Financing Corporations

Oct 8, 2013

Four Types of Cash Flows

1. Lump Sum Type Time

2. Annuity Type

Time

3. Bond Type

Time

4. Irregular Payment Type

Time

Four Types of Cash Flows

1. Lump Sum Type Time

Lump Sums – Single payment in the future

Question 1

What is the value of $150,000 today if it is paid seven years from now and you want to make 10%?

Answer = 150,000/(1.17) = 76,973.71

Four Types of Cash Flows

1. Lump Sum Type Time

2. Annuity Type

Time

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 10,000.00 2 10,000.00 3 10,000.00 4 10,000.00 5 10,000.00

0.934580.873440.816300.762900.71299

9,345.79 8,734.39 8,162.98 7,628.95 7,129.86

4.10020 41,001.97 TOTAL

Factor from Annuity Table

1/(1+r) n

Four Types of Cash Flows

1. Lump Sum Type Time

2. Annuity Type

Time

3. Bond Type

Time

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

Answer1. First, we calculate the coupons – 250,000 X 5% = 12,500

2. Next, we calculate the value of the coupons as though they are an annuity at market rate (7 years @ 8%) – 12,500 X 5.206 = 65,075

3. 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

4. Add the two numbers together, and that is the present value (PV) of the bond

65,075 + 145,872.60 = 210,947.60

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.

Four Types of Cash Flows

1. Lump Sum Type Time

2. Annuity Type

Time

3. Bond Type

Time

4. Irregular Payment Type

Time

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%

Net Present Value

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?

Period Cash Flows

0 10,000.00-

1 -400.00

2 1,000.00$

3 1,200.00$

4 1,100.00$

5 1,400.00$

6 1,500.00$

7 1,700.00$

8 11,600.00$

Answer:Period Cash Flows 10.00%

0 10,000.00- 10,000.00-

1 -400.00 -363.64

2 1,000.00$ 826.45

3 1,200.00$ 901.58

4 1,100.00$ 751.31

5 1,400.00$ 869.29

6 1,500.00$ 846.71

7 1,700.00$ 872.37

8 11,600.00$ 5,411.49

10,115.56

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

Question 5

What is the Net Present Value of this investment?

Answer

10,115.56 – 10,000 = 115.56.

We can see that the return is greater than 10%, but by how much?

Question 6

What is the IRR (Internal Rate of Return) of this investment?

Answer: Table 1

Variable Discount Rates for Given Cash Flows

Period Cash Flows 9.80% 9.90% 10.00% 10.10% 10.20% 10.30%

0 10,000.00- 10,000.00- 10,000.00- 10,000.00- 10,000.00- 10,000.00- 10,000.00-

1 -400.00 -364.30 -363.97 -363.64 -363.31 -362.98 -362.65

2 1,000.00$ 829.46 827.95 826.45 824.95 823.45 821.96

3 1,200.00$ 906.51 904.04 901.58 899.12 896.68 894.24

4 1,100.00$ 756.80 754.05 751.31 748.59 745.88 743.17

5 1,400.00$ 877.24 873.25 869.29 865.35 861.43 857.53

6 1,500.00$ 856.01 851.34 846.71 842.11 837.53 832.99

7 1,700.00$ 883.55 877.94 872.37 866.84 861.35 855.89

8 11,600.00$ 5,490.85 5,451.00 5,411.49 5,372.29 5,333.41 5,294.85

NPV 236.22 175.72 115.66 56.04 -3.15 -61.91

IRR is somewhere here

Table 2

Net Present Value at 10.1945%

Period CF 10.1945%

0 10,000.00-$ 10,000.00-

1 400.00-$ -362.99

2 1,000.00$ 823.53

3 1,200.00$ 896.81

4 1,100.00$ 746.02

5 1,400.00$ 861.65

6 1,500.00$ 837.78

7 1,700.00$ 861.65

8 11,600.00$ 5335.54

NPV 0.09

-600.00

-500.00

-400.00

-300.00

-200.00

-100.00

-

100.00

200.00

300.00

400.00

500.00

NPV 420. 358. 297. 236. 175. 115. 56.0 -3.15 -61.9 -120. -178. -235. -292. -349. -405. -461.

Exp. Return 9.50 9.60 9.70 9.80 9.90 10.0 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9 11.0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

NPV Line

IRR = 10.1945%

Net Present Values

of Cash Flow s from 9.5% to 11%

What is duration???

The amount of time it takes to recuperate an “average” Dollar, Crown, Pound, Euro, etc.

from a bond. It is helpful because two investments may have identical PV’s, but may turn out to have higher time risk.

Question 7 – Duration

Which is a preferable investment, all other things being equal:

a) A ten year bond for $10,000 which pays nominally 10% or

b) An investment of $11,342.02 which will pay $ 24,486.56 after 10 years

when the market rate is 8%

a) Let’s start with the cash flows

1 2 3 4 5 6 7 8 9

10

1,000.00 1,000.00 1,000.00 1,000.00 1,000.00 1,000.00 1,000.00 1,000.00 1,000.00

11,000.00

Then we need the present values of the cash flows @ 8%

925.93 857.34 793.83 735.03 680.58 630.17 583.49 540.27 500.25

5,095.13

Total the values

11,342.02

000000000

24,486.56

- - - - - - - - -

11,342.02

000000000

113,420.16

Multiply the present values by the year of paymentTake the sum and divide by the present valueThis is the duration

925.93 1,714.68 2,381.50 2,940.12 3,402.92 3,781.02 4,084.43 4,322.15 4,502.24

50,951.28

79,006.26

6.97

11,342.02 113,420.16

10DURATION

We can conclude from this that even though these two investments may be sold to you at the same price, and will give the same return (8%), you will not get your money back as quickly with the second one, and the first one is therefore a more attractive investment, all other things being equal.