BME
2017

2. Basics of financial calculations Annuity
A series of payments made at equal
intervals.
Types according to timing:
Annuity-immediate/ordinary: payments are made at the end of payment periods (interest accrues
between the issue of the annuity and the first payment.
Annuity-due: payments are made at the beginning of payment periods, so a payment is made immediately on issue

3. Annuity Fixed annuities:These are annuities with fixed payments
(If provided by an insurance company, the company guarantees a fixed return on the initial investment)
Growing/indexed annuities: the yields are growing at a specific rate of „g”
Examples of annuities are regular deposits to a savings account, monthly home mortgage payments, monthly insurance payments and pension payments
Annuities can also be classified by the frequency of payment dates (weekly, monthly, quarterly, yearly, or at any other regular interval of time)
We will deal with fixed annuities

4. Future Value annuity-immediate
Future value of annuity-immediate:
FV = C x (1+r)t - 1 r
Example 1: Suppose you are saving up for a camera which is worth HUF You make deposits in equal sums each year for five years. Simply put you need this amount in five years. How much money do you have to deposit annually if the interest rate is 10%? (C ?)

5. Future value of annuity-immediate
Solution: = C x (1+.1) C = / [(1+.1)5 – 1) / .1] = HUF 6 000

6. Future value of annuity-due
FV = C x [ (1+r)t - 1 ] x (1 +r) r
Example 1: Peter saves money in the following way: he deposits equal sums of HUF at the beginning of each year for three years. How much money will he have by the end of the third year if the interest rate is 10%? (FV?)
FV =
x [(1+.1)3 – 1) / .1] x (1 +.1) = x = HUF

7. Future value of annuity-due
Example 2: The agent of a life insurance company offers us the following saving opportunity for ten years:
We make payments to our savings account in the amount of HUF at the beginning of each year for 10 years (adjusted with CPI). Based on his experience in the past the agent promises us a real return rate of 4%. Suppose we believe him, what will the real value of the amount be on our account in 10 years ?

8. Future value of annuity-due
Solution:
FV = C x [ (1+r)t - 1 ] x (1 +r) r
that is:
FV = x ( – 1) x = HUF
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9. Present value of annuity -immediate
Present value of annuity-immediate (annuity valuation):
PV = C x [ 1/r – 1/(r x (1 +r)t]
The expression in square brackets: annuity factor
Example 1: Suppose I will get an annuity of fixed payments HUF each
year for five years. How much could I get for this annuity in the market when
market return rate (rm) at present is 10%?
Solution: PV = x [1/0,1 – 1/(0,1x 1,15)] = HUF
That is : I should get at least HUF in the market ( or more)

10. Present value of annuity -immediate
Example 2: Suppose our acquaintance is a sole
proprietor and needs HUF for his business. He
offers us the following deal:
If we lend him the money, he will pay back equal sums of
HUF for five years at the end of each year.
Should we lend him if our expected return rate is 30%?
Solution: Present value of annuity –immediate
PV = C x [ 1/r – 1/(r x (1 +r)t] that is:
PV = x [1/ .3 – 1/( .3 x 1.35)] = HUF

11. Present value of annuity -immediate
Net present value of the loan: NPV= C0+ PV, That is: HUF HUF = HUF where C0 is the yield of period 0, the present, the cost of the asset/initial outlay, which is negative ! (In the example this is the amount loanable, HUF , which provides yields in the future ,while PV is the present value of the series of five payments of HUF ) Our decision: We reject the offer because the present value of the series of five payments (HUF ) is less than the amount of the loan (HUF ) calculated with our expected return rate (30%).

12. Internal rate of return (IRR)
Internal rate of return is a metric used in capital budgeting measuring the profitability of potential investments. IRR is a discount rate that makes the net present value (NPV) from all cashflows from a particular project equal to zero. PV = Ct/(1+i)t 0 = NPV = C0 + ∑ Ci/(1+IRR)i

13. Issues with IRR
In general, the higher a project’s IRR, the more desirable it is to undertake the project
In theory, any project with an IRR greater than its cost of capital is a profitable one
It should always be used in conjunction with NPV for a clearer picture of the value represented by a potential project
E.g. a longer project may have a low IRR, earning returns slowly and steadily, but may add a large amount of value to the company over time

14. Issues with IRR A common misuse of IRR:
When positive cashflows are generated during
the course of a project, the money will be
reinvested at the project’s rate of return, which
can be rarely the case.
Rather, positive cashflows are reinvested at a
rate that more resembles the cost of capital
It may lead to the belief that a project is more
profitable than it actually is in reality