5. In this exercise we solve iteratively for the internal rate of return. Consid
ID: 2813808 • Letter: 5
Question
5. In this exercise we solve iteratively for the internal rate of return. Consider an investment which costs 800 and has cash flows of 300, 200, 150, 122, 133 in years 1–5. Setting up the loan table below shows that 10% is greater than the IRR (since the return of principal at the end of year 5 is less than the principal at the beginning of the year):
47 Basic Financial Calculations
A
B
C
D
E
F
G
H
1
IRR?
10.00%
2
LOAN TABLE
Division of payment between:
3
Year
Cash flow
Year
Principal at beginning of year
Payment at end of year
Interest
Principal
4
0
-800
1
800.00
300.00
80.00
220.00
5
1
300
2
580.00
200.00
58.00
142.00
6
2
200
3
438.00
150.00
43.80
106.20
7
3
150
4
331.80
122.00
33.18
88.82
8
4
122
5
242.98
133.00
24.30
108.70
9
5
133
6
134.28
<-- Should be zero for IRR
Setting the IRR? cell equal to 3% shows that 3% is less than the IRR, since the return of principal at the end of year 5 is greater than the principal at the beginning of year 5.
By changing the IRR? cell, find the internal rate of return of the investment.
A
B
C
D
E
F
G
H
1
IRR?
3.00%
2
LOAN TABLE
Division of payment between:
3
Year
Cash flow
Year
Principal at beginning of year
Payment at end of year
Interest
Principal
4
0
-800
1
800.00
300.00
24.00
276.00
5
1
300
2
524.00
200.00
15.72
184.28
6
2
200
3
339.72
150.00
10.19
139.81
7
3
150
4
199.91
122.00
6.00
116.00
8
4
122
5
83.91
133.00
2.52
130.48
9
5
133
6
-46.57
<-- Should be zero for IRR
A
B
C
D
E
F
G
H
1
IRR?
10.00%
2
LOAN TABLE
Division of payment between:
3
Year
Cash flow
Year
Principal at beginning of year
Payment at end of year
Interest
Principal
4
0
-800
1
800.00
300.00
80.00
220.00
5
1
300
2
580.00
200.00
58.00
142.00
6
2
200
3
438.00
150.00
43.80
106.20
7
3
150
4
331.80
122.00
33.18
88.82
8
4
122
5
242.98
133.00
24.30
108.70
9
5
133
6
134.28
<-- Should be zero for IRR
Explanation / Answer
At 6%
<-- Should be zero for IRR
At 5%:
Very near but still a bit far at 5%
At 5.1%:
At 5.07%:
<-- Should be zero for IRR
Hence IRR = 5.07%
Year Cash flow Year Principal at beginning of year Payment at end of year Interest Principal 0 -800 1 800 300 48 252 1 300 2 548 200 32.88 167.12 2 200 3 380.88 150 22.8528 127.1472 3 150 4 253.7328 122 15.223968 106.77603 4 122 5 146.9568 133 8.81740608 124.18259 5 133 6 22.77417<-- Should be zero for IRR
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