1. Fundamentals of Finance
Jan 14, 2011

2. Four Types of Cash Flows
Time
1. Lump Sum Type
Time
2. Annuity Type
Time
3. Bond Type
Time
4. Irregular
Payment Type

3. Four Types of Cash Flows
Time
1. Lump Sum Type

4. Lump Sums – Single payment in the future
Question 1
What is the value of $150,000 seven years
From now if you want to make 10%?
Answer = 150,000/(1.17) = 76,973.71

5. Four Types of Cash Flows
Time
1. Lump Sum Type
Time
2. Annuity Type

6. Question 2 Annuity Payments
What is the value of a series of equal payments of
$10, 000 per year for 5 years at 7%
Answer
1/(1+r) n 1
10,000.00 2 3 4 5
9,345.79
8,734.39
8,162.98
7,628.95
7,129.86
TOTAL
41,001.97
Factor from Annuity Table

7. Four Types of Cash Flows
Time
1. Lump Sum Type
Time
2. Annuity Type
Time
3. Bond Type

8. Question 3 – Bond type Payments
What is the value of a bond issued for $250,000 with coupons paying 5% in a market paying 8%. The bond expires in 7 years
Answer
First, we calculate the coupons –
250,000 X 5% = 12,500
Next, we calculate the value of the coupons as though they are an annuity at market rate (7 8%) –
12,500 X = 65,075
Then we treat the final payment of $250,000 as a lump sum payment 7 years from now at 8%
250,000/(1.087) = 145,872.60
Add the two numbers together, and that is the present value
(PV) of the bond
65, , = 210,947.60

9. The figures representing the amount you would pay today
are called the Present Value or PV.
These tell you how much the investment is worth.

10. Four Types of Cash Flows
Time
1. Lump Sum Type
Time
2. Annuity Type
Time
3. Bond Type
Time
4. Irregular
Payment Type

11. Net Present Value
The PV minus the amount paid out is called the Net Present Value. If the Net Present Value of an investment at a given rate of return is zero, then we know that the return on that investment is exactly that rate of return. In the last case, the NPV was negative, so the return was less than 10%

12. Question 4 – Irregular Payment Types
The following investment has been proposed to you. And you want a return of at least 10% on the investment. What is the Present Value?

13. Note – each payment must be handled as a lump sum
payment, then the PVs must all be totalled

14. Question 5
What is the Net Present Value of this investment?
Answer
10, – 10,000 =
We can see that the return is greater than 10%,
but by how much?

15. Question 6
What is the IRR (Internal Rate of Return) of this investment?
IRR is somewhere here